LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0
2: 3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0
3: 3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0
4: 3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0 ∧ 3 − x52 ≤ 0
5: 3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0 ∧ 3 − x52 ≤ 0
6: 3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0 ∧ 3 − x52 ≤ 0
7: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
2 11 2: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
3 18 3: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
5 25 5: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
6 32 6: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 5, 6, 10 using the following ranking functions, which are bounded by −23.

7: 0
0: 0
1: 0
2: 0
3: 0
4: 0
5: 0
6: 0
7: −7
0: −8
1: −9
2: −10
3: −10
2_var_snapshot: −10
2*: −10
3_var_snapshot: −10
3*: −10
4: −15
5: −16
6: −16
5_var_snapshot: −16
5*: −16
6_var_snapshot: −16
6*: −16

4 Location Addition

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

2* 14 2: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

5 Location Addition

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

2 12 2_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

6 Location Addition

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

3* 21 3: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

7 Location Addition

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

3 19 3_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

8 Location Addition

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

5* 28 5: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

9 Location Addition

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

5 26 5_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

10 Location Addition

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

6* 35 6: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

11 Location Addition

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

6 33 6_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

12 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

12.1 SCC Subproblem 1/2

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

12.1.1 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 4.

5: 2 − 4⋅arg2 + 4⋅arg3
6: −4⋅arg2 + 4⋅arg4
5_var_snapshot: 1 − 4⋅arg2 + 4⋅arg3
5*: 3 − 4⋅arg2 + 4⋅arg3
6_var_snapshot: −4⋅arg2 + 4⋅arg4
6*: −4⋅arg2 + 4⋅arg4

12.1.2 Transition Removal

We remove transitions 26, 28, 8 using the following ranking functions, which are bounded by −3.

5: −2
6: 0
5_var_snapshot: − arg1P
5*: −1
6_var_snapshot: 0
6*: 0

12.1.3 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 2.

5: 0
6: 1 − 3⋅arg3 + 3⋅arg4
5_var_snapshot: 0
5*: 0
6_var_snapshot: −3⋅arg3 + 3⋅arg4
6*: 2 − 3⋅arg3 + 3⋅arg4

12.1.4 Transition Removal

We remove transitions 33, 35 using the following ranking functions, which are bounded by −1.

5: 0
6: 0
5_var_snapshot: 0
5*: 0
6_var_snapshot: − arg1P
6*: x41

12.1.5 Splitting Cut-Point Transitions

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

12.1.5.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 25.

12.1.5.1.1 Splitting Cut-Point Transitions

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

12.1.5.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 32.

12.1.5.2.1 Splitting Cut-Point Transitions

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

12.2 SCC Subproblem 2/2

Here we consider the SCC { 2, 3, 2_var_snapshot, 2*, 3_var_snapshot, 3* }.

12.2.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by −14.

2: 2 − 7⋅arg2
3: −7⋅arg2
2_var_snapshot: 1 − 7⋅arg2
2*: 3 − 7⋅arg2
3_var_snapshot: −7⋅arg2
3*: −7⋅arg2

12.2.2 Transition Removal

We remove transitions 12, 14, 3 using the following ranking functions, which are bounded by −1.

2: 0
3: 2⋅arg1
2_var_snapshot: −1
2*: 3
3_var_snapshot: 2⋅arg1
3*: 2⋅arg1

12.2.3 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by −7.

2: 0
3: 1 − 3⋅arg3
2_var_snapshot: 0
2*: 0
3_var_snapshot: −3⋅arg3
3*: 2 − 3⋅arg3

12.2.4 Transition Removal

We remove transitions 19, 21 using the following ranking functions, which are bounded by −2.

2: 0
3: −1
2_var_snapshot: 0
2*: 0
3_var_snapshot: −2
3*: 0

12.2.5 Splitting Cut-Point Transitions

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

12.2.5.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 11.

12.2.5.1.1 Splitting Cut-Point Transitions

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

12.2.5.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 18.

12.2.5.2.1 Splitting Cut-Point Transitions

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

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