  Rewriting logic and its implementation Maude are a natural and expressive
framework for the specification of concurrent systems and logics. Its
nondeterministic local transformations are described by rewriting rules, which
can be controlled at a higher level using a builtin strategy language added to
Maude~3. This specification resource would not be of much interest without
tools to analyze their models, so in a previous work, we extended the Maude LTL
model checker to verify strategy-controlled systems. In this paper, CTL* and
$\mu$-calculus are added to the repertoire of supported logics, after
discussing which adaptations are needed for branching-time properties. The new
extension relies on some external model checkers that are exposed the Maude
models through general and efficient connections, profitable for future
extensions and further applications. The performance of these model checkers is
compared.
