LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f218_0_times_Return f218_0_times_Return f218_0_times_Return: x1 = x1x2 = x2x3 = x3
f469_0_times_InvokeMethod f469_0_times_InvokeMethod f469_0_times_InvokeMethod: x1 = x1x2 = x2x3 = x3
f484_0_plus_LE f484_0_plus_LE f484_0_plus_LE: x1 = x1x2 = x2x3 = x3
f127_0_times_NE f127_0_times_NE f127_0_times_NE: x1 = x1x2 = x2x3 = x3
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2x3 = x3
__init __init __init: x1 = x1x2 = x2x3 = x3
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { f127_0_times_NE }.

2.1.1 Transition Removal

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

f127_0_times_NE: x2

2.1.2 Trivial Cooperation Program

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

2.2 SCC Subproblem 2/2

Here we consider the SCC { f484_0_plus_LE }.

2.2.1 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 0.

f484_0_plus_LE: −1 + x1

2.2.2 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 0.

f484_0_plus_LE: x2

2.2.3 Trivial Cooperation Program

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

Tool configuration

AProVE