A Bound for Higher Degree Automorphisms of $F_n$

The Whitehead Model of free groups can be used to measure the complexity, or degree, of automorphisms of free groups. The bound for the degree of the $f\circ g$ for deg$(f)=$ deg($g)=0$ had previously been discovered. We extend this result to the case where at least one of our automorphisms has degree 0.