Every 7r-calculus expression can be translated to a term in "nannal form ll built from +, input and output prefix, match, and inaction. Many difficulties of the 7r-calculus are easier to understand and address at this simpler normal form level. We introduce a theory called Basic Conditional Process Algebra (BCPA), which we use to study these issues. BCPA is BPA extended with a conditional ... [Show full abstract] construct over Boolean expressions which can contain free variables. In this article, we consider a restricted setting without bound variables, since it already presents many non-trivial problems. Note: Supported by NWO, the Netherlands Organization for Scientific Re-search, project 612-16-433, HOOP: Higher-Order and Object-Oriented Processes.