LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f908_0_main_InvokeMethod f908_0_main_InvokeMethod f908_0_main_InvokeMethod: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
f358_0_createTree_Return f358_0_createTree_Return f358_0_createTree_Return: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
f940_0_gopher_NONNULL f940_0_gopher_NONNULL f940_0_gopher_NONNULL: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
f1019_0_insert_GT f1019_0_insert_GT f1019_0_insert_GT: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
f880_0_createTree_GE f880_0_createTree_GE f880_0_createTree_GE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
__init __init __init: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6
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 { f880_0_createTree_GE }.

2.1.1 Transition Removal

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

f880_0_createTree_GE: x2 + 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 { f1019_0_insert_GT }.

2.2.1 Transition Removal

We remove transitions 9, 10 using the following ranking functions, which are bounded by 0.

f1019_0_insert_GT: x1

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 { f940_0_gopher_NONNULL }.

2.3.1 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 0.

f940_0_gopher_NONNULL: x2

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