Bergstra, Bethke and Ponse proposed an axiomatization for Basic Proces
s Algebra extended with (binary) iteration. In this paper, we prove th
at this axiomatization is complete with respect to strong bisimulation
equivalence. To obtain this result, we will set up a term rewriting s
ystem, based on the axioms, and prove that this term rewriting system
is terminating, and that bisimilar normal forms are syntactically equa
l module commutativity and associativity of the +.