# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 2
• Transitions: (pre-variables and post-variables)  0 0 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ tmp_0 − tmp_post ≤ 0 ∧ − tmp_0 + tmp_post ≤ 0 ∧ x35_0 − x35_post ≤ 0 ∧ − x35_0 + x35_post ≤ 0 ∧ x68_0 − x68_post ≤ 0 ∧ − x68_0 + x68_post ≤ 0 2 1 0: − x68_post + x68_post ≤ 0 ∧ x68_post − x68_post ≤ 0 ∧ − x68_0 + x68_0 ≤ 0 ∧ x68_0 − x68_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
and for every transition t, a duplicate t is considered.

### 2 Transition Removal

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

 2: 0 0: 0 1: 0 2: −4 0: −5 1: −6
Hints:
 0 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] ] 1 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] ]

### 3 SCC Decomposition

There exist no SCC in the program graph.

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• version: 1.0