Postprojective components of quiver algebras

Question

Let $A=kQ/I$ be a quiver algebra with acyclic quiver $Q$. An indecomposable module $M$ is called postprojective in case $M \cong \tau^{-1}(P)$ for an indecomposble projective module $P$. A component of the Auslander-Reiten quiver of $A$ is called postprojective in case every module in the component is postprojective. Assume $A$ has at least one postprojective component.

Question 1: Is there a (quick) way to obtain the number of postprojective components of such an algebra?

Question 2: Is there an easy way to see whether any indecomposable projective module is postprojective?

Im especially interested wheter such a thing is possible using the GAP-package QPA.

Answer 1

One place to start is to look at the paper "An algorithm for finding all preprojective components of the Auslander-Reiten quiver" by Peter Draexler and Klara Kögerler.