There is an arxiv paper of Martin Lustig giving a positive answer to the conjugacy problem for the outer automorphism group of the free group $F_n$. On the other hand, there seems not to be a publication in a journal about this, but several related publications. Is it possible to say which are the "best" results in this direction, with a complete proof ? (For example, a result by Sela if the outer automorphism group is finite, etc.).

There is a paper of Martin Lustig on his webpage giving a positive answer to the conjugacy problem for the outer automorphism group of the free group $F_n$. On the other hand, there seems not to be a publication in a journal about this, but several related publications. Is it possible to say which are the "best" results in this direction, with a complete proof ? (For example, a result by Sela if the outer automorphism group is finite, etc.).