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Prove procedure to compute Fibinocci(n) where F0 = 0, F1 = 1, Fn = Fn-2 +...

Prove procedure to compute Fibinocci(n) where F0 = 0, F1 = 1, Fn = Fn-2 + Fn-1. Prove by establishing and proving loop invariant then using induction to prove soundness and termination.

1: Procedure Fib(n)

2: i←0,j←1,k←1,m←n

3: while m ≥ 3 do

4:   m←m−3

5:   i←j+k

6:   j←i+k

7:   k←i+j

8: if m = 0 then

9: return i

10: else if m = 1 then

11: return j

12: else

13.   return k

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