In this paper we work over linearly ordered data domains equipped with finitely many unary predicates and constants. We consider nondeterministic automata processing words and storing finitely many variables ranging over the domain. During a transition, these automata can compare the data values of the current configuration with those of the previous configuration using the linear order, the unary predicates and the constants. We show that emptiness for such automata is decidable, both over finite and infinite words, under reasonable computability assumptions on the linear order. Finally, we show how our automata model can be used for verifying properties of workflow specifications in the presence of an underlying database.