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The size-change principle and dependency pairs for termination of term rewriting

René Thiemann, Jürgen Giesl
2005 Applicable Algebra in Engineering, Communication and Computing  
We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs).  ...  To benefit from their respective advantages, we show how to combine the size-change principle with classical orders and with dependency pairs.  ...  We are grateful to the referees for many helpful suggestions and remarks.  ... 
doi:10.1007/s00200-005-0179-7 fatcat:ks2afhk7vjcsjh26awlipxt2ou

Size-Change Termination for Term Rewriting [chapter]

René Thiemann, Jürgen Giesl
2003 Lecture Notes in Computer Science  
The Size-Change Principle We assume familiarity with the basics of term rewriting (see e.g., [3] ).  ...  We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs).  ...  However, up to now the connection between this principle and existing approaches for termination proofs of term rewriting was unclear.  ... 
doi:10.1007/3-540-44881-0_19 fatcat:fyge57hmwzbmvksuz23v5p6as4

Automated Termination Proofs with AProVE [chapter]

Jürgen Giesl, René Thiemann, Peter Schneider-Kamp, Stephan Falke
2004 Lecture Notes in Computer Science  
For this system, we have developed and implemented efficient algorithms based on classical simplification orders, dependency pairs, and the size-change principle.  ...  We describe the system AProVE, an automated prover to verify (innermost) termination of term rewrite systems (TRSs).  ...  Termination Proofs with the Size-Change Principle A new size-change principle for termination of functional programs was presented in [23] and extended to TRSs in [27] .  ... 
doi:10.1007/978-3-540-25979-4_15 fatcat:kg7bso7vkjezbe4qxfmeilkmpu

VMTL–A Modular Termination Laboratory [chapter]

Felix Schernhammer, Bernhard Gramlich
2009 Lecture Notes in Computer Science  
The automated analysis of termination of term rewriting systems (TRSs) has drawn a lot of attention in the scientific community during the last decades and many different methods and approaches have been  ...  Apart from modular extensibility, VMTL focuses on analyzing the termination behaviour of conditional term rewriting systems (CTRSs).  ...  Moreover, an extension to new classes of rewrite systems and termination problems (e.g. higher-order rewrite systems and innermost/outermost or relative termination) and programming languages (e.g.  ... 
doi:10.1007/978-3-642-02348-4_20 fatcat:ythas3pszvautf6ate5saaqs6m

Termination of λΠ modulo rewriting using the size-change principle (work in progress) [article]

Frédéric Blanqui, Guillaume Genestier (DEDUCTEAM, LSV, CRI, ENS Paris Saclay)
2018 arXiv   pre-print
The Size-Change Termination principle was first introduced to study the termination of first-order functional programs.  ...  In this work, we show that it can also be used to study the termination of higher-order rewriting in a system of dependent types extending LF.  ...  The authors thank Olivier Hermant for his comments, as well as the anonymous referees.  ... 
arXiv:1812.01853v1 fatcat:gl74wuw5svco7meouuqc2shytq

Automated termination proofs for haskell by term rewriting

Jürgen Giesl, Matthias Raffelsieper, Peter Schneider-Kamp, Stephan Swiderski, René Thiemann
2011 ACM Transactions on Programming Languages and Systems  
In particular, we show how termination techniques for ordinary rewriting can be used to handle those features of Haskell which are missing in term rewriting (e.g., lazy evaluation, polymorphic types, and  ...  There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages.  ...  ACKNOWLEDGMENTS We thank the reviewers for many helpful suggestions and remarks.  ... 
doi:10.1145/1890028.1890030 fatcat:uiaosb7xwzgkbcdpumpzwwrweu

A fine-grained parallel completion procedure

Reinhard Bündgen, Manfred Göbel, Wolfgang Küchlin
1994 Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94  
The selection of the best new rule in the outer loop, and hence the completion strategy, is exactly the same as for the sequential algorithm.  ...  We present a parallel Knuth-Bendiz completion algorithm where the inner loop, deriving the consequences of adding a new rule to the system, is multi-threaded.  ...  We also thank Michael Sperber for his implementation of the ALDES-to-C Compiler and Nick Nevin and Jeff Ward for their contributions to the S-threads system.  ... 
doi:10.1145/190347.190427 dblp:conf/issac/BundgenGK94 fatcat:m2dwt3dhtvg6haikc4bqjbtrre

The Certification Problem Format

Christian Sternagel, René Thiemann
2014 Electronic Proceedings in Theoretical Computer Science  
Whereas CPF was originally invented to combine three different formats for termination proofs into a single one, in the meanwhile proofs for several other properties of term rewrite systems are also expressible  ...  Its acceptance is also demonstrated in international competitions: the certified tracks of both the termination and the confluence competition utilized CPF as exchange format between automated tools and  ...  There are certificates for termination and nontermination of (relative) TRSs and dependency pair problems.  ... 
doi:10.4204/eptcs.167.8 fatcat:a3jzqlr3ajgb3obnz65z3obivq

The Termination and Complexity Competition [chapter]

Jürgen Giesl, Albert Rubio, Christian Sternagel, Johannes Waldmann, Akihisa Yamada
2019 Msphere  
The termination and complexity competition (termCOMP) focuses on automated termination and complexity analysis for various kinds of programming paradigms, including categories for term rewriting, integer  ...  The goal of the competition is to demonstrate the power and advances of the stateof-the-art tools in each of these areas. A.  ...  Finally, SizeChangeTool [10] extends the size-change termination principle [41] to higher-order rewriting.  ... 
doi:10.1007/978-3-030-17502-3_10 fatcat:mixhnq6ylbhgxotdihx3xqz73m

Proof Theory at Work: Complexity Analysis of Term Rewrite Systems [article]

Georg Moser
2009 arXiv   pre-print
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis.  ...  The aim of this introduction is to present the main ideas in an easily accessible fashion to make the result presented accessible to the general public.  ...  In particular my gratitude goes to my co-authors Andreas Schabl, Andreas Weiermann, Martin Avanzini, Nao Hirokawa, and Toshiaysu Arai, who kindly allowed me to include our joint papers into this thesis  ... 
arXiv:0907.5527v2 fatcat:jxonbatpw5hdlabp5z7swfrgdy

The taming of the rew: a type theory with computational assumptions

Jesper Cockx, Nicolas Tabareau, Théo Winterhalter
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
We further describe an algorithm to check that the triangle criterion indeed holds for a given rewrite system, as well as our implementation of rewrite rules for the Agda system, in Sect. 7.  ...  The properties of RTT have been formally verified using the MetaCoq framework and an implementation of rewrite rules is already available in the Agda proof assistant.  ...  The size-change termination principle [Lee et al. 2001] has been extended to dependently typed rewriting systems by Blanqui [2004 Blanqui [ , 2018 and has recently been implemented in the SizeChangeTool  ... 
doi:10.1145/3434341 fatcat:nuswqtklpfgi3f6xmkzfksnudi

Static Dependency Pair Method in Functional Programs

Keiichirou KUSAKARI
2018 IEICE transactions on information and systems  
Keiichirou KUSAKARI †a) , Member SUMMARY We have previously introduced the static dependency pair method that proves termination by analyzing the static recursive structure of various extensions of term  ...  The key is to succeed with the formalization of recursive structures based on the notion of strong computability, which is introduced for the termination of typed λ-calculi.  ...  Acknowledgments We would like to thank the anonymous referees for their helpful comments.  ... 
doi:10.1587/transinf.2017fop0004 fatcat:seyqyw4tabd67iwb64ef6r37qi

Automated verification of termination certificates [article]

Frédéric Blanqui
2012 arXiv   pre-print
In this paper, we report on our progress in developing a standalone tool for checking the correctness of certificates for the termination of term rewrite systems, and formally proving its correctness in  ...  To this end, we use the extraction mechanism of Coq and the library on rewriting theory and termination called CoLoR.  ...  Then, new sets are introduced when needed, like it is the case for marked symbols in the dependency pairs transformation. Moreover, some termination techniques may change the arity of symbols.  ... 
arXiv:1212.2350v1 fatcat:ogdlfx64mjac5il5k2aodada3m

Tyrolean termination tool: Techniques and features

Nao Hirokawa, Aart Middeldorp
2007 Information and Computation  
It incorporates several new refinements of the dependency pair method that are easy to implement, increase the power of the method, result in simpler termination proofs, and make the method more efficient  ...  The Tyrolean Termination Tool (T T T for short) is a powerful tool for automatically proving termination of rewrite systems.  ...  Acknowledgements We are grateful to Daniel Laimer for improving the web interface of T T T. We thank the anonymous referees for providing numerous suggestions which helped to improve the presentation.  ... 
doi:10.1016/j.ic.2006.08.010 fatcat:sdnzqmynrveaxpk3a4vnbwstk4

Resource Analysis by Sup-interpretation [chapter]

Jean-Yves Marion, Romain Péchoux
2006 Lecture Notes in Computer Science  
The dependency pairs were initially introduced for proving termination of term rewriting systems automatically.  ...  Since we try to control the arguments of a recursive call together, the sup-interpretation is closer from the dependency pairs method than from the size-change principle method of [15] which consider the  ...  Jones, and Amir M. Ben-Amram. The size-change principle for program termination. In Symposium on Principles of Programming Languages, volume 28, pages 81-92.  ... 
doi:10.1007/11737414_12 fatcat:xusneer4x5hwhkk3diekxgzr5a
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