  Completeness is a desirable property of test suites. Roughly, completeness
guarantees that a non-equivalent implementation under test will always be
identified. Several approaches proposed sufficient, and sometimes also
necessary, conditions on the specification model and on the test suite in order
to guarantee completeness. Usually, these approaches impose several
restrictions on the specification and on the implementations, such as requiring
them to be reduced or complete. Further, test cases are required to be
non-blocking --- that is, they must run to completion --- on both the
specification and the implementation models. In this work we deal test cases
that can be blocking, we define a new notion that captures completeness, and we
characterize test suite completeness in this new scenario. We establish an
upper bound on the number of states of implementations beyond which no test
suite can be complete, both in the classical sense and in the new scenario with
blocking test cases.
