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 = x3x4 = x4
f723_0_init_GE' f723_0_init_GE' f723_0_init_GE': x1 = x1x2 = x2x3 = x3x4 = x4
f723_0_init_GE f723_0_init_GE f723_0_init_GE: x1 = x1x2 = x2x3 = x3x4 = x4
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2x3 = x3x4 = x4
f873_0_init_GE f873_0_init_GE f873_0_init_GE: x1 = x1x2 = x2x3 = x3x4 = x4
f1037_0_imprimer_GE f1037_0_imprimer_GE f1037_0_imprimer_GE: x1 = x1x2 = x2x3 = x3x4 = x4
__init __init __init: x1 = x1x2 = x2x3 = x3x4 = x4
f1074_0_imprimer_GE f1074_0_imprimer_GE f1074_0_imprimer_GE: 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 { f723_0_init_GE, f873_0_init_GE }.

2.1.1 Transition Removal

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

f723_0_init_GE: 2 − x2
f873_0_init_GE: 1 − x2

2.1.2 Transition Removal

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

f873_0_init_GE: 0
f723_0_init_GE: −1

2.1.3 Transition Removal

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

f873_0_init_GE: 2 − x3

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 { f1037_0_imprimer_GE, f1074_0_imprimer_GE }.

2.2.1 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by 0.

f1037_0_imprimer_GE: 4⋅x3 − 4⋅x2 + 2
f1074_0_imprimer_GE: −4⋅x2 + 4⋅x4 + 1

2.2.2 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 0.

f1074_0_imprimer_GE: 0
f1037_0_imprimer_GE: −1

2.2.3 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 0.

f1074_0_imprimer_GE: x4x3

2.2.4 Trivial Cooperation Program

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

Tool configuration

AProVE