  Let F_2 be a free group of rank 2. We prove that there is an algorithm that
decides whether or not, for given two elements u, v of F_2, u and v are
translation equivalent in F_2, that is, whether or not u and v have the
property that the cyclic length of phi(u) equals the cyclic length of phi(v)
for every automorphism phi of F_2. This gives an affirmative solution to
problem F38a in the online version (http://www.grouptheory.info) of [1] for the
case of F_2.
