LTS Termination Proof

Input

Integer Transition System

Initial Location: f389_0_dupList_NONNULL, f117_0_createList_GE, f1_0_main_Load, __init, f232_0_main_InvokeMethod

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f117_0_createList_GE:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 ≤ _arg1 − 1 ∧ 0 ≤ _arg2 − 1 ∧ −1 ≤ _arg1P − 1
f1_0_main_Load	2	f232_0_main_InvokeMethod:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ −1 ≤ _x6 − 1 ∧ 0 ≤ _x1 − 1 ∧ _x3 ≤ _x ∧ 0 ≤ _x − 1 ∧ 0 ≤ _x3 − 1 ∧ 3 ≤ _x4 − 1 ∧ 0 = _x5
f1_0_main_Load	3	f232_0_main_InvokeMethod:	x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x1 = _x11 ∧ x2 = _x13 ∧ x3 = _x14 ∧ −1 ≤ _x16 − 1 ∧ 0 ≤ _x9 − 1 ∧ _x11 ≤ _x8 ∧ _x13 − 1 ≤ _x8 ∧ 0 ≤ _x8 − 1 ∧ 0 ≤ _x11 − 1 ∧ 1 ≤ _x13 − 1 ∧ 0 = _x14
f117_0_createList_GE	4	f117_0_createList_GE:	x1 = _x17 ∧ x2 = _x18 ∧ x3 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ _x17 − 1 = _x20 ∧ _x17 − 1 ≤ _x17 − 1 ∧ −1 ≤ _x17 − 1
f232_0_main_InvokeMethod	5	f389_0_dupList_NONNULL:	x1 = _x23 ∧ x2 = _x24 ∧ x3 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ x3 = _x28 ∧ _x26 ≤ _x24 ∧ 0 ≤ _x29 − 1 ∧ _x27 + 2 ≤ _x24 ∧ 0 ≤ _x23 − 1 ∧ 1 ≤ _x24 − 1 ∧ 1 ≤ _x26 − 1 ∧ −1 ≤ _x27 − 1 ∧ 0 = _x25 ∧ 0 = _x28
f389_0_dupList_NONNULL	6	f389_0_dupList_NONNULL:	x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x35 + 2 ≤ _x31 ∧ _x32 + 2 ≤ _x30 ∧ _x35 + 4 ≤ _x30 ∧ −1 ≤ _x34 − 1 ∧ 0 ≤ _x33 − 1 ∧ 0 ≤ _x31 − 1 ∧ 2 ≤ _x30 − 1 ∧ _x34 + 1 ≤ _x31 ∧ _x34 + 3 ≤ _x30 ∧ _x33 ≤ _x31 ∧ _x32 ≤ −1 ∧ _x33 + 2 ≤ _x30
f389_0_dupList_NONNULL	7	f389_0_dupList_NONNULL:	x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x41 + 2 ≤ _x37 ∧ _x38 + 2 ≤ _x36 ∧ _x41 + 4 ≤ _x36 ∧ −1 ≤ _x40 − 1 ∧ 0 ≤ _x39 − 1 ∧ 0 ≤ _x37 − 1 ∧ 2 ≤ _x36 − 1 ∧ _x40 + 1 ≤ _x37 ∧ _x40 + 3 ≤ _x36 ∧ _x39 ≤ _x37 ∧ 0 ≤ _x38 − 1 ∧ _x39 + 2 ≤ _x36
f389_0_dupList_NONNULL	8	f389_0_dupList_NONNULL:	x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ 1 = _x47 ∧ 0 = _x44 ∧ 0 ≤ _x46 − 1 ∧ 2 ≤ _x45 − 1 ∧ 0 ≤ _x43 − 1 ∧ 2 ≤ _x42 − 1 ∧ _x46 ≤ _x43 ∧ _x46 + 2 ≤ _x42 ∧ _x45 − 2 ≤ _x43 ∧ _x45 ≤ _x42
__init	9	f1_0_main_Load:	x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f389_0_dupList_NONNULL	f389_0_dupList_NONNULL	f389_0_dupList_NONNULL:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f117_0_createList_GE	f117_0_createList_GE	f117_0_createList_GE:	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
f232_0_main_InvokeMethod	f232_0_main_InvokeMethod	f232_0_main_InvokeMethod:	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 { f389_0_dupList_NONNULL }.

2.1.1 Transition Removal

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

f389_0_dupList_NONNULL:

−1 + x1

2.1.2 Transition Removal

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

f389_0_dupList_NONNULL:

− x3

2.1.3 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 { f117_0_createList_GE }.

2.2.1 Transition Removal

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

f117_0_createList_GE:

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 % (8 real / 0 unknown / 0 assumptions / 8 total proof steps)