@ARTICLE{HanusLucasMiddeldorp98IPL,
author = "Hanus, M. and Lucas, S. and Middeldorp, A.",
title = "Strongly sequential and inductively sequential term rewriting systems",
year = "1998",
journal = "Information Processing Letters",
volume = "67",
number = "1",
pages = "1--8",
abstract = {
The concept of definitional tree by Antoy serves to introduce
control information into the bare set of rules of a constructor-based
term rewriting system (TRS). TRSs whose rules can be
arranged into a definitional tree are called <EM>inductively sequential</EM>.
By relying on the existence of such a definitional tree, an
optimal rewriting strategy, the <EM>outermost-needed strategy</EM> is
defined. Optimality was proved w.r.t. the Huet and L&eacute;evy's
theory of neededness. In this paper, we prove that
strongly sequential and inductively sequential constructor-based TRSs
coincide.  We also show that outermost-needed rewriting only reduces strongly
needed redexes. 
} }