Example: recursive implementation of the product between two integers

We exploit the following recursive definition of the product between two non-negative integers:

product(x, y) = $$\cases{ 0, & if \(y=0\)\cr \mathit{sum}(x, \mathit{product}(x, y-1)), & if \(y>0\)}$$

Implementation (we assume that the method sum() is defined in the same class):

public static int product(int x, int y) {
  if (y == 0)
    return 0;
  else
    return sum(x, product(x, y-1));
}