LTS Termination Proof

Input

Integer Transition System

Initial Location: f81_0_fib_Return, f1_0_main_Load, f142_0_fib_InvokeMethod, f31_0_fib_NE, __init

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f31_0_fib_NE:	x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ _arg2 = _arg1P ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1
f31_0_fib_NE	2	f31_0_fib_NE:	x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x − 1 = _x2 ∧ _x − 1 ≤ _x − 1 ∧ 1 ≤ _x − 1
f31_0_fib_NE	3	f142_0_fib_InvokeMethod:	x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ 0 = _x7 ∧ 2 = _x6 ∧ 2 = _x4
f31_0_fib_NE	4	f142_0_fib_InvokeMethod:	x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x8 − 2 = _x11 ∧ _x8 = _x10 ∧ _x8 − 1 ≤ _x8 − 1 ∧ 1 ≤ _x8 − 1
f81_0_fib_Return	5	f142_0_fib_InvokeMethod:	x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x12 − 2 = _x15 ∧ _x12 = _x14 ∧ 0 ≤ _x12 − 1
f142_0_fib_InvokeMethod	6	f31_0_fib_NE:	x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x17 = _x18 ∧ _x17 ≤ _x16 − 1 ∧ 1 ≤ _x16 − 1
__init	7	f1_0_main_Load:	x1 = _x20 ∧ x2 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ 0 ≤ 0

We consider the following cutpoint-transitions:

and for every transition t, a duplicate t is considered.

We consider subproblems for each of the 1 SCC(s) of the program graph.

Here we consider the SCC { f142_0_fib_InvokeMethod, f31_0_fib_NE }.

We remove transitions 2, 6, 4, 3 using the following ranking functions, which are bounded by 0.

f31_0_fib_NE:	2⋅x1
f142_0_fib_InvokeMethod:	−1 + 2⋅x1

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

version: AProVE Commit ID: unknown
strategy: Statistics for single proof: 100.00 % (5 real / 0 unknown / 0 assumptions / 5 total proof steps)