LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 4 − arg1P ≤ 0 ∧ 4 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x6 ≤ 0
3: 1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x18 ≤ 0 ∧ 1 − x19 ≤ 0 ∧ − x20 ≤ 0
5: − arg1P ≤ 0 ∧ − arg1 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x6 ≤ 0
6: TRUE
7: − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 0
8: 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg6 ≤ 0 ∧ − arg7 ≤ 0 ∧ − x6 ≤ 0
9: − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − x6 ≤ 0
10: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
5 20 5: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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 27 6: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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 34 7: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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 41 9: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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, 2, 4, 5, 6, 7, 8, 19 using the following ranking functions, which are bounded by −23.

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

4 Location Addition

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

5* 23 5: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

5 21 5_var_snapshot: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

6* 30 6: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

6 28 6_var_snapshot: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

7* 37 7: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

7 35 7_var_snapshot: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

9* 44 9: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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.

9 42 9_var_snapshot: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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, 8, 9, 5_var_snapshot, 5*, 9_var_snapshot, 9* }.

12.1.1 Transition Removal

We remove transitions 21, 23, 42, 44, 12, 13, 14, 15, 16, 17, 18 using the following ranking functions, which are bounded by −1.

5: 8 + 7⋅arg1
8: 9⋅arg3 + 7⋅arg6
9: 3 + 7⋅arg2
5_var_snapshot: 5 + 7⋅arg1
5*: 11 + 7⋅arg1
9_var_snapshot: 7⋅arg2
9*: 6 + 7⋅arg2

12.1.2 Splitting Cut-Point Transitions

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

12.1.2.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 20.

12.1.2.1.1 Splitting Cut-Point Transitions

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

12.1.2.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 41.

12.1.2.2.1 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 { 6, 7, 6_var_snapshot, 6*, 7_var_snapshot, 7* }.

12.2.1 Transition Removal

We remove transitions 9, 10 using the following ranking functions, which are bounded by 9.

6: 2 + 5⋅arg1
7: 5⋅arg1
6_var_snapshot: 1 + 5⋅arg1
6*: 4 + 5⋅arg1
7_var_snapshot: 5⋅arg1
7*: 5⋅arg1

12.2.2 Transition Removal

We remove transitions 30, 11 using the following ranking functions, which are bounded by −1.

6: 0
7: 1 − 3⋅arg2 + 3⋅arg3
6_var_snapshot: −1
6*: 1
7_var_snapshot: −3⋅arg2 + 3⋅arg3
7*: 2 − 3⋅arg2 + 3⋅arg3

12.2.3 Transition Removal

We remove transitions 28, 35, 37 using the following ranking functions, which are bounded by −1.

6: 0
7: 0
6_var_snapshot: −1
6*: 0
7_var_snapshot: −1
7*: arg1

12.2.4 Splitting Cut-Point Transitions

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

12.2.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 27.

12.2.4.1.1 Splitting Cut-Point Transitions

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

12.2.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 34.

12.2.4.2.1 Splitting Cut-Point Transitions

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

Tool configuration

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