Given a finite poset $P$ (we can assume it is connected), the reduced incidence algebra of $P$ is the subalgebra of the incidence algebra of $P$ consisting of functions constant on isomorphic intervals.

The incidence algebra is isomorphic to the quiver algebra with quiver the Hasse poset of $P$ and the relations are such that paths of the same start and end get identified.

Question: Is it possible with the GAP-package QPA to obtain the reduced incidence algebra (as quiver and relations) of a poset in an easy way from the quiver of the incidence algebra?

Easy way could mean that one uses only functions that are already available in QPA, for example taking endomorphism rings of module or quotient algebras (and combinations). I can not think of a method how to do it but maybe I overlook something simple.