  We consider expressions built up from binary relation names using the
operators union, composition, and set difference. We show that it is
undecidable to test whether a given such expression $e$ is finitely
satisfiable, i.e., whether there exist finite binary relations that can be
substituted for the relation names so that $e$ evaluates to a nonempty result.
This result already holds in restriction to expressions that mention just a
single relation name, and where the difference operator can be nested at most
once.
