  We study the IS-algorithm, a well-known linear-time algorithm for computing
the suffix array of a word. This algorithm relies on transforming the input
word $w$ into another word, called the reduced word of $w$, that will be at
least twice shorter; then, the algorithm recursively computes the suffix array
of the reduced word. In this article, we study the reduction ratio of the
IS-algorithm, i.e., the ratio between the lengths of the input word and the
word obtained after reducing $k$ times the input word. We investigate both
worst cases, in which we find precise results, and random cases, where we prove
some strong convergence phenomena. Finally, we prove that, if the input word is
a randomly chosen word of length $n$, we should not expect much more than
$\log(\log(n))$ recursive function calls.
