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
Prove procedure to compute Fibinocci(n) where F0 = 0, F1 = 1, Fn = Fn-2 +...
Let f0, f1, f2, . . . be the Fibonacci sequence defined as f0 = 0, f1 = 1, and for every k > 1, fk = fk-1 + fk-2. Use induction to prove that for every n ? 0, fn ? 2n-1 . Base case should start at f0 and f1. For the inductive case of fk+1 , you’ll need to use the inductive hypothesis for both k and k ? 1.
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