Commutation, transformation, and termination

In this paper we study the use of commutation properties for proving termination of rewrite systems. Commutation properties may be used to prove termination of a combined system R∪S by proving termination of R and S separately. We present termination methods for ordinary and for equational rewrite systems. Commutation is also important for transformation techniques. We outline the application of transforms—mappings from terms to terms—to termination in general, and describe various specific transforms, including transforms for associative-commutative rewrite systems.