LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: i_post ≤ 0i_post ≤ 0−1 + j_post ≤ 01 − j_post ≤ 0i_0 ≤ 0i_0 ≤ 0−1 + j_0 ≤ 01 − j_0 ≤ 0
1: i_post ≤ 0i_post ≤ 0−1 + j_post ≤ 01 − j_post ≤ 0i_0 ≤ 0i_0 ≤ 0−1 + j_0 ≤ 01 − j_0 ≤ 0
2: i_post ≤ 0i_post ≤ 0−1 + j_post ≤ 01 − j_post ≤ 0i_0 ≤ 0i_0 ≤ 0−1 + j_0 ≤ 01 − j_0 ≤ 0
3: TRUE
4: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

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

3 Transition Removal

We remove transitions 0, 1, 2, 3, 4 using the following ranking functions, which are bounded by −12.

4: 0
3: 0
0: 0
1: 0
2: 0
4: −6
3: −7
0: −8
1: −9
2: −10

4 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

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