LTS Termination Proof

Input

Integer Transition System

Initial Location: f236_0_main_InvokeMethod, f358_0_duplicate_NULL, f169_0_createList_Return, f208_0_createList_LE, f1_0_main_Load, __init

Transitions: (pre-variables and post-variables)

f169_0_createList_Return	1	f236_0_main_InvokeMethod:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ −1 ≤ _arg2P − 1 ∧ 0 ≤ _arg1P − 1 ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg2P ≤ _arg2 ∧ _arg1P − 1 ≤ _arg2 ∧ _arg1P ≤ _arg1
f1_0_main_Load	2	f236_0_main_InvokeMethod:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ −1 ≤ _x4 − 1 ∧ 0 ≤ _x3 − 1 ∧ 0 ≤ _x − 1 ∧ _x3 ≤ _x
f1_0_main_Load	3	f208_0_createList_LE:	x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ 0 ≤ _x6 − 1 ∧ −1 ≤ _x9 − 1 ∧ −1 ≤ _x7 − 1
f208_0_createList_LE	4	f208_0_createList_LE:	x1 = _x12 ∧ x2 = _x14 ∧ x3 = _x15 ∧ x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ _x12 − 1 = _x16 ∧ 0 ≤ _x12 − 1
f236_0_main_InvokeMethod	5	f358_0_duplicate_NULL:	x1 = _x19 ∧ x2 = _x20 ∧ x3 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ x3 = _x24 ∧ _x22 ≤ _x20 ∧ 0 ≤ _x25 − 1 ∧ _x24 ≤ _x20 ∧ 0 ≤ _x19 − 1 ∧ −1 ≤ _x20 − 1 ∧ −1 ≤ _x22 − 1 ∧ −1 ≤ _x24 − 1 ∧ 1 = _x23
f358_0_duplicate_NULL	6	f358_0_duplicate_NULL:	x1 = _x26 ∧ x2 = _x27 ∧ x3 = _x28 ∧ x1 = _x29 ∧ x2 = _x30 ∧ x3 = _x31 ∧ 1 = _x30 ∧ 0 = _x27 ∧ −1 ≤ _x31 − 1 ∧ −1 ≤ _x29 − 1 ∧ 0 ≤ _x28 − 1 ∧ 0 ≤ _x26 − 1 ∧ _x31 + 1 ≤ _x28 ∧ _x31 + 1 ≤ _x26 ∧ _x29 + 1 ≤ _x28 ∧ _x29 + 1 ≤ _x26
f358_0_duplicate_NULL	7	f358_0_duplicate_NULL:	x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x1 = _x35 ∧ x2 = _x36 ∧ x3 = _x37 ∧ 0 = _x36 ∧ 1 = _x33 ∧ 0 ≤ _x37 − 1 ∧ 0 ≤ _x35 − 1 ∧ 0 ≤ _x34 − 1 ∧ 0 ≤ _x32 − 1 ∧ _x37 ≤ _x34 ∧ _x37 ≤ _x32 ∧ _x35 ≤ _x34 ∧ _x35 ≤ _x32
__init	8	f1_0_main_Load:	x1 = _x38 ∧ x2 = _x39 ∧ x3 = _x40 ∧ x1 = _x41 ∧ x2 = _x42 ∧ x3 = _x43 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f236_0_main_InvokeMethod	f236_0_main_InvokeMethod	f236_0_main_InvokeMethod:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f358_0_duplicate_NULL	f358_0_duplicate_NULL	f358_0_duplicate_NULL:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f169_0_createList_Return	f169_0_createList_Return	f169_0_createList_Return:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f208_0_createList_LE	f208_0_createList_LE	f208_0_createList_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f1_0_main_Load	f1_0_main_Load	f1_0_main_Load:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
__init	__init	__init:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3

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 { f208_0_createList_LE }.

2.1.1 Transition Removal

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

f208_0_createList_LE:

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 { f358_0_duplicate_NULL }.

2.2.1 Transition Removal

We remove transitions 6, 7 using the following ranking functions, which are bounded by 0.

f358_0_duplicate_NULL:

2⋅x1 + x2

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

version: AProVE Commit ID: unknown
strategy: Statistics for single proof: 100.00 % (7 real / 0 unknown / 0 assumptions / 7 total proof steps)