Consider the following algorithm.

Input: Integers a > 0, and b 0

Output: ^{(3^b)}

BigExponent(a, b)

result <- a // line 1

for i <- 1 to b do // line 2

result<- result * result * result // line 3

return result // line 4

Prove by induction on i that after the ith iteration of the for loop (lines 2 and 3), where the 1st iteration is the iteration when i = 1, the variable result contains the value (3). (Note that once we have proved this statement, we can say that the for loop exits after the iteration when i = b, and so result contains (3), which is returned in line 4.)