Termination of Term Rewriting

Abstract

Given a TRS (E, R), how to prove or disprove that it is terminating? It is well-known ([35]) that this question is undecidable for finite TRSs. This means that it is impossible to develop a method that decides whether a given finite TRS is terminating or not. However, we may expect that there are methods that can be used to establish termination for many TRSs occurring in practical situations. Indeed such methods have been developed, and in this chapter an overview of them is given.