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On termination of one rule rewrite systems

Pierre Lescanne
1994 Theoretical Computer Science  
., On termination of one rule rewrite systems, Theoretical Computer Science 132 (1994) 3955401.  ...  In particular, Dauchet proves the undecidability of the termination of one rule rewrite systems by coding Turing machines into one rule rewrite systems.  ...  Reduction of the termination of one rule rewrite systems to the termination of semi-Thue systems Let us call abstract machines rewrite systems where rules are all of the form and where sl, . . . , s,,  ... 
doi:10.1016/0304-3975(94)00029-8 fatcat:blq7jlcworac7kkkl3kdfel3be

Termination and derivational complexity of confluent one-rule string-rewriting systems

Yuji Kobayashi, Masashi Katsura, Kayoko Shikishima-Tsuji
2001 Theoretical Computer Science  
develop techniques to attack the termination and complexity problems of con uent one-rule string-rewriting systems.  ...  It is not known whether the termination problem is decidable for one-rule string-rewriting systems, though the con uence of such systems is decidable by Wrathall (in: Word Equations and In this paper we  ...  One-rule string-rewriting systems are thus considered to be the most simple example of rewriting systems.  ... 
doi:10.1016/s0304-3975(00)00367-4 fatcat:bleuisb22zajnlx6oqtbjwupni

Page 3206 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
Basically, termination of a rewrite system R is proved by means of termination of a simplified rewrite system S and an auxiliary rewrite system U connecting R and S.  ...  In fact, we show that the Knuth-Bendix completion procedure always terminates when ap- plied to prefix-rewriting systems on virtually free presentations of context-free groups.  ... 

Termination modulo equations by abstract commutation with an application to iteration

Wan Fokkink, Hans Zantema
1997 Theoretical Computer Science  
Hence, the only sensible strategy to prove termination of such a rewrite system is to transform it into a rewrite system without self-embedding rules, for which termination can be derived.  ...  Again this rewrite system contains self-embedding rules.  ...  Basically, termination of a rewrite system R is proved by means of termination of a simplified rewrite system S and an auxiliary rewrite system U connecting R and S.  ... 
doi:10.1016/s0304-3975(96)00254-x fatcat:j3d36b7omfh4doauzyf7t24umq

Commutation, transformation, and termination [chapter]

Leo Bachmair, Nachum Dershowitz
1986 Lecture Notes in Computer Science  
In this paper we study the use of commutation properties for proving termination of rewrite systems.  ...  Commutation properties may be used to prove termination of a combined system RUS by proving termination of R and S separately.  ...  A rewrite system is any set R of rewrite rules.  ... 
doi:10.1007/3-540-16780-3_76 fatcat:czdyqo6gubf7hniihajvrcviwm

Persistence Of Termination For Term Rewriting Systems With Ordered Sorts

Munehiro Iwami
2007 Zenodo  
Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules.  ...  In this paper, we show that the Zantema's result can be extended to term rewriting systems on ordered sorts, i.e., termination is persistent for term rewriting systems on ordered sorts without collapsing  ...  The notion of termination for rewrite systems corresponds to the existence of answers of computations. So termination is the fundamental notion of term rewriting systems as computation models [7] .  ... 
doi:10.5281/zenodo.1081045 fatcat:e5elhfr6knewvcjvlmo7htjere

Simulation as a correct transformation of rewrite systems [chapter]

Wan Fokkink, Jaco van de Pol
1997 Lecture Notes in Computer Science  
Kamperman and Walters proposed the notion of a simulation of one rewrite system by another one, whereby each term of the simulating rewrite system is related to a term in the original rewrite system.  ...  In this paper it is shown that if such a simulation is sound and complete and preserves termination, then the transformation of the original into the simulating rewrite system constitutes a correct step  ...  Recently, Kamperman and Walters [7, 8, 6) proposed a notion of simulation of one rewrite system by another rewrite system.  ... 
doi:10.1007/bfb0029968 fatcat:d5fasnjdh5g6tauk62oqnnegfu

Simulation of SOS definitions with term rewriting systems [chapter]

Karl-Heinz Buth
1994 Lecture Notes in Computer Science  
Since only standard unconditional rewrite rules are used, every theorem prover based on rewriting can be employed to implement this kind of semantics definitions, and so to reason about them.  ...  This paper presents a method to transform a structured operational semantics (SOS) definition 8, given by a special form of deduction system, into a term rewriting system 7~.  ...  of rewrite systems.  ... 
doi:10.1007/3-540-57880-3_10 fatcat:cy2hxwvttvazrigvp2nazfdyaq

Transforming Cycle Rewriting into String Rewriting

David Sabel, Hans Zantema, Marc Herbstritt
2015 International Conference on Rewriting Techniques and Applications  
Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system.  ...  We present new techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected.  ...  We thank Johannes Waldmann for fruitful remarks, in particular for his suggestions leading to Section 4 on trace decreasing matrix interpretations.  ... 
doi:10.4230/lipics.rta.2015.285 dblp:conf/rta/SabelZ15 fatcat:huejxncs6bbhtmjhckkcglqyo4

An on-line problem database [chapter]

Nachum Dershowitz, Ralf Treinen
1998 Lecture Notes in Computer Science  
For the current proceedings, the main subjects were Term rewriting systems Symbolic and algebraic computation Uni cation and matching Completion techniques String and graph rewriting Conditional and typed  ...  The RTA list seeks to summarize open problems and subsequent solutions in elds of interest to this conference.  ...  Termination is undecidable for nonlength-increasing monadic systems of rules 7 . For one monadic rule, con uence is decidable 37,83 . What about con uence of one nonmonadic rule?  ... 
doi:10.1007/bfb0052380 fatcat:x57lyotlxrh5bdan42az6tileq

Problems in rewriting III [chapter]

Nachum Dershowitz, Jean-Pierre Jouannaud, Jan Willem Klop
1995 Lecture Notes in Computer Science  
The union of two totally terminating rewrite systems which do not share any symbols is totally terminating if at least one of them does not contain a rule that has more occurrences of some variable on  ...  Termination of string-rewriting systems is known to be undecidable [49] . Termination of a single term-rewriting rule was proved undecidable in [32; 64] .  ... 
doi:10.1007/3-540-59200-8_82 fatcat:in5aspimbrbvngnrhzcm7tfwei

Confluent term rewriting systems with membership conditions [chapter]

Yoshihito Toyama
1988 Lecture Notes in Computer Science  
We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution  ...  We study the confluence of membership-conditional term rewriting systems that are nonterminating and nonlinear.  ...  A term rewriting system R on T is a reduction system R = (T, --~) such that the reduction relation --* is defined by a set t> of rewriting rules on T. If R has Mt ~, Mr, then we write Ms ~> M~ E R.  ... 
doi:10.1007/3-540-19242-5_17 fatcat:rkyoyv3ibvfq5aticm735dvtgq

Hierarchical termination [chapter]

Nachum Dershowitz
1995 Lecture Notes in Computer Science  
Some (largely syntactic) sufficient conditions are given here for the union of terminating rewrite systems to be terminating, particularly in the hierarchical case, when one of the systems makes no reference  ...  -A left-linear system has no rule with more than one occurrence of a variable on its left-hand side.  ...  to first apply the green rule as many times as necessary to rewrite the (one or more) occurrences of that variable on the left-hand side of the purple rule, followed by the same purple step.  ... 
doi:10.1007/3-540-60381-6_6 fatcat:2cpjqo6k6nhetdb7nhuf2kxm2u

When are two rewrite systems more than none? [chapter]

Nachum Dershowitz
1997 Lecture Notes in Computer Science  
We present some old and new su cient conditions under which termination existence of normal forms, regardless of computation strategy and con uence uniqueness are preserved by s u c h c o m binations.  ...  We look at non-deterministic programs expressed as termrewriting systems which compute normal forms of input terms and consider the case where individual systems share constructors, but not de ned symbols  ...  the top of the left side of a rule of one system are prohibited from also appearing at the top left of a rule in the conjoined system.  ... 
doi:10.1007/bfb0029947 fatcat:g7qrw35qljgy5dzqo7zxh4t45u

From Conditional to Unconditional Rewriting [chapter]

Grigore Roşu
2005 Lecture Notes in Computer Science  
An automated technique to translate conditional rewrite rules into unconditional ones is presented, which is suitable to implement, or compile, conditional rewriting on top of much simpler and easier to  ...  optimize unconditional rewrite systems.  ...  The algorithm above, taking a conditional Σ-rewrite system R and a Σ-term α as input, terminates iff R terminates on α.  ... 
doi:10.1007/978-3-540-31959-7_13 fatcat:iirh3zqu4jfcteosiw4rwk64oe
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