  We consider the model of hard dimers coupled to two-dimensional Causal
Dynamical Triangulations (CDT) with all dimer types present and solve it
exactly subject to a single restriction. Depending on the dimer weights there
are, in addition to the usual gravity phase of CDT, two tri-critical and two
dense dimer phases. We establish the properties of these phases, computing
their cylinder and disk amplitudes, and their scaling limits.
