  In this paper we consider a general system of activities that can, but do not
have to, occur. This system is governed by a set of two types of constraints:
precedence and response. A precedence constraint dictates that an activity can
only occur if it has been preceded by some other specified activity. Response
constraints are similarly defined. An execution of the system is a listing of
activities in the order they occur and which satisfies all constraints. Such
systems naturally arise in areas of theoretical computer science and decision
science. An outcome of the freedom with which activities can occur is that
there are many different possible executions, and gaining a combinatorial
insight into these is a non-trivial problem.
  We characterize all of the ways in which such a system can be executed. Our
approach uses order theory to provide a classification in terms of the linear
extensions of posets constructed from the constraint sets. This
characterization is essential in calculating the stakeholder utility metrics
that have been developed by the first author that allow for quantitative
comparisons of such systems/processes. It also allows for a better
understanding of the theoretical backbone to these processes and their
deconstruction as a shuffle product of smaller systems.
