  We consider a coupled bulk--surface Allen--Cahn system affixed with a
Robin-type boundary condition between the bulk and surface variables. This
system can also be viewed as a relaxation to a bulk--surface Allen--Cahn system
with non-trivial transmission conditions. Assuming that the nonlinearities are
real analytic, we prove the convergence of every global strong solution to a
single equilibrium as time tends to infinity. Furthermore, we obtain an
estimate on the rate of convergence. The proof relies on an extended
Lojasiewicz--Simon type inequality for the bulk--surface coupled system.
Compared with previous works, new difficulties arise as in our system the
surface variable is no longer the trace of the bulk variable, but now they are
coupled through a nonlinear Robin boundary condition.
