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 = x2
l4 l4 l4: x1 = x1x2 = x2
l1 l1 l1: x1 = x1x2 = x2
l0 l0 l0: x1 = x1x2 = x2
l2 l2 l2: x1 = x1x2 = x2
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 { l1, l0, l2 }.

2.1.1 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by −7.

l0: −3⋅x2 + 1
l1: −3⋅x2 + 3
l2: −3⋅x2 + 2

2.1.2 Transition Removal

We remove transitions 1, 5, 2 using the following ranking functions, which are bounded by −1.

l0: 0
l1: −1
l2: −2

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