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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ R_post ≤ 0 ∧ − R_post ≤ 0 ∧ A_post − R_post ≤ 0 ∧ − A_post + R_post ≤ 0 ∧ A_0 − A_post ≤ 0 ∧ − A_0 + A_post ≤ 0 ∧ NBuffers_0 − NBuffers_post ≤ 0 ∧ − NBuffers_0 + NBuffers_post ≤ 0 ∧ NLocBuffer_0 − NLocBuffer_post ≤ 0 ∧ − NLocBuffer_0 + NLocBuffer_post ≤ 0 ∧ R_0 − R_post ≤ 0 ∧ − R_0 + R_post ≤ 0 ∧ istemp_0 − istemp_post ≤ 0 ∧ − istemp_0 + istemp_post ≤ 0
  2	1	0:		− istemp_post + istemp_post ≤ 0 ∧ istemp_post − istemp_post ≤ 0 ∧ − istemp_0 + istemp_0 ≤ 0 ∧ istemp_0 − istemp_0 ≤ 0 ∧ − R_post + R_post ≤ 0 ∧ R_post − R_post ≤ 0 ∧ − R_0 + R_0 ≤ 0 ∧ R_0 − R_0 ≤ 0 ∧ − NLocBuffer_post + NLocBuffer_post ≤ 0 ∧ NLocBuffer_post − NLocBuffer_post ≤ 0 ∧ − NLocBuffer_0 + NLocBuffer_0 ≤ 0 ∧ NLocBuffer_0 − NLocBuffer_0 ≤ 0 ∧ − NBuffers_post + NBuffers_post ≤ 0 ∧ NBuffers_post − NBuffers_post ≤ 0 ∧ − NBuffers_0 + NBuffers_0 ≤ 0 ∧ NBuffers_0 − NBuffers_0 ≤ 0 ∧ − A_post + A_post ≤ 0 ∧ A_post − A_post ≤ 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)		A_post ≤ 0 ∧ R_post ≤ 0 ∧ − R_post ≤ 0 ∧ A_0 ≤ 0 ∧ R_0 ≤ 0 ∧ − R_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