LTS Termination Proof

by manual

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

l0: TRUE
l1: z < 0
l2: z < −1

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
l2 e l2: x = xy = yz = z
and for every transition t, a duplicate t is considered.

3 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

3.1 SCC Subproblem 1/1

Here we consider the SCC { l1, l2 }.

3.1.1 Transition Removal

We remove transition t2 using the following ranking functions, which are bounded by −5.

l1: x
l2: x
Hints:

3.1.2 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

3.1.2.1 SCC Subproblem 1/1

Here we consider the SCC { l2 }.

3.1.2.1.1 Transition Removal

We remove transition t3 using the following ranking functions, which are bounded by 0.

l2: xy
Hints:

3.1.2.1.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

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