LTS Termination Proof

Input

Integer Transition System

Initial Location: f540_0_random_ArrayAccess, f289_0_appendNewList_Return, f422_0_random_ArrayAccess, f673_0_main_InvokeMethod, f1_0_main_Load, f760_0_copy_NONNULL, __init

Transitions: (pre-variables and post-variables)

f289_0_appendNewList_Return	1	f540_0_random_ArrayAccess:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ _arg5 = _arg4P ∧ 0 = _arg3P ∧ 0 = _arg4 ∧ _arg5 + 2 ≤ _arg2 ∧ 3 ≤ _arg1P − 1 ∧ 3 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg1P ≤ _arg2
f1_0_main_Load	2	f540_0_random_ArrayAccess:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x1 = _x5 ∧ x2 = _x6 ∧ x3 = _x7 ∧ x4 = _x8 ∧ x5 = _x9 ∧ 0 = _x7 ∧ _x1 = _x6 ∧ 3 ≤ _x5 − 1 ∧ 0 ≤ _x − 1
f540_0_random_ArrayAccess	3	f673_0_main_InvokeMethod:	x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ x4 = _x13 ∧ x5 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ x4 = _x18 ∧ x5 = _x19 ∧ 0 ≤ _x20 − 1 ∧ _x20 ≤ _x11 − 1 ∧ −1 ≤ _x21 − 1 ∧ _x15 + 3 ≤ _x10 ∧ 3 ≤ _x10 − 1 ∧ 0 ≤ _x15 − 1 ∧ 3 ≤ _x16 − 1 ∧ _x13 + 2 ≤ _x10 ∧ 0 = _x12 ∧ _x13 = _x19
f673_0_main_InvokeMethod	4	f760_0_copy_NONNULL:	x1 = _x22 ∧ x2 = _x23 ∧ x3 = _x24 ∧ x4 = _x25 ∧ x5 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x5 = _x31 ∧ _x24 = _x28 ∧ _x25 + 4 ≤ _x23 ∧ _x26 + 2 ≤ _x23 ∧ 3 ≤ _x27 − 1 ∧ 3 ≤ _x23 − 1 ∧ 0 ≤ _x22 − 1 ∧ 0 ≤ _x24 − 1 ∧ _x27 ≤ _x23
f1_0_main_Load	5	f422_0_random_ArrayAccess:	x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x4 = _x35 ∧ x5 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ 1 = _x39 ∧ 0 ≤ _x40 − 1 ∧ 0 ≤ _x32 − 1 ∧ −1 ≤ _x33 − 1 ∧ _x40 ≤ _x32
f540_0_random_ArrayAccess	6	f422_0_random_ArrayAccess:	x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x48 ∧ x5 = _x49 ∧ x1 = _x50 ∧ x2 = _x53 ∧ x3 = _x54 ∧ x4 = _x55 ∧ x5 = _x56 ∧ 0 ≤ _x57 − 1 ∧ _x57 ≤ _x46 − 1 ∧ −1 ≤ _x50 − 1 ∧ −1 ≤ _x46 − 1 ∧ _x53 + 3 ≤ _x45 ∧ 3 ≤ _x45 − 1 ∧ 0 ≤ _x53 − 1 ∧ _x48 + 2 ≤ _x45 ∧ 0 = _x47
f422_0_random_ArrayAccess	7	f422_0_random_ArrayAccess:	x1 = _x58 ∧ x2 = _x60 ∧ x3 = _x61 ∧ x4 = _x62 ∧ x5 = _x63 ∧ x1 = _x64 ∧ x2 = _x65 ∧ x3 = _x66 ∧ x4 = _x67 ∧ x5 = _x68 ∧ _x69 ≤ _x70 − 1 ∧ 1 ≤ _x58 − 1 ∧ −1 ≤ _x69 − 1 ∧ −1 ≤ _x71 − 1 ∧ −1 ≤ _x70 − 1 ∧ _x58 − 1 ≤ _x58 − 1 ∧ _x65 ≤ _x60 ∧ 0 ≤ _x60 − 1 ∧ 0 ≤ _x65 − 1 ∧ _x58 − 1 = _x64
f760_0_copy_NONNULL	8	f760_0_copy_NONNULL:	x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x1 = _x77 ∧ x2 = _x78 ∧ x3 = _x79 ∧ x4 = _x80 ∧ x5 = _x81 ∧ _x73 = _x78 ∧ −1 ≤ _x77 − 1 ∧ 0 ≤ _x72 − 1 ∧ 0 ≤ _x73 − 1 ∧ _x77 + 1 ≤ _x72
__init	9	f1_0_main_Load:	x1 = _x82 ∧ x2 = _x83 ∧ x3 = _x84 ∧ x4 = _x85 ∧ x5 = _x86 ∧ x1 = _x87 ∧ x2 = _x88 ∧ x3 = _x89 ∧ x4 = _x90 ∧ x5 = _x91 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f540_0_random_ArrayAccess	f540_0_random_ArrayAccess	f540_0_random_ArrayAccess:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
f289_0_appendNewList_Return	f289_0_appendNewList_Return	f289_0_appendNewList_Return:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
f422_0_random_ArrayAccess	f422_0_random_ArrayAccess	f422_0_random_ArrayAccess:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
f673_0_main_InvokeMethod	f673_0_main_InvokeMethod	f673_0_main_InvokeMethod:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
f1_0_main_Load	f1_0_main_Load	f1_0_main_Load:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
f760_0_copy_NONNULL	f760_0_copy_NONNULL	f760_0_copy_NONNULL:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
__init	__init	__init:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5

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 { f422_0_random_ArrayAccess }.

2.1.1 Transition Removal

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

f422_0_random_ArrayAccess:

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 { f760_0_copy_NONNULL }.

2.2.1 Transition Removal

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

f760_0_copy_NONNULL:

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)