LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 8

Transitions: (pre-variables and post-variables)

3	2	4:	1 + selected_11_0 ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0
3	3	4:	1 − selected_11_0 ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0
4	4	5:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ ____cil_tmp6_12_post − selected_11_0 ≤ 0 ∧ − ____cil_tmp6_12_post + selected_11_0 ≤ 0 ∧ Result_4_post − ____cil_tmp6_12_post ≤ 0 ∧ − Result_4_post + ____cil_tmp6_12_post ≤ 0 ∧ Result_4_0 − Result_4_post ≤ 0 ∧ − Result_4_0 + Result_4_post ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_post ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0
3	5	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ selected_11_0 ≤ 0 ∧ − selected_11_0 ≤ 0 ∧ maxRetries_9_0 − retryCount_10_0 ≤ 0 ∧ ____cil_tmp6_12_post − selected_11_0 ≤ 0 ∧ − ____cil_tmp6_12_post + selected_11_0 ≤ 0 ∧ Result_4_post − ____cil_tmp6_12_post ≤ 0 ∧ − Result_4_post + ____cil_tmp6_12_post ≤ 0 ∧ Result_4_0 − Result_4_post ≤ 0 ∧ − Result_4_0 + Result_4_post ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_post ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0
3	6	1:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ selected_11_0 ≤ 0 ∧ − selected_11_0 ≤ 0 ∧ 1 − maxRetries_9_0 + retryCount_10_0 ≤ 0 ∧ ____cil_tmp2_6_post − x_5_0 ≤ 0 ∧ − ____cil_tmp2_6_post + x_5_0 ≤ 0 ∧ Result_4_1 − ____cil_tmp2_6_post ≤ 0 ∧ − Result_4_1 + ____cil_tmp2_6_post ≤ 0 ∧ − Result_4_1 + selected_11_post ≤ 0 ∧ Result_4_1 − selected_11_post ≤ 0 ∧ Result_4_0 − Result_4_post ≤ 0 ∧ − Result_4_0 + Result_4_post ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_post ≤ 0 ∧ selected_11_0 − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_post ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0
1	7	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − retryCount_10_0 + retryCount_10_post ≤ 0 ∧ 1 + retryCount_10_0 − retryCount_10_post ≤ 0 ∧ retryCount_10_0 − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_post ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0
7	8	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ retryCount_10_post ≤ 0 ∧ − retryCount_10_post ≤ 0 ∧ selected_11_post ≤ 0 ∧ − selected_11_post ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_post ≤ 0 ∧ retryCount_10_0 − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_post ≤ 0 ∧ selected_11_0 − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_post ≤ 0 ∧ − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0
8	9	7:	− x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

1:	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
3:	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
4:	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
5:	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
6:	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0 ∧ selected_11_0 ≤ 0 ∧ − selected_11_0 ≤ 0 ∧ Result_4_post ≤ 0 ∧ ____cil_tmp6_12_post ≤ 0 ∧ Result_4_0 ≤ 0 ∧ ____cil_tmp6_12_0 ≤ 0
7:	TRUE
8:	TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

nodes (location) invariant:

1	(1)	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
3	(3)	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
4	(4)	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
5	(5)	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ −4 + maxRetries_9_0 ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0
6	(6)	−4 + maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_post ≤ 0 ∧ 4 − maxRetries_9_0 ≤ 0 ∧ selected_11_0 ≤ 0 ∧ − selected_11_0 ≤ 0 ∧ Result_4_post ≤ 0 ∧ ____cil_tmp6_12_post ≤ 0 ∧ Result_4_0 ≤ 0 ∧ ____cil_tmp6_12_0 ≤ 0
7	(7)	TRUE
8	(8)	TRUE

initial node: 8
cover edges:
transition edges:

1 7 3

3 2 4

3 3 4

3 5 6

3 6 1

4 4 5

7 8 3

8 9 7

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

− x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0

and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 2, 3, 4, 5, 8, 9 using the following ranking functions, which are bounded by −17.

8:	0
7:	0
1:	0
3:	0
4:	0
5:	0
6:	0
8:	−7
7:	−8
1:	−9
3:	−9
3_var_snapshot:	−9
3*:	−9
4:	−13
5:	−14
6:	−15

4 Location Addition

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

3* 13 3: − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0

5 Location Addition

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

3 11 3_var_snapshot: − x_5_0 + x_5_0 ≤ 0 ∧ x_5_0 − x_5_0 ≤ 0 ∧ − selected_11_post + selected_11_post ≤ 0 ∧ selected_11_post − selected_11_post ≤ 0 ∧ − selected_11_0 + selected_11_0 ≤ 0 ∧ selected_11_0 − selected_11_0 ≤ 0 ∧ − retryCount_10_post + retryCount_10_post ≤ 0 ∧ retryCount_10_post − retryCount_10_post ≤ 0 ∧ − retryCount_10_0 + retryCount_10_0 ≤ 0 ∧ retryCount_10_0 − retryCount_10_0 ≤ 0 ∧ − maxRetries_9_post + maxRetries_9_post ≤ 0 ∧ maxRetries_9_post − maxRetries_9_post ≤ 0 ∧ − maxRetries_9_0 + maxRetries_9_0 ≤ 0 ∧ maxRetries_9_0 − maxRetries_9_0 ≤ 0 ∧ − ____cil_tmp6_12_post + ____cil_tmp6_12_post ≤ 0 ∧ ____cil_tmp6_12_post − ____cil_tmp6_12_post ≤ 0 ∧ − ____cil_tmp6_12_0 + ____cil_tmp6_12_0 ≤ 0 ∧ ____cil_tmp6_12_0 − ____cil_tmp6_12_0 ≤ 0 ∧ − ____cil_tmp2_6_post + ____cil_tmp2_6_post ≤ 0 ∧ ____cil_tmp2_6_post − ____cil_tmp2_6_post ≤ 0 ∧ − ____cil_tmp2_6_0 + ____cil_tmp2_6_0 ≤ 0 ∧ ____cil_tmp2_6_0 − ____cil_tmp2_6_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_1 + Result_4_1 ≤ 0 ∧ Result_4_1 − Result_4_1 ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_0 ≤ 0

6 SCC Decomposition

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

6.1 SCC Subproblem 1/1

Here we consider the SCC { 1, 3, 3_var_snapshot, 3* }.

6.1.1 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by −22.

1:	− maxRetries_9_0 − 7⋅retryCount_10_0
3:	1 − 7⋅retryCount_10_0
3_var_snapshot:	−7⋅retryCount_10_0
3*:	2 − 7⋅retryCount_10_0

6.1.2 Transition Removal

We remove transitions 11, 13, 7 using the following ranking functions, which are bounded by −5.

1:	1
3:	− maxRetries_9_0
3_var_snapshot:	−1 − maxRetries_9_0
3*:	0

6.1.3 Splitting Cut-Point Transitions

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

6.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 10.

6.1.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

version: 1.0