  We study the monoid of global invariant types modulo domination-equivalence
in the context of o-minimal theories. We reduce its computation to the problem
of proving that it is generated by classes of 1-types. We show this to hold in
Real Closed Fields, where generators of this monoid correspond to invariant
convex subrings of the monster model. Combined with arxiv:1702.06504, this
allows us to compute the domination monoid in the weakly o-minimal theory of
Real Closed Valued Fields.
