LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
l4 l4 l4: x1 = x1x2 = x2
l7 l7 l7: x1 = x1x2 = x2
l6 l6 l6: x1 = x1x2 = x2
l1 l1 l1: x1 = x1x2 = x2
l3 l3 l3: 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 { l4, l1, l3, l0, l2 }.

2.1.1 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 0.

l0: −2 + x1x2
l1: −1 + x1x2
l3: −2 + x1x2
l2: −2 + x1x2
l4: −1 + x1x2

2.1.2 Transition Removal

We remove transitions 1, 4, 2, 3, 7 using the following ranking functions, which are bounded by 0.

l0: 2
l1: 1
l3: 4
l2: 3
l4: 0

2.1.3 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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