LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2x3 = x3x4 = x4
f278_0_main_LE f278_0_main_LE f278_0_main_LE: x1 = x1x2 = x2x3 = x3x4 = x4
__init __init __init: x1 = x1x2 = x2x3 = x3x4 = x4
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 { f278_0_main_LE }.

2.1.1 Transition Removal

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

f278_0_main_LE: −1 + x1

2.1.2 Transition Removal

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

f278_0_main_LE: x2

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