LTS Termination Proof

by T2Cert

Input

• Initial Location: 2
• Transitions: (pre-variables and post-variables)

  0	0	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + a_1 ≤ 0 ∧ 1 − a_1 ≤ 0 ∧ 1 + a_post ≤ 0 ∧ −1 − a_post ≤ 0 ∧ a_0 − a_post ≤ 0 ∧ − a_0 + a_post ≤ 0
  2	1	0:		0 ≤ 0 ∧ 0 ≤ 0 ∧ − a_post + a_post ≤ 0 ∧ a_post − a_post ≤ 0 ∧ − a_1 + a_1 ≤ 0 ∧ a_1 − a_1 ≤ 0 ∧ − a_0 + a_0 ≤ 0 ∧ a_0 − a_0 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

The invariants are proved as follows.

IMPACT Invariant Proof

• nodes (location) invariant:

  0		(0)		TRUE
  1		(1)		1 + a_0 ≤ 0 ∧ −1 − a_0 ≤ 0 ∧ 1 + a_post ≤ 0 ∧ −1 − a_post ≤ 0 ∧ −1 + a_1 ≤ 0 ∧ 1 − a_1 ≤ 0
  2		(2)		TRUE

• initial node: 2
• cover edges:
• transition edges:

  0	0 1
  2	1 0

2 Switch to Cooperation Termination Proof

3 Transition Removal

We remove transitions 0, 1 using the following ranking functions, which are bounded by −8.

4 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

T2Cert

• version: 1.0