  Since it was realized that the Curry-Howard isomorphism can be extended to
the case of classical logic as well, several calculi have appeared as
candidates for the encodings of proofs in classical logic. One of the most
extensively studied among them is the $\lambda\mu$-calculus of Parigot. In this
paper, based on the result of Xi presented for the $\lambda$-calculus Xi, we
give an upper bound for the lengths of the reduction sequences in the
$\lambda\mu$-calculus extended with the $\rho$- and $\theta$-rules.
Surprisingly, our results show that the new terms and the new rules do not add
to the computational complexity of the calculus despite the fact that
$\mu$-abstraction is able to consume an unbounded number of arguments by virtue
of the $\mu$-rule.
