LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
1: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
2: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
3: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
4: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
5: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
6: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
7: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
8: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
9: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
10: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
11: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
12: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
13: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
14: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
15: −15 + edgecount_post ≤ 0 ∧ 15 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −15 + edgecount_0 ≤ 0 ∧ 15 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0
16: TRUE
17: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
2 25 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0
4 32 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0
7 39 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0
9 46 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0
13 53 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 3, 4, 9, 17, 23, 24 using the following ranking functions, which are bounded by −27.

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

4 Location Addition

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

2* 28 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

5 Location Addition

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

2 26 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

6 Location Addition

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

4* 35 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

7 Location Addition

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

4 33 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

8 Location Addition

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

7* 42 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

9 Location Addition

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

7 40 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

10 Location Addition

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

9* 49 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

11 Location Addition

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

9 47 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

12 Location Addition

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

13* 56 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

13 Location Addition

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

13 54 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 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_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 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 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 { 0, 2, 2_var_snapshot, 2* }.

14.1.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 0.

0: −6⋅i_0 + 6⋅nodecount_0 − nodecount_post
2: −1 − 6⋅i_0 + 6⋅nodecount_0
2_var_snapshot: −12 + edgecount_post − 6⋅i_0 + 6⋅nodecount_0 − nodecount_post
2*: −6⋅i_0 + 6⋅nodecount_0

14.1.2 Transition Removal

We remove transitions 26, 28, 22 using the following ranking functions, which are bounded by −1.

0: − nodecount_0
2: edgecount_0
2_var_snapshot: 0
2*: edgecount_0 + edgecount_post

14.1.3 Splitting Cut-Point Transitions

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

14.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 25.

14.1.3.1.1 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 { 3, 4, 5, 4_var_snapshot, 4* }.

14.2.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by −689.

3: −2⋅edgecount_0 − edgecount_post − 47⋅i_0
4: −47⋅i_0
5: −2⋅edgecount_0 − edgecount_post − 47⋅i_0 + 3⋅nodecount_post
4_var_snapshot: −2⋅edgecount_0 − 47⋅i_0 + 3⋅nodecount_post
4*: 31 − 2⋅edgecount_0 − 47⋅i_0

14.2.2 Transition Removal

We remove transitions 35, 2, 21 using the following ranking functions, which are bounded by −31.

3: edgecount_post
4: −3⋅nodecount_post
5: −2⋅edgecount_0 − nodecount_0
4_var_snapshot: −2⋅edgecount_0
4*: 0

14.2.3 Transition Removal

We remove transition 33 using the following ranking functions, which are bounded by 4.

3: 0
4: nodecount_0
5: 0
4_var_snapshot: 0
4*: 0

14.2.4 Splitting Cut-Point Transitions

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

14.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 32.

14.2.4.1.1 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 { 6, 7, 8, 9, 10, 7_var_snapshot, 7*, 9_var_snapshot, 9* }.

14.3.1 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 75.

6: −61⋅i_0 + 61⋅nodecount_0
7: −61⋅i_0 + 61⋅nodecount_0
8: −61⋅i_0 + 61⋅nodecount_0
9: 4⋅edgecount_post − 61⋅i_0 + 61⋅nodecount_0 − 3⋅nodecount_post
10: −15 − 61⋅i_0 + 61⋅nodecount_0 + 6⋅nodecount_post
7_var_snapshot: −61⋅i_0 + 61⋅nodecount_0
7*: −61⋅i_0 + 61⋅nodecount_0
9_var_snapshot: −61⋅i_0 + 61⋅nodecount_0 + 6⋅nodecount_post
9*: 4⋅edgecount_post − 61⋅i_0 + 61⋅nodecount_0

14.3.2 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by −85.

6: −9 + 2⋅edgecount_0 − 9⋅j_0 + 4⋅nodecount_post
7: 2⋅edgecount_0 − 9⋅j_0 + 3⋅nodecount_post
8: 12 + edgecount_0 − 9⋅j_0 + 3⋅nodecount_post
9: 14 + edgecount_0 − 9⋅j_0
10: −2 + 2⋅edgecount_0 − 9⋅j_0
7_var_snapshot: edgecount_0 + edgecount_post − 9⋅j_0 + 3⋅nodecount_post
7*: 4 + 2⋅edgecount_0 − 9⋅j_0 + 3⋅nodecount_post
9_var_snapshot: 13 + edgecount_0 − 9⋅j_0
9*: edgecount_0 − 9⋅j_0 + 3⋅nodecount_post

14.3.3 Transition Removal

We remove transitions 40, 42, 47, 49, 6, 7, 19, 20 using the following ranking functions, which are bounded by −1.

6: edgecount_post + 12⋅nodecount_0
7: 50 + nodecount_0
8: − edgecount_0 + 3⋅edgecount_post + nodecount_0
9: nodecount_0
10: − nodecount_post
7_var_snapshot: 3⋅edgecount_post + nodecount_0
7*: 12⋅nodecount_0
9_var_snapshot: 0
9*: −30 + 3⋅edgecount_post + nodecount_0

14.3.4 Splitting Cut-Point Transitions

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

14.3.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 39.

14.3.4.1.1 Splitting Cut-Point Transitions

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

14.3.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 46.

14.3.4.2.1 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 { 11, 12, 13, 14, 15, 13_var_snapshot, 13* }.

14.4.1 Transition Removal

We remove transitions 15, 16, 18 using the following ranking functions, which are bounded by −253.

11: −2⋅edgecount_post − 63⋅i_0 + 63⋅source_0
12: −31 − 63⋅i_0 + 63⋅source_0
13: 2⋅edgecount_post − 63⋅i_0 + 63⋅source_0
14: 15 + edgecount_0 − 2⋅edgecount_post − 63⋅i_0 + 63⋅source_0
15: edgecount_0 − 2⋅edgecount_post − 63⋅i_0 + 63⋅source_0
13_var_snapshot: edgecount_0 − 63⋅i_0 + 63⋅source_0
13*: 31 − 63⋅i_0 + 63⋅source_0

14.4.2 Transition Removal

We remove transitions 54, 56, 11, 12, 13 using the following ranking functions, which are bounded by −12.

11: 1
12: 0
13: − nodecount_0 − nodecount_post
14: −7 − nodecount_0
15: 2
13_var_snapshot: −6 − nodecount_0
13*: − nodecount_post

14.4.3 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 4.

11: 0
12: 0
13: 0
14: 0
15: nodecount_post
13_var_snapshot: 0
13*: 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 53.

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

T2Cert