Well Rewrite Orderings and Well Quasi-Orderings

Abstract This paper studies well (quasi) orderings described as rewrite orderings and proposes a new family of well (quasi) orderings that extends the embedding or divisibility order of G. Higman. For instance, the well (quasi) orderings proposed in this paper may contain pairs of the form f ( f ( χ )) > f ( g ( f ( χ ))). Conditions called basicity and projectivity under which the transitive closure of a well-founded rewrite relation is a well-quasi-ordering are given. A tool based on narrowing is proposed for proving projectivity.

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