# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 8
• Transitions: (pre-variables and post-variables)  3 2 4: − 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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 3 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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 4 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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 6 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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 7 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − ___const_400_0 + maxRetries_9_post ≤ 0 ∧ ___const_400_0 − 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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 8 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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

The following invariants are asserted.

 1: TRUE 3: TRUE 4: TRUE 5: TRUE 6: 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) TRUE 3 (3) TRUE 4 (4) TRUE 5 (5) TRUE 6 (6) 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 6 3 3 2 4 3 4 6 3 5 1 4 3 5 7 7 3 8 8 7

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 3 9 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 ∧ − ___const_400_0 + ___const_400_0 ≤ 0 ∧ ___const_400_0 − ___const_400_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, 7, 8 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
Hints:
 10 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 5 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 6 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 2 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 3 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 4 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 7 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 8 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

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

3* 12 3: x_5_0 + x_5_0 ≤ 0x_5_0x_5_0 ≤ 0selected_11_post + selected_11_post ≤ 0selected_11_postselected_11_post ≤ 0selected_11_0 + selected_11_0 ≤ 0selected_11_0selected_11_0 ≤ 0retryCount_10_post + retryCount_10_post ≤ 0retryCount_10_postretryCount_10_post ≤ 0retryCount_10_0 + retryCount_10_0 ≤ 0retryCount_10_0retryCount_10_0 ≤ 0maxRetries_9_post + maxRetries_9_post ≤ 0maxRetries_9_postmaxRetries_9_post ≤ 0maxRetries_9_0 + maxRetries_9_0 ≤ 0maxRetries_9_0maxRetries_9_0 ≤ 0___const_400_0 + ___const_400_0 ≤ 0___const_400_0___const_400_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 ≤ 0Result_4_post + Result_4_post ≤ 0Result_4_postResult_4_post ≤ 0Result_4_1 + Result_4_1 ≤ 0Result_4_1Result_4_1 ≤ 0Result_4_0 + Result_4_0 ≤ 0Result_4_0Result_4_0 ≤ 0

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

3 10 3_var_snapshot: x_5_0 + x_5_0 ≤ 0x_5_0x_5_0 ≤ 0selected_11_post + selected_11_post ≤ 0selected_11_postselected_11_post ≤ 0selected_11_0 + selected_11_0 ≤ 0selected_11_0selected_11_0 ≤ 0retryCount_10_post + retryCount_10_post ≤ 0retryCount_10_postretryCount_10_post ≤ 0retryCount_10_0 + retryCount_10_0 ≤ 0retryCount_10_0retryCount_10_0 ≤ 0maxRetries_9_post + maxRetries_9_post ≤ 0maxRetries_9_postmaxRetries_9_post ≤ 0maxRetries_9_0 + maxRetries_9_0 ≤ 0maxRetries_9_0maxRetries_9_0 ≤ 0___const_400_0 + ___const_400_0 ≤ 0___const_400_0___const_400_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 ≤ 0Result_4_post + Result_4_post ≤ 0Result_4_postResult_4_post ≤ 0Result_4_1 + Result_4_1 ≤ 0Result_4_1Result_4_1 ≤ 0Result_4_0 + Result_4_0 ≤ 0Result_4_0Result_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 5 using the following ranking functions, which are bounded by 4.

 1: 4⋅maxRetries_9_0 − 4⋅retryCount_10_0 3: 2 + 4⋅maxRetries_9_0 − 4⋅retryCount_10_0 3_var_snapshot: 1 + 4⋅maxRetries_9_0 − 4⋅retryCount_10_0 3*: 3 + 4⋅maxRetries_9_0 − 4⋅retryCount_10_0
Hints:
 10 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 12 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 5 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 6 lexWeak[ [0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 6.1.2 Transition Removal

We remove transitions 10, 12, 6 using the following ranking functions, which are bounded by −3.

 1: 0 3: −2 3_var_snapshot: −3 3*: −1
Hints:
 10 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 12 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 6 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 9.

### 6.1.3.1.1 Splitting Cut-Point Transitions

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

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• version: 1.0