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InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schem ..."
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Cited by 779 (24 self)
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In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a more general cler of inductive types, cals, "strictly positive", and to ease the strong normalgAg9Ik proof of theresulGGg system. Thisresul provides a computation model for the combination of anal"DAfGI specification language based on abstract data types and of astrongl typed functional language with strictly positive inductive types.
ORDERINGS FOR TERMREWRITING SYSTEMS
, 1982
"... Methods of proving that a termrewriting system terminates are presented. They are based on the intuitive notion of 'simplification orderings'. orderings in which any term that is syntactically simpler than another is smaller than the other. M a consequence of Kruskal's Tree Theorem ..."
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Cited by 272 (24 self)
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Methods of proving that a termrewriting system terminates are presented. They are based on the intuitive notion of 'simplification orderings'. orderings in which any term that is syntactically simpler than another is smaller than the other. M a consequence of Kruskal's Tree Theorem, any nonterminating system must be selfembedding in the sense that it allows for the derivation of some term from a simpler one; thus termination is guaranteed jf every rule in the system as a reduction in some simplification ordering. Most 01 the orderings that have been used for proving tennination are indeed simplication orderings; using this notion often allows for much easier proofs. A particularly useful class of simplification orderings, the 'recursive path orderings', is defined. Examples of the use of simplification orderings in termination proofs are given.
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
Natural termination
 Theoretical Computer Science
"... Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1 ..."
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Cited by 84 (11 self)
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Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1
lambdacalculi with explicit substitutions and composition which preserve beta strong normalization (Extended Abstract)
, 1996
"... ) Maria C. F. Ferreira 1 and Delia Kesner 2 and Laurence Puel 2 1 Dep. de Inform'atica, Fac. de Ciencias e Tecnologia, Univ. Nova de Lisboa, Quinta da Torre, 2825 Monte de Caparica, Portugal, cf@fct.unl.pt. 2 CNRS & Lab. de Rech. en Informatique, Bat 490, Univ. de ParisSud, 91405 O ..."
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Cited by 28 (4 self)
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) Maria C. F. Ferreira 1 and Delia Kesner 2 and Laurence Puel 2 1 Dep. de Inform'atica, Fac. de Ciencias e Tecnologia, Univ. Nova de Lisboa, Quinta da Torre, 2825 Monte de Caparica, Portugal, cf@fct.unl.pt. 2 CNRS & Lab. de Rech. en Informatique, Bat 490, Univ. de ParisSud, 91405 Orsay Cedex, France, fkesner,puelg@lri.fr. Abstract. We study preservation of fistrong normalization by d and dn , two confluent calculi with explicit substitutions defined in [10]; the particularity of these calculi is that both have a composition operator for substitutions. We develop an abstract simulation technique allowing to reduce preservation of fistrong normalization of one calculus to that of another one, and apply said technique to reduce preservation of fistrong normalization of d and dn to that of f , another calculus having no composition operator. Then, preservation of fistrong normalization of f is shown using the same technique as in [2]. As a consequence, d and dn become the fir...
The SizeChange Principle and Dependency Pairs for Termination of Term Rewriting
 APPEARED IN APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING, 16(4):229270, 2005.
, 2005
"... In [24], a new sizechange principle was proposed to verify termination of functional programs automatically. We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs). Moreover, we compare this approach with existing techniques for ter ..."
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Cited by 27 (7 self)
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In [24], a new sizechange principle was proposed to verify termination of functional programs automatically. We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs). Moreover, we compare this approach with existing techniques for termination analysis of TRSs (such as recursive path orders or dependency pairs). It turns out that the sizechange principle on its own fails for many examples that can be handled by standard techniques for rewriting, but there are also TRSs where it succeeds whereas existing rewriting techniques fail. Moreover, we also compare the complexity of the respective methods. To this end, we develop the first complexity analysis for the dependency pair approach. While the sizechange principle is PSPACEcomplete, we prove that the dependency pair approach (in combination with classical path orders) is only NPcomplete. To benefit from their respective advantages, we show how to combine the sizechange principle with classical orders and with dependency pairs. In this way, we obtain a new approach for automated termination proofs of TRSs which is more powerful than previous approaches. We also show that the combination with dependency pairs does not increase the complexity of the sizechange principle, i.e., the combined approach is still PSPACEcomplete.
33 Examples of Termination
 In Proc. French Spring School of Theoretical Computer Science, LNCS 909
, 1995
"... . A graded sequence of examplespresented in a uniform frameworkspotlights stages in the development of methods for proving termination of rewrite systems. Let T be the set of all terms over some vocabulary.Arewrite system over T is a ##nite or in#nite# set of rules, eachoftheforml ! r, where ..."
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Cited by 23 (0 self)
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. A graded sequence of examplespresented in a uniform frameworkspotlights stages in the development of methods for proving termination of rewrite systems. Let T be the set of all terms over some vocabulary.Arewrite system over T is a ##nite or in#nite# set of rules, eachoftheforml ! r, where l and r are terms containing variables ranging over T . A rule l ! r applies to a term t in T if a subterm s of t matches the lefthand side l with some substitution # of terms in T for variables appearing in l. The rule is applied by replacing the redex s in t with the corresponding righthand side r# of the rule, to which the same substitution # of terms for variables has been applied. We write t !u to indicate that the term t in T rewrites in this waytothetermu in T by a single application of some rule. Note that more than one rule can apply to t and rules can apply at more than one subterm s. Rewrite systems have long been used as decision procedures for validity in equational theories,...
The termination competition
 In Proc. RTA ’07, LNCS 4533
, 2007
"... Abstract. Since 2004, a Termination Competition is organized every year. This competition boosted a lot the development of automatic termination tools, but also the design of new techniques for proving termination. We present the background, results, and conclusions of the three first editions, and ..."
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Abstract. Since 2004, a Termination Competition is organized every year. This competition boosted a lot the development of automatic termination tools, but also the design of new techniques for proving termination. We present the background, results, and conclusions of the three first editions, and discuss perspectives and challenges for the future. 1 Motivation and