  A famous result by Drozd says that a finite-dimensional
representation-infinite algebra is of either tame or wild representation type.
But one has to make assumption on the ground field. The Gabriel-Roiter measure
might be an alternative approach to extend these concepts of tame and wild to
arbitrary artin algebras. In particular, the infiniteness of the number of GR
segments, i.e. sequences of Gabriel-Roiter measures which are closed under
direct predecessors and successors, might relate to the wildness of artin
algebras. As the first step, we are going to study the wild quiver with three
vertices, labeled by $1$,$2$ and $3$, and one arrow from $1$ to $2$ and two
arrows from $2$ to $3$. The Gabriel-Roiter submodules of the indecomposable
preprojective modules and quasi-simple modules $\tau^{-i}M$, $i\geq 0$ are
described, where $M$ is a Kronecker module and $\tau=DTr$ is the
Auslander-Reiten translation. Based on these calculations, the existence of
infinitely many GR segments will be shown. Moreover, it will be proved that
there are infinitely many Gabriel-Roiter measures admitting no direct
predecessors.
