Full-commutation and fair-termination in equational (and combined) term-rewriting systems
In [PF-85] the concepts of fair derivations and fair-termination in term-rewriting systems were introduced and studied. In this paper, we define the notion of fairness in equational term-rewriting systems, where a derivation step is a composition of the equality generated by a (finite) set of equations with one step rewriting using a set of rules. A natural generalization of E-termination (termination of equational term-rewriting systems), namely E-fair-termination, is presented. We show that fair-termination and E-fair-termination are the same whenever the underlying rewriting relation is E-fully-commuting, a property inspired by Jouannaud and Munoz' E-commutation property. We obtain analogous results for combined term-rewriting systems.
KeywordsFree Algebra Full Derivation Fair Termination Infinite Chain Derivation Step
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