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You did not say that. Rather, you asked if "the complexity of the inner loop is O(2^n)". It isn't, as you yourself have now concluded. What you probably have in mind is the idea that the value of...

If that were true, then this C++ program:

#include <iostream>

int main()
{
int n = 5;
for (int count = 1; count < n; count++)
{
int count2 = 1;

Not quite: notice that count2 is doubled, not incremented, on each iteration of the inner loop. As such, what is the complexity of the inner loop?