LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f389_0_dupList_NONNULL f389_0_dupList_NONNULL f389_0_dupList_NONNULL: x1 = x1x2 = x2x3 = x3
f117_0_createList_GE f117_0_createList_GE f117_0_createList_GE: 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
f232_0_main_InvokeMethod f232_0_main_InvokeMethod f232_0_main_InvokeMethod: 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 { f389_0_dupList_NONNULL }.

2.1.1 Transition Removal

We remove transitions 6, 7 using the following ranking functions, which are bounded by 0.

f389_0_dupList_NONNULL: −1 + x1

2.1.2 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by 0.

f389_0_dupList_NONNULL: x3

2.1.3 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 { f117_0_createList_GE }.

2.2.1 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

f117_0_createList_GE: x1

2.2.2 Trivial Cooperation Program

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

Tool configuration

AProVE