LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f163_0_factorial_GT f163_0_factorial_GT f163_0_factorial_GT: x1 = x1
f149_0_doSum_LT f149_0_doSum_LT f149_0_doSum_LT: x1 = x1
f1_0_main_ConstantStackPush f1_0_main_ConstantStackPush f1_0_main_ConstantStackPush: x1 = x1
__init __init __init: x1 = x1
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { f149_0_doSum_LT }.

2.1.1 Transition Removal

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

f149_0_doSum_LT: x1

2.1.2 Trivial Cooperation Program

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

2.2 SCC Subproblem 2/2

Here we consider the SCC { f163_0_factorial_GT }.

2.2.1 Transition Removal

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

f163_0_factorial_GT: x1

2.2.2 Trivial Cooperation Program

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

Tool configuration

AProVE