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Termination of Narrowing Revisited 1 Maria Alpuente a,, Santiago Escobar a

Summary: Termination of Narrowing Revisited 1
Mar´ia Alpuente a,, Santiago Escobar a
, Jos´e Iborra a
a Universidad Polit´ecnica de Valencia, Valencia, Spain
This paper describes several classes of term rewriting systems (TRS's) where nar-
rowing has a finite search space and is still (strongly) complete as a mechanism
for solving reachability goals. These classes do not assume confluence of the TRS.
We also ascertain purely syntactic criteria that suffice to ensure the termination
of narrowing and include several subclasses of popular TRS's such as right-linear
TRS's, almost orthogonal TRS's, topmost TRS's, and left-flat TRS's. Our results
improve and/or generalize previous criteria in the literature regarding narrowing
1 Introduction
Narrowing is a generalization of term rewriting that allows free variables in
terms (as in logic programming) and replaces pattern matching with syntactic
unification in order to (non­deterministically) reduce these terms. Narrowing
was originally introduced as a mechanism for solving equational unification
problems (Fay, 1979) and then generalized to solve the more general problem
of symbolic reachability (Meseguer and Thati, 2007). The narrowing mecha-


Source: Alpuente, María - Departamento de Sistemas Informáticos y Computación, Universitat Politècnica de València


Collections: Computer Technologies and Information Sciences