For adaptive methoids resorting to the bulk chasing or Dörfler marking strategy, the proof of optimal algebraic convergence rates relies on a threshold condition for the marking parameter. It is, however, an open quastion whether or not this condition is necessary in general.
We present a (non-PDE) example fitting into the common abstract convergence adaptivity framework for finte elements with Dörfler strategy (axioms of adaptivity), which allows for convergence with exponential rates. However, for marking parameters violating the threshold condition the algebraic rate can be arbitrarily small.