Term rewriting is a conceptually simple but powerful
abstract model of computation that underlies much of declarative
programming. In order to assess the complexity of a (terminating)
rewrite system it is natural to look at the maximal length of
derivation sequences. The "runtime complexity function" relates the
length of the longest derivation sequence to the size of the arguments
of the initial term, where the arguments are supposed to be in normal
form.
In this talk I will present a variant of the dependency pair method
for analysing runtime complexities of term rewrite systems
automatically. This technique, called "weak dependency pair method"
is easy to implement, but significantly extends the analytic power of
existing methods. In particular my talk will focus on very recent
extension of the method that suitably adapts "context-sensitive
rewriting" for the area of complexity of rewriting.