LTS Termination Proof

Input

Integer Transition System

Initial Location: f147_0_get_LE, f1_0_main_Load, f80_0_create_LE, __init, f108_0_main_ArrayAccess

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f80_0_create_LE:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ _arg2 = _arg4P ∧ 0 = _arg3P ∧ _arg2 − 1 = _arg2P ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg2 − 1 ∧ _arg1P ≤ _arg1
f80_0_create_LE	2	f108_0_main_ArrayAccess:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x1 = _x4 ∧ x2 = _x5 ∧ x3 = _x6 ∧ x4 = _x7 ∧ _x3 = _x6 ∧ 0 ≤ _x4 − 1 ∧ 0 ≤ _x − 1 ∧ _x4 ≤ _x ∧ _x2 ≤ _x5 − 1 ∧ 0 ≤ _x2 − 1 ∧ _x1 ≤ 0
f80_0_create_LE	3	f108_0_main_ArrayAccess:	x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x4 = _x11 ∧ x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x4 = _x15 ∧ _x11 = _x14 ∧ 1 = _x13 ∧ 0 ≤ _x12 − 1 ∧ 0 ≤ _x8 − 1 ∧ _x9 ≤ 0 ∧ _x12 ≤ _x8
f80_0_create_LE	4	f80_0_create_LE:	x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ x4 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x24 ∧ _x19 = _x24 ∧ _x17 − 1 = _x21 ∧ 0 ≤ _x20 − 1 ∧ 0 ≤ _x16 − 1 ∧ 0 ≤ _x17 − 1 ∧ _x20 ≤ _x16
f108_0_main_ArrayAccess	5	f147_0_get_LE:	x1 = _x25 ∧ x2 = _x26 ∧ x3 = _x28 ∧ x4 = _x29 ∧ x1 = _x31 ∧ x2 = _x32 ∧ x3 = _x33 ∧ x4 = _x34 ∧ 0 ≤ _x28 − 1 ∧ −1 ≤ _x35 − 1 ∧ 0 ≤ _x25 − 1 ∧ _x35 − 1 = _x31 ∧ _x26 = _x32
f147_0_get_LE	6	f147_0_get_LE:	x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x4 = _x39 ∧ x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ −1 ≤ _x37 − 1 ∧ 0 ≤ _x44 − 1 ∧ _x44 ≤ _x37 − 1 ∧ 0 ≤ _x36 − 1 ∧ _x44 ≤ _x41 − 1 ∧ _x36 − 1 = _x40
f147_0_get_LE	7	f147_0_get_LE:	x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x48 ∧ x1 = _x49 ∧ x2 = _x50 ∧ x3 = _x51 ∧ x4 = _x52 ∧ 0 ≤ _x45 − 1 ∧ _x53 ≤ _x46 − 1 ∧ −1 ≤ _x46 − 1 ∧ _x45 − 1 = _x49 ∧ 1 = _x50
__init	8	f1_0_main_Load:	x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x4 = _x57 ∧ x1 = _x58 ∧ x2 = _x59 ∧ x3 = _x60 ∧ x4 = _x61 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f147_0_get_LE	f147_0_get_LE	f147_0_get_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f1_0_main_Load	f1_0_main_Load	f1_0_main_Load:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f80_0_create_LE	f80_0_create_LE	f80_0_create_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
__init	__init	__init:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f108_0_main_ArrayAccess	f108_0_main_ArrayAccess	f108_0_main_ArrayAccess:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4

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 { f80_0_create_LE }.

2.1.1 Transition Removal

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

f80_0_create_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 { f147_0_get_LE }.

2.2.1 Transition Removal

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

f147_0_get_LE:

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)