LTS Termination Proof

by AProVE


Integer Transition System


1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f81_0_fib_Return f81_0_fib_Return f81_0_fib_Return: x1 = x1x2 = x2
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2
f142_0_fib_InvokeMethod f142_0_fib_InvokeMethod f142_0_fib_InvokeMethod: x1 = x1x2 = x2
f31_0_fib_NE f31_0_fib_NE f31_0_fib_NE: x1 = x1x2 = x2
__init __init __init: 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 { f142_0_fib_InvokeMethod, f31_0_fib_NE }.

2.1.1 Transition Removal

We remove transitions 2, 6, 4, 3 using the following ranking functions, which are bounded by 0.

f31_0_fib_NE: 2⋅x1
f142_0_fib_InvokeMethod: −1 + 2⋅x1

2.1.2 Trivial Cooperation Program

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

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