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 = x3
f227_0_main_LE f227_0_main_LE f227_0_main_LE: x1 = x1x2 = x2x3 = x3
f213_0_main_LE f213_0_main_LE f213_0_main_LE: 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 1 SCC(s) of the program graph.

2.1 SCC Subproblem 1/1

Here we consider the SCC { f227_0_main_LE, f213_0_main_LE }.

2.1.1 Transition Removal

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

f213_0_main_LE: −1 + x1x3
f227_0_main_LE: −1 + x2x3

2.1.2 Transition Removal

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

f213_0_main_LE: x2x3
f227_0_main_LE: −1 + x1x3

2.1.3 Transition Removal

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

f227_0_main_LE: 0
f213_0_main_LE: −1

2.1.4 Trivial Cooperation Program

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

Tool configuration

AProVE