LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f179_0_main_GT f179_0_main_GT f179_0_main_GT: x1 = x1x2 = x2x3 = x3x4 = x4
f350_0_fact_GT f350_0_fact_GT f350_0_fact_GT: x1 = x1x2 = x2x3 = x3x4 = x4
f1_0_main_ConstantStackPush f1_0_main_ConstantStackPush f1_0_main_ConstantStackPush: x1 = x1x2 = x2x3 = x3x4 = x4
f535_0_main_GT f535_0_main_GT f535_0_main_GT: x1 = x1x2 = x2x3 = x3x4 = x4
f535_0_main_GT' f535_0_main_GT' f535_0_main_GT': 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 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { f179_0_main_GT, f535_0_main_GT, f535_0_main_GT' }.

2.1.1 Transition Removal

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

f179_0_main_GT: x2 + x3
f535_0_main_GT: −1 − x2 + x4
f535_0_main_GT': −1 − x2 + x4

2.1.2 Transition Removal

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

f535_0_main_GT: 0
f179_0_main_GT: −1
f535_0_main_GT': 0

2.1.3 Transition Removal

We remove transitions 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27 using the following ranking functions, which are bounded by 0.

f535_0_main_GT': −2⋅x3 + 2⋅x4
f535_0_main_GT: 1 − 2⋅x3 + 2⋅x4

2.1.4 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 { f350_0_fact_GT }.

2.2.1 Transition Removal

We remove transition 29 using the following ranking functions, which are bounded by 0.

f350_0_fact_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