LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
l5 l5 l5: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5
l4 l4 l4: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5
l3 l3 l3: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5
l0 l0 l0: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5
l2 l2 l2: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

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

2.1 SCC Subproblem 1/1

Here we consider the SCC { l0, l2 }.

2.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

l0: −1 − x4 + 101⋅x5
l2: −1 − x4 + 101⋅x5

2.1.2 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

l2: 0
l0: −1

2.1.3 Trivial Cooperation Program

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

Tool configuration

AProVE