LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f152_0_gcd_LE f152_0_gcd_LE f152_0_gcd_LE: x1 = x1x2 = x2
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2
f219_0_mod_LT f219_0_mod_LT f219_0_mod_LT: 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 { f152_0_gcd_LE, f219_0_mod_LT }.

2.1.1 Transition Removal

We remove transitions 2, 3 using the following ranking functions, which are bounded by 0.

f152_0_gcd_LE: x1 + 3⋅x2 + 1
f219_0_mod_LT: x1 + 3⋅x2

2.1.2 Transition Removal

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

f219_0_mod_LT: 0
f152_0_gcd_LE: −1

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