LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 1 + a_0 ≤ 0−1 − a_0 ≤ 01 + a_post ≤ 0−1 − a_post ≤ 0−1 + a_1 ≤ 01 − a_1 ≤ 0
2: 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 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] ]
1 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0] ]

4 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

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