  We investigate a graphical representation of session invocation
interdependency in order to prove progress for the pi-calculus with sessions
under the usual session typing discipline. We show that those processes whose
associated dependency graph is acyclic can be brought to reduce. We call such
processes transparent processes. Additionally, we prove that for well-typed
processes where services contain no free names, such acyclicity is preserved by
the reduction semantics.
  Our results encompass programs (processes containing neither free nor
restricted session channels) and higher-order sessions (delegation).
Furthermore, we give examples suggesting that transparent processes constitute
a large enough class of processes with progress to have applications in modern
session-based programming languages for web services.
