Looks like a home work problem to me. And it's void of any Perl content.

As for your question, technically, the question is incomplete. You aren't telling us where n is going to. I'll be so bold to assume n is going towards infinity.

Since it's a homework problem, which has nothing to do with Perl, I'm not going to give you a complete answer. Let me just say that both functions are in O(n²log log n). But that bound is tight for one of the functions, and not tight for the other. I'll leave it as an exercise to figure out which function can be estimated more tightly.