  Every rotationless outer automorphism of a finite rank free group is
represented by a particularly useful relative train track map called a CT. The
main result of this paper is that the constructions of CTs can be made
algorithmic. A key step in our argument is proving that it is algorithmic to
check if an inclusion of one invariant free factor system in another is
reduced. Several applications are included, as well as algorithmic
constructions for relative train track maps in the general case.
