  Let (L;C) be the (up to isomorphism unique) countable homogeneous structure
carrying a binary branching C-relation. We study the reducts of (L;C), i.e.,
the structures with domain L that are first-order definable in (L;C). We show
that up to existential interdefinability, there are finitely many such reducts.
This implies that there are finitely many reducts up to first-order
interdefinability, thus confirming a conjecture of Simon Thomas for the special
case of (L;C). We also study the endomorphism monoids of such reducts and show
that they fall into four categories.
