  We prove that every strongly commuting pair of CP_0-semigroups has a minimal
E_0-dilation. This is achieved in two major steps, interesting in themselves:
1: we show that a strongly commuting pair of CP_0-semigroups can be represented
via a two parameter product system representation; 2: we prove that every fully
coisometric product system representation has a fully coisometric, isometric
dilation. In particular, we obtain that every commuting pair of CP_0-semigroups
on B(H), H finite dimensional, has an E_0-dilation.
