Lazy Rewriting and Context-Sensitive Rewriting

Lazy rewriting (LR) is intended to improve the termination behavior of TRSs. This is attempted by restricting reductions for selected arguments of functions. Similarly, context-sensitive rewriting (CSR) forbids any reduction on those arguments. We show that, under certain conditions, LR and CSR coincide. On the basis of this result, we also describe a transformation which permits proving termination of LR as termination of CSR for the transformed system. Since there is a number of diierent techniques for proving termination of CSR, this provides a ((rst) formal framework for proving termination of lazy rewriting.