Prove correctness of recursive algorithm

Question

I have this java function:

public int foo(ArrayList l, int n)
{
  if(n <= 1)
    return l.get(0);

  if(l.get(0) < l.get(1))
    l.remove(1);
  else
    l.remove(0);

  foo(l, n-1);
}

So I figure to show that the algorithm is correct I would use an induction proof. However what I am not so sure about is how to go about doing the proof. Will I fist need to derive some sort of mathematical formula for this function and prove that?