  We prove a new version of the classical peak-reduction theorem for
automorphisms of free groups in the setting of right-angled Artin groups. We
use this peak-reduction theorem to prove two important corollaries about the
action of the automorphism group of a right-angled Artin group $A_\Gamma$ on
the set of $k$-tuples of conjugacy classes from $A_\Gamma$: orbit membership is
decidable, and stabilizers are finitely presentable. Further, we explain
procedures for checking orbit membership and building presentations of
stabilizers. This improves on a previous result of the author's. We overcome a
technical difficulty from the previous work by considering infinite generating
sets for the automorphism groups. The method also involves a variation on the
Hermite normal form for matrices.
