Abstract

this paper we introduce the notion of a monotone algebra as the natural concept for semantical methods. Though we focus on `pure' TRS, the ideas are easily extended to conditional TRS, typed TRS and TRS modulo equations. We propose a classification of types of termination based upon the types of orderings of the underlying monotone algebras. Some remarks and examples are not claimed to be new but are included for completeness and for illustrating the setting of monotone algebras.

Citations

431	Associative-commutative rewriting - Dershowitz, Hsiang, et al. - 1983
359	Explicit Substitutions - Abadi, Cardelli, et al. - 1992
172	Proving termination with multiset orderings - Dershowitz, Manna - 1979
79	Termination of rewriting systems by polynomial interpretations and its implementation - Cherifa, Lescanne
20	Simulation of Turing machines by a regular rewrite rule - Dauchet - 1992
8	Strong normalization of substitutions - Curien, Hardin, et al. - 1992