  It is an open question if the threshold condition $\theta < \theta_\star$ for
the D\"orfler marking parameter is necessary to obtain optimal algebraic rates
of adaptive finite element methods. We present a (non-PDE) example fitting into
the common abstract convergence framework (axioms of adaptivity) and which is
potentially converging with exponential rates. However, for D\"orfler marking
$\theta > \theta_\star$ the algebraic converges rate can be made arbitrarily
small.
