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Summary: Modular Termination of Basic Narrowing
Mar´ia Alpuente, Santiago Escobar, and Jos´e Iborra
Universidad Polit´ecnica de Valencia, Spain.
{alpuente,sescobar,jiborra}@dsic.upv.es
Abstract. Basic narrowing is a restricted form of narrowing which con-
strains narrowing steps to a set of non-blocked (or basic) positions. Basic
narrowing has a number of important applications including equational
unification in canonical theories. Another application is analyzing ter-
mination of narrowing by checking the termination of basic narrowing,
as done in pioneering work by Hullot. In this work, we study the modu-
larity of termination of basic narrowing in hierarchical combinations of
TRSs, including a generalization of proper extensions with shared sub-
system. This provides new algorithmic criteria to prove termination of
basic narrowing.
1 Introduction
Narrowing [11] is a generalization of term rewriting that allows free variables
in terms (as in logic programming) and replaces pattern matching with syntac-
tic unification. Narrowing was originally introduced as a mechanism for solving
equational unification problems [15], hence termination results for narrowing
have been traditionally achieved as a byproduct of addressing the decidabil-
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