LTS Termination Proof

by T2Cert

Input

• 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

1 Invariant Updates

The following invariants are asserted.

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

3 Transition Removal

We remove transitions 2, 3, 4, 7, 8 using the following ranking functions, which are bounded by −17.

4 Location Addition

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 ≤ 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

5 Location Addition

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 ≤ 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

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.

6.1.2 Transition Removal

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

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

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