LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f355_0_reverse_NULL f355_0_reverse_NULL f355_0_reverse_NULL: x1 = x1x2 = x2x3 = x3x4 = x4
f385_0_reverse_FieldAccess f385_0_reverse_FieldAccess f385_0_reverse_FieldAccess: x1 = x1x2 = x2x3 = x3x4 = x4
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2x3 = x3x4 = x4
f172_0_createList_LE f172_0_createList_LE f172_0_createList_LE: x1 = x1x2 = x2x3 = x3x4 = x4
f370_0_reverse_FieldAccess f370_0_reverse_FieldAccess f370_0_reverse_FieldAccess: 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 3 SCC(s) of the program graph.

2.1 SCC Subproblem 1/3

Here we consider the SCC { f172_0_createList_LE }.

2.1.1 Transition Removal

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

f172_0_createList_LE: x3

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 2/3

Here we consider the SCC { f370_0_reverse_FieldAccess }.

2.2.1 Transition Removal

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

f370_0_reverse_FieldAccess: x4

2.2.2 Trivial Cooperation Program

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

2.3 SCC Subproblem 3/3

Here we consider the SCC { f355_0_reverse_NULL, f385_0_reverse_FieldAccess }.

2.3.1 Transition Removal

We remove transitions 7, 9, 8 using the following ranking functions, which are bounded by 0.

f355_0_reverse_NULL: −1 + 2⋅x2
f385_0_reverse_FieldAccess: 2⋅x1

2.3.2 Trivial Cooperation Program

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

Tool configuration

AProVE