  We say that a reversible boolean function on n bits has alternation depth d
if it can be written as the sequential composition of d reversible boolean
functions, each of which acts only on the top n-1 bits or on the bottom n-1
bits. Moreover, if the functions on n-1 bits are even, we speak of even
alternation depth. We show that every even reversible boolean function of n >=
4 bits has alternation depth at most 9 and even alternation depth at most 13.
