  We give an algorithm which computes a presentation for a subgroup, denoted
$\AM_{g,1,p}$, of the automorphism group of a free group. It is known that
$\AM_{g,1,p}$ is isomorphic to the mapping-class group of an orientable
genus-$g$ surface with one boundary component and $p$ punctures. We define a
variation of Auter space.
