  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 $\FN$ relative to local
Dehn twist automorphisms is either an honest Dehn twist automorphism, or else
has quadratic growth.
