  Let $\Lambda$ be an Artin algebra. A GR segment of $\Lambda$ is a sequence of
GR measures which is closed under direct successors and direct predecessors.
The number of the GR segments was conjectured to relate to the representation
type of $\Lambda$. In this paper, let $k$ be an algebraically closed field and
$\Lambda$ be a finite-dimensional hereditary $k$-algebra. We show that
$\Lambda$ admits infinitely many GR segments if and only if $\Lambda$ is of
wild representation type. Thus the finiteness of the number of the GR segments
might be an alternative characterization of the tameness of finite dimensional
algebras over algebraically closed fields. Therefore, this might give a
possibility to generalize Drozd's tameness and wildness to arbitrary Artin
algebras.
