  We show that for each element $g$ of a Garside group, there exists a positive
integer $m$ such that $g^m$ is conjugate to a periodically geodesic element
$h$, an element with $|h^n|_\D=|n|\cdot|h|_\D$ for all integers $n$, where
$|g|_\D$ denotes the shortest word length of $g$ with respect to the set $\D$
of simple elements. We also show that there is a finite-time algorithm that
computes, given an element of a Garside group, its stable super summit set.
