LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
2 37 2: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
4 44 4: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
7 51 7: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
9 58 9: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
10 65 10: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
13 72 13: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
15 79 15: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0
and for every transition t, a duplicate t is considered.

2 Transition Removal

We remove transitions 0, 36 using the following ranking functions, which are bounded by −23.

23: 0
0: 0
2: 0
3: 0
4: 0
5: 0
6: 0
7: 0
8: 0
9: 0
10: 0
11: 0
12: 0
13: 0
14: 0
15: 0
16: 0
17: 0
18: 0
19: 0
20: 0
21: 0
22: 0
1: 0
23: −4
2: −5
3: −5
4: −5
5: −5
6: −5
8: −5
9: −5
10: −5
11: −5
12: −5
13: −5
14: −5
15: −5
16: −5
17: −5
18: −5
19: −5
20: −5
21: −5
22: −5
0: −5
7: −5
2_var_snapshot: −5
2*: −5
4_var_snapshot: −5
4*: −5
7_var_snapshot: −5
7*: −5
9_var_snapshot: −5
9*: −5
10_var_snapshot: −5
10*: −5
13_var_snapshot: −5
13*: −5
15_var_snapshot: −5
15*: −5
1: −18

3 Location Addition

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

2* 40 2: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

4 Location Addition

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

2 38 2_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

5 Location Addition

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

4* 47 4: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

6 Location Addition

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

4 45 4_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

7 Location Addition

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

7* 54 7: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

8 Location Addition

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

7 52 7_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

9 Location Addition

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

9* 61 9: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

10 Location Addition

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

9 59 9_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

11 Location Addition

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

10* 68 10: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

12 Location Addition

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

10 66 10_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

13 Location Addition

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

13* 75 13: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

14 Location Addition

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

13 73 13_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

15 Location Addition

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

15* 82 15: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

16 Location Addition

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

15 80 15_var_snapshot: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − m_post + m_post ≤ 0 ∧ m_post − m_post ≤ 0 ∧ − m_0 + m_0 ≤ 0 ∧ m_0 − m_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0

17 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

17.1 SCC Subproblem 1/1

Here we consider the SCC { 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 7, 2_var_snapshot, 2*, 4_var_snapshot, 4*, 7_var_snapshot, 7*, 9_var_snapshot, 9*, 10_var_snapshot, 10*, 13_var_snapshot, 13*, 15_var_snapshot, 15* }.

17.1.1 Transition Removal

We remove transitions 8, 10, 23 using the following ranking functions, which are bounded by −1.

2: −5⋅j_0 + 5⋅n_0
3: −5⋅j_0 + 5⋅n_0
4: −5⋅j_0 + 5⋅n_0
5: −5⋅j_0 + 5⋅n_0
6: −5⋅j_0 + 5⋅n_0
8: −5⋅j_0 + 5⋅n_0
9: −5⋅j_0 + 5⋅n_0
10: −5⋅j_0 + 5⋅n_0
11: −5⋅j_0 + 5⋅n_0
12: −5⋅j_0 + 5⋅n_0
13: −5⋅j_0 + 5⋅n_0
14: −5⋅j_0 + 5⋅n_0
15: −5⋅j_0 + 5⋅n_0
16: −5⋅j_0 + 5⋅n_0
17: −5⋅j_0 + 5⋅n_0
18: −5⋅j_0 + 5⋅n_0
19: −5⋅j_0 + 5⋅n_0
20: −5⋅j_0 + 5⋅n_0
21: −2 − 5⋅j_0 + 5⋅n_0
22: −5⋅j_0 + 5⋅n_0
0: −5⋅j_0 + 5⋅n_0
7: −5⋅j_0 + 5⋅n_0
2_var_snapshot: −5⋅j_0 + 5⋅n_0
2*: −5⋅j_0 + 5⋅n_0
4_var_snapshot: −5⋅j_0 + 5⋅n_0
4*: −5⋅j_0 + 5⋅n_0
7_var_snapshot: −5⋅j_0 + 5⋅n_0
7*: −5⋅j_0 + 5⋅n_0
9_var_snapshot: −5⋅j_0 + 5⋅n_0
9*: −5⋅j_0 + 5⋅n_0
10_var_snapshot: −5⋅j_0 + 5⋅n_0
10*: −5⋅j_0 + 5⋅n_0
13_var_snapshot: −5⋅j_0 + 5⋅n_0
13*: −5⋅j_0 + 5⋅n_0
15_var_snapshot: −5⋅j_0 + 5⋅n_0
15*: −5⋅j_0 + 5⋅n_0

17.1.2 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 12.

2: −1 − 13⋅m_0 + 13⋅n_0
3: −1 − 13⋅m_0 + 13⋅n_0
4: −3 − 13⋅m_0 + 13⋅n_0
5: −3 − 13⋅m_0 + 13⋅n_0
6: −10 − 13⋅m_0 + 13⋅n_0
8: −9 − 13⋅m_0 + 13⋅n_0
9: −9 − 13⋅m_0 + 13⋅n_0
10: −5 − 13⋅m_0 + 13⋅n_0
11: −7 − 13⋅m_0 + 13⋅n_0
12: −9 − 13⋅m_0 + 13⋅n_0
13: −9 − 13⋅m_0 + 13⋅n_0
14: −9 − 13⋅m_0 + 13⋅n_0
15: −9 − 13⋅m_0 + 13⋅n_0
16: −9 − 13⋅m_0 + 13⋅n_0
17: −9 − 13⋅m_0 + 13⋅n_0
18: −9 − 13⋅m_0 + 13⋅n_0
19: −8 − 13⋅m_0 + 13⋅n_0
20: −2 − 13⋅m_0 + 13⋅n_0
21: −1 − 13⋅m_0 + 13⋅n_0
22: −1 − 13⋅m_0 + 13⋅n_0
0: −13⋅m_0 + 13⋅n_0
7: 1 − 13⋅m_0 + 13⋅n_0
2_var_snapshot: −1 − 13⋅m_0 + 13⋅n_0
2*: −1 − 13⋅m_0 + 13⋅n_0
4_var_snapshot: −3 − 13⋅m_0 + 13⋅n_0
4*: −3 − 13⋅m_0 + 13⋅n_0
7_var_snapshot: −13⋅m_0 + 13⋅n_0
7*: 2 − 13⋅m_0 + 13⋅n_0
9_var_snapshot: −9 − 13⋅m_0 + 13⋅n_0
9*: −9 − 13⋅m_0 + 13⋅n_0
10_var_snapshot: −6 − 13⋅m_0 + 13⋅n_0
10*: −4 − 13⋅m_0 + 13⋅n_0
13_var_snapshot: −9 − 13⋅m_0 + 13⋅n_0
13*: −9 − 13⋅m_0 + 13⋅n_0
15_var_snapshot: −9 − 13⋅m_0 + 13⋅n_0
15*: −9 − 13⋅m_0 + 13⋅n_0

17.1.3 Transition Removal

We remove transitions 52, 54, 66, 68, 4, 6, 16, 18, 19, 20, 22, 26, 27, 28, 35 using the following ranking functions, which are bounded by −11.

2: 0
3: 0
4: −1
5: −1
6: −7
8: −6
9: −6
10: −2
11: −4
12: −6
13: −6
14: −6
15: −6
16: −6
17: −6
18: −6
19: −5
20: 0
21: 0
22: 0
0: −11
7: −9
2_var_snapshot: 0
2*: 0
4_var_snapshot: −1
4*: −1
7_var_snapshot: −10
7*: −8
9_var_snapshot: −6
9*: −6
10_var_snapshot: −3
10*: −1
13_var_snapshot: −6
13*: −6
15_var_snapshot: −6
15*: −6

17.1.4 Transition Removal

We remove transitions 17, 25, 34 using the following ranking functions, which are bounded by −3.

2: 2 − 4⋅j_0 + 4⋅n_0
3: −4⋅j_0 + 4⋅n_0
4: −4⋅j_0 + 4⋅n_0
5: −2 − 4⋅j_0 + 4⋅n_0
6: 0
8: −2 − 14⋅i_0 + 14⋅n_0
9: 10 − 14⋅i_0 + 14⋅n_0
10: 0
11: 0
12: −1 − 14⋅i_0 + 14⋅n_0
13: 1 − 14⋅i_0 + 14⋅n_0
14: 3 − 14⋅i_0 + 14⋅n_0
15: 4 − 14⋅i_0 + 14⋅n_0
16: 6 − 14⋅i_0 + 14⋅n_0
17: 7 − 14⋅i_0 + 14⋅n_0
18: 8 − 14⋅i_0 + 14⋅n_0
19: 0
20: −4⋅j_0 + 4⋅n_0
21: −2 − 4⋅j_0 + 4⋅n_0
22: −1 − 4⋅j_0 + 4⋅n_0
0: 0
7: 0
2_var_snapshot: 1 − 4⋅j_0 + 4⋅n_0
2*: 2 − 4⋅j_0 + 4⋅n_0
4_var_snapshot: −1 − 4⋅j_0 + 4⋅n_0
4*: 1 − 4⋅j_0 + 4⋅n_0
7_var_snapshot: 0
7*: 0
9_var_snapshot: 9 − 14⋅i_0 + 14⋅n_0
9*: 11 − 14⋅i_0 + 14⋅n_0
10_var_snapshot: 0
10*: −3 − 4⋅j_0 + 4⋅n_0
13_var_snapshot: −14⋅i_0 + 14⋅n_0
13*: 2 − 14⋅i_0 + 14⋅n_0
15_var_snapshot: 4 − 14⋅i_0 + 14⋅n_0
15*: 5 − 14⋅i_0 + 14⋅n_0

17.1.5 Transition Removal

We remove transitions 38, 40, 45, 47, 59, 61, 73, 75, 80, 82, 2, 3, 5, 7, 9, 11, 12, 13, 14, 15, 21, 24, 29, 30, 31, 32, 33 using the following ranking functions, which are bounded by −6.

2: −2
3: −4
4: 0
5: −2
6: 0
8: −2
9: −4
10: 0
11: 0
12: −1
13: 1
14: 3
15: 5
16: 7
17: 8
18: −6
19: 0
20: −5
21: 0
22: 1
0: 0
7: 0
2_var_snapshot: −3
2*: −1
4_var_snapshot: −1
4*: 1
7_var_snapshot: 0
7*: 0
9_var_snapshot: −5
9*: −3
10_var_snapshot: 0
10*: −3
13_var_snapshot: 0
13*: 2
15_var_snapshot: 4
15*: 6

17.1.6 Splitting Cut-Point Transitions

We consider 7 subproblems corresponding to sets of cut-point transitions as follows.

17.1.6.1 Cut-Point Subproblem 1/7

Here we consider cut-point transition 37.

17.1.6.1.1 Splitting Cut-Point Transitions

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

17.1.6.2 Cut-Point Subproblem 2/7

Here we consider cut-point transition 44.

17.1.6.2.1 Splitting Cut-Point Transitions

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

17.1.6.3 Cut-Point Subproblem 3/7

Here we consider cut-point transition 51.

17.1.6.3.1 Splitting Cut-Point Transitions

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

17.1.6.4 Cut-Point Subproblem 4/7

Here we consider cut-point transition 58.

17.1.6.4.1 Splitting Cut-Point Transitions

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

17.1.6.5 Cut-Point Subproblem 5/7

Here we consider cut-point transition 65.

17.1.6.5.1 Splitting Cut-Point Transitions

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

17.1.6.6 Cut-Point Subproblem 6/7

Here we consider cut-point transition 72.

17.1.6.6.1 Splitting Cut-Point Transitions

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

17.1.6.7 Cut-Point Subproblem 7/7

Here we consider cut-point transition 79.

17.1.6.7.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert