  A (fragment of a) process algebra satisfies unique parallel decomposition if
the definable behaviours admit a unique decomposition into indecomposable
parallel components. In this paper we prove that finite processes of the
pi-calculus, i.e. processes that perform no infinite executions, satisfy this
property modulo strong bisimilarity and weak bisimilarity. Our results are
obtained by an application of a general technique for establishing unique
parallel decomposition using decomposition orders.
