  For a surface $S$ of sufficient complexity, Dehn twists act elliptically on
the arc, curve, and relative arc graph of $S$. We show that composing a Dehn
twist with a shift map results in a loxodromic isometry of the relative arc
graph $\mathcal{A}(S,p)$ for any surface $S$ with an isolated puncture $p$
admitting a shift map. Therefore, shift maps are not type-preserving.
