  We construct two practical algorithms for twisted conjugacy classes of
polycyclic-by-finite groups. The first algorithm determines whether two
elements of a group are twisted conjugate for two given endomorphisms, under
the condition that the Reidemeister coincidence number of these endomorphisms
is finite. The second algorithm determines representatives of the Reidemeister
coincidence classes of two endomorphisms if their Reidemeister coincidence
number is finite, or returns "fail" if the Reidemeister coincidence number is
infinite.
