  We define pullback and separated presentations of modules over pullback
rings, and, if the ring is a pullback of epimorphisms over a semisimple ring,
an algorithm reducing such a presentation of a module to an $R$-diagram. The
latter is the input for a classification algorithm of finitely generated
modules over a pullback ring of two Dedekind domains. As an example we show how
to obtain an $R$-diagram for homology of a chain complex of free modules over a
$p$-pullback ring.
