Termination of rewriting

Termination of Priority Rewriting

Introducing priorities in rewriting increases the expressive power of rules and helps to limit computations. Priority rewriting is used in rule-based programming as well as in functional programming. Termination of priority rewriting is then important to guarantee that programs give a result. We describe an inductive proof method for termination of priority rewriting, relying on an explicit ind...

Termination of Term Rewriting

Termination of Cycle Rewriting

String rewriting can not only be applied on strings, but also on cycles and even on general graphs. In this paper we investigate termination of string rewriting applied on cycles, shortly denoted as cycle rewriting, which is a strictly stronger requirement than termination on strings. Most techniques for proving termination of string rewriting fail for proving termination of cycle rewriting, bu...

Termination of Lazy Rewriting Revisited

Lazy rewriting is a proper restriction of term rewriting that dynamically restricts the reduction of certain arguments of functions in order to obtain termination. In contrast to context-sensitive rewriting, reductions at such argument positions are not completely forbidden but delayed. Based on the observation that the only existing (non-trivial) approach to prove termination of such lazy rewr...

Termination of Integer Term Rewriting

When using rewrite techniques for termination analysis of programs, a main problem are predefined data types like integers. We extend term rewriting by built-in integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically.