  Recently, we have introduced and modified graph-decomposition theorems based
on a graph product motivated by applications in the context of synchronising
periodic real-time processes. This vertex-removing synchronised product (VRSP)
is based on modifications of the well-known Cartesian product and is closely
related to the synchronised product due to W\"ohrle and Thomas. Here, we
introduce a new graph-decomposition theorem based on the VRSP that decomposes
an edge-labelled acyclic n-partite multigraph where all labels are the same.
