On Implementing Relative Complexity We recall the recent approach from (Zankl and Korp, 2010) that allows to combine different criteria to prove polynomial upper bounds on the derivational complexity of rewrite systems. In contrast to the question of termination, which is a plain yes/no problem, the question of the (derivational) complexity of a rewrite system is more fine-grained. Hence a complexity prover should not stop as soon as it managed to obtain an upper bound but try to tighten this bound. We show that the mentioned approach allows to achieve this goal.