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 ∧ −5 + x_post ≤ 0 ∧ 5 − x_post ≤ 0 ∧ − x_post + y_post ≤ 0 ∧ x_post − y_post ≤ 0 ∧ y_post ≤ 0 ∧ x_0 − x_post ≤ 0 ∧ − x_0 + x_post ≤ 0 ∧ y_0 − y_post ≤ 0 ∧ − y_0 + y_post ≤ 0
  2	1	0:		− 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

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)		−5 + x_post ≤ 0 ∧ 5 − x_post ≤ 0 ∧ y_post ≤ 0 ∧ −5 + x_0 ≤ 0 ∧ 5 − x_0 ≤ 0 ∧ y_0 ≤ 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