Partial Dehn twists of free groups relative to local Dehn twists - a dichotomy

A criterion for quadratic or higher growth of group automorphisms is established which are represented by graph-of-groups automorphisms with certain well specified properties. As a consequence, it is derived (using results of a previous paper of the author) that every partial Dehn twist automorphism of $\text{FN}$ relative to local Dehn twist automorphisms is either an honest Dehn twist automorphism, or else has quadratic growth.