LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f192_0_main_LT f192_0_main_LT f192_0_main_LT: x1 = x1x2 = x2
f151_0_main_LT f151_0_main_LT f151_0_main_LT: x1 = x1x2 = x2
f1_0_main_Load f1_0_main_Load f1_0_main_Load: 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 { f192_0_main_LT, f151_0_main_LT }.

2.1.1 Transition Removal

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

f151_0_main_LT: 2 + 2⋅x1
f192_0_main_LT: −1 + 2⋅x1

2.1.2 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

f192_0_main_LT: x1x2

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