  Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and
Wehrman in 2009 as a framework to reason about concurrent programs. We prove
that the axioms for CKA with bounded parallelism are complete for the semantics
proposed in the original paper; consequently, these semantics are the free
model for this fragment. This result settles a conjecture of Hoare and
collaborators. Moreover, the techniques developed along the way are reusable;
in particular, they allow us to establish pomset automata as an operational
model for CKA.
