LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f194_0_main_LE f194_0_main_LE f194_0_main_LE: x1 = x1x2 = x2
f142_0_main_LE f142_0_main_LE f142_0_main_LE: x1 = x1x2 = x2
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2
f209_0_main_LE f209_0_main_LE f209_0_main_LE: 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 { f194_0_main_LE, f142_0_main_LE, f209_0_main_LE }.

2.1.1 Transition Removal

We remove transitions 4, 5 using the following ranking functions, which are bounded by 0.

f142_0_main_LE: −1 + 3⋅x1
f194_0_main_LE: 1 + x2
f209_0_main_LE: −1 + 3⋅x1

2.1.2 Transition Removal

We remove transitions 6, 7, 3 using the following ranking functions, which are bounded by 0.

f142_0_main_LE: −5 + 4⋅x2
f194_0_main_LE: −5 + 4⋅x1
f209_0_main_LE: x2

2.1.3 Transition Removal

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

f142_0_main_LE: 0
f194_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