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Generating Polynomial Orderings for Termination Proofs
 In Proc. 6th RTA, LNCS 914
, 1995
"... Most systems for the automation of termination proofs using polynomial orderings are only semiautomatic, i.e. the "right" polynomial ordering has to be given by the user. We show that a variation of Lankford's partial derivative technique leads to an easier and slightly more powerful ..."
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Cited by 46 (22 self)
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Most systems for the automation of termination proofs using polynomial orderings are only semiautomatic, i.e. the "right" polynomial ordering has to be given by the user. We show that a variation of Lankford's partial derivative technique leads to an easier and slightly more powerful method than most other semiautomatic approaches. Based on this technique we develop a method for the automated synthesis of a suited polynomial ordering.
Termination of Nested and Mutually Recursive Algorithms
, 1996
"... This paper deals with automated termination analysis for functional programs. Previously developed methods for automated termination proofs of functional programs often fail for algorithms with nested recursion and they cannot handle algorithms with mutual recursion. We show that termination proofs ..."
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Cited by 44 (9 self)
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This paper deals with automated termination analysis for functional programs. Previously developed methods for automated termination proofs of functional programs often fail for algorithms with nested recursion and they cannot handle algorithms with mutual recursion. We show that termination proofs for nested and mutually recursive algorithms can be performed without having to prove the correctness of the algorithms simultaneously. Using this result, nested and mutually recursive algorithms do no longer constitute a special problem and the existing methods for automated termination analysis can be extended to nested and mutual recursion in a straightforward way. We give some examples of algorithms whose termination can now be proved automatically (including wellknown challenge problems such as McCarthy's f_91 function).
Termination analysis for functional programs using term orderings
 IN PROCEEDINGS OF THE SECOND INTERNATIONAL STATIC ANALYSIS SYMPOSIUM, LNCS 983
, 1995
"... To prove the termination of a functional program there has to be a wellfounded ordering such that the arguments in each recursive call are smaller than the corresponding inputs. In this paper we present a procedure for automated termination proofs of functional programs. In contrast to previously p ..."
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Cited by 32 (12 self)
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To prove the termination of a functional program there has to be a wellfounded ordering such that the arguments in each recursive call are smaller than the corresponding inputs. In this paper we present a procedure for automated termination proofs of functional programs. In contrast to previously presented methods a suited wellfounded ordering does not have to be fixed in advance by the user, but can be synthesized automatically. For that purpose we use approaches developed in the area of term rewriting systems for the automated generation of suited wellfounded term orderings. But unfortunately term orderings cannot be directly used for termination proofs of functional programs which call other algorithms in the arguments of their recursive calls. The reason is that while for the termination of term rewriting systems orderings between terms are needed, for functional programs we need orderings between objects of algebraic data types. Our method solves this problem and enables term orderings to be used for termination proofs of functional programs.
Equational Termination by Semantic Labelling
, 2000
"... Semantic labelling is a powerful tool for proving termination of term rewrite systems. The usefulness of the extension to equational term rewriting described in Zantema [24] is however rather limited. In this paper we introduce a stronger version of equational semantical labelling, parameterized ..."
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Cited by 4 (1 self)
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Semantic labelling is a powerful tool for proving termination of term rewrite systems. The usefulness of the extension to equational term rewriting described in Zantema [24] is however rather limited. In this paper we introduce a stronger version of equational semantical labelling, parameterized by three choices: (1) the order on the underlying algebra (partial order vs. quasiorder), (2) the relation between the algebra and the rewrite system (model vs. quasimodel), and (3) the labelling of the function symbols appearing in the equations (forbidden vs.
Reducing ACTermination to Termination
 Proc. 23rd MFCS, LNCS 1450
, 1997
"... We present a new technique for proving ACtermination. We show that if certain conditions are met, ACtermination can be reduced to termination, i. e., termination of a TRS S modulo an ACtheory can be inferred from termination of another TRS R with no ACtheory involved. This is a new perspective a ..."
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Cited by 4 (0 self)
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We present a new technique for proving ACtermination. We show that if certain conditions are met, ACtermination can be reduced to termination, i. e., termination of a TRS S modulo an ACtheory can be inferred from termination of another TRS R with no ACtheory involved. This is a new perspective and opens new possibilities to deal with ACtermination. 1 Introduction Termination of term rewriting systems (TRS's) is crucial for the use of rewriting in proofs and computations, and many theories have been developed in this field, especially for the case where function symbols do not obey any particular law or property. However, many interesting and useful systems have operators which are associative and commutative (AC), and most techniques developed for proving termination of TRS's do not carry over to rewriting modulo equational theories so that the theory developed to study termination of TRS's needs to be adapted to the equational case. Along these lines, a lot of work has been done...
On the relative power of polynomials. . .
 APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
, 2006
"... ..."
A Reduction Ordering for HigherOrder Terms
, 1995
"... We investigate one of the classical problems of the theory of term rewriting, namely termination. We present an ordering for comparing higherorder terms that can be utilized for testing termination and decreasingness of higherorder conditional term rewriting systems. The ordering relies on a f ..."
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We investigate one of the classical problems of the theory of term rewriting, namely termination. We present an ordering for comparing higherorder terms that can be utilized for testing termination and decreasingness of higherorder conditional term rewriting systems. The ordering relies on a firstorder interpretation of higherorder terms and a suitable extension of the RPO.
Recursively Defined (Quasi) Orders on Terms
, 1997
"... We study the problems involved in the recursive definition of (quasi) orders on terms, focussing on the question of establishing welldefinedness, and the properties required for partial and quasiorders: irreflexivity and transitivity, and reflexivity and transitivity, respectively. These propertie ..."
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We study the problems involved in the recursive definition of (quasi) orders on terms, focussing on the question of establishing welldefinedness, and the properties required for partial and quasiorders: 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 welldefined and represent partial or quasiorders. Known path orders as semantic, recursive and lexicographic path order as well as KnuthBendix order fit into the scheme. Additionally we will also discuss how to obtain other properties commonly found in term orders (amongst which wellfoundedness) as an integrated feature of the scheme. Keywords: Path Orders, term rewriting, semantic path order , recursive path order , lexicographic path order, KnuthBendix order . Contents 1 Introduction 2 2 Prelimi...