On the derivational complexity of Kachinuki orderings

ABSTRACT. For string rewriting systems compatible with the standard Kachinuki ordering it is known that their derivational complexity is primitive recursively bounded. However, in case the definition of Kachinuki orderings comprises a possibly different lexicographic status for different letters, the standard upper bound proof method by monotone interpretations fails, and primitive recursive complexity bounds are an open problem, to the best of our knowledge. In this talk, such an upper bound result is shown by examining worst case rewriting strategies.