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Abstract: We study the problems involved in the recursive definition of (quasi) orders on terms, focussing on the question of establishing well-definedness, and the properties required for partial and quasi-orders: irreflexivity and transitivity, and reflexivity and transitivity, respectively. These properties are in general difficult to establish and this has in many cases come down in the literature as folklore results. Here we present a general scheme that allows us to show that relations are... (Update)
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2.0: Recursively Defined (Quasi) Orders on Terms - Ferreira (1997) (Correct)
0.4: Combinations of Simplifying Conditional Term Rewriting Systems - Ohlebusch (1992) (Correct)
0.3: Simple Termination of Rewrite Systems - Middeldorp, Zantema (1997) (Correct)
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BibTeX entry: (Update)
@misc{ ferreira-recursively,
author = "M.C.F. Ferreira",
title = "Recursively Defined (Quasi) Orders on Terms",
url = "citeseer.comp.nus.edu.sg/117840.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
474 Term rewriting systems - Klop - 1992
384 Simple words problems in Universal Algebras (context) - Knuth, Bendix - 1970
214 Orderings for term rewriting systems (context) - Dershowitz - 1979
214 Orderings for term rewriting systems (context) - Dershowitz - 1982
172 Journal of Symbolic Computation (context) - Dershowitz - 1987
151 Proving termination with multiset orderings (context) - Dershowitz, Manna - 1979
59 On termination of the direct sum of term rewriting systems (context) - Rusinowitch - 1987
50 Simplification Orderings: History of results (context) - Steinbach - 1995
49 Cambridge Mathematical Textbooks (context) - Davey, Priestley - 1991
44 Equational reasoning and term rewriting systems - Plaisted - 1993
38 On well-quasi ordering finite trees (context) - Nash-Williams - 1963
31 What's so special about Kruskal's theorem and the ordinal \G.. (context) - Gallier - 1991
20 Attempts for generalizing the recursive path orderings (context) - Kamin, L'evy - 1980
19 the recursive decomposition ordering with lexicographical st.. (context) - Lescanne - 1990
19 Automating the Knuth Bendix ordering (context) - Dick, Kalmus et al. - 1990
19 A recursively defined ordering for proving termination of te.. (context) - Plaisted - 1978
18 Extensions and comparison of simplification orderings (context) - Steinbach - 1989
15 A path ordering for proving termination of term rewriting sy.. (context) - Kapur, Narendran et al. - 1985
11 Termination of Term Rewriting - Well-foundedness (context) - Ferreira - 1995
10 Well-foundedness of term orderings - Ferreira, Zantema - 1994
9 American Mathematical Society (context) - Kruskal - 1960
7 Well-founded orderings for proving termination of systems of.. (context) - Plaisted - 1978
7 Comparison and Automatic Generation of Simplification Orderi.. (context) - Steinbach, of - 1994
4 Termination of term rewriting - Zantema - 1997
4 Recursive decomposition ordering (context) - Jouannaud, Lescanne et al. - 1982
2 Recursively defined term orders (context) - Ferreira - 1996
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