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On termination of one rule rewrite systems

1994
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(94)00029-8
fatcat:blq7jlcworac7kkkl3kdfel3be
*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,, ...##
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Termination and derivational complexity of confluent one-rule string-rewriting systems

2001
*
Theoretical Computer Science
*

develop techniques to attack the

doi:10.1016/s0304-3975(00)00367-4
fatcat:bleuisb22zajnlx6oqtbjwupni
*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*. ...##
###
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

1997
*
Theoretical Computer Science
*

Hence, the only sensible strategy to prove

doi:10.1016/s0304-3975(96)00254-x
fatcat:j3d36b7omfh4doauzyf7t24umq
*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. ...##
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Commutation, transformation, and termination
[chapter]

1986
*
Lecture Notes in Computer Science
*

In this paper we study the use

doi:10.1007/3-540-16780-3_76
fatcat:czdyqo6gubf7hniihajvrcviwm
*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*. ...##
###
Persistence Of Termination For Term Rewriting Systems With Ordered Sorts

2007
*
Zenodo
*

Zantema showed that

doi:10.5281/zenodo.1081045
fatcat:e5elhfr6knewvcjvlmo7htjere
*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] . ...##
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Simulation as a correct transformation of rewrite systems
[chapter]

1997
*
Lecture Notes in Computer Science
*

Kamperman and Walters proposed the notion

doi:10.1007/bfb0029968
fatcat:d5fasnjdh5g6tauk62oqnnegfu
*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*. ...##
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Simulation of SOS definitions with term rewriting systems
[chapter]

1994
*
Lecture Notes in Computer Science
*

Since only standard unconditional

doi:10.1007/3-540-57880-3_10
fatcat:cy2hxwvttvazrigvp2nazfdyaq
*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*. ...##
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Transforming Cycle Rewriting into String Rewriting

2015
*
International Conference on Rewriting Techniques and Applications
*

Our main technique is to transform cycle

doi:10.4230/lipics.rta.2015.285
dblp:conf/rta/SabelZ15
fatcat:huejxncs6bbhtmjhckkcglqyo4
*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. ...##
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An on-line problem database
[chapter]

1998
*
Lecture Notes in Computer Science
*

For the current proceedings, the main subjects were Term

doi:10.1007/bfb0052380
fatcat:x57lyotlxrh5bdan42az6tileq
*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*? ...##
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Problems in rewriting III
[chapter]

1995
*
Lecture Notes in Computer Science
*

The union

doi:10.1007/3-540-59200-8_82
fatcat:in5aspimbrbvngnrhzcm7tfwei
*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] . ...##
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Confluent term rewriting systems with membership conditions
[chapter]

1988
*
Lecture Notes in Computer Science
*

We propose a new type

doi:10.1007/3-540-19242-5_17
fatcat:rkyoyv3ibvfq5aticm735dvtgq
*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. ...##
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Hierarchical termination
[chapter]

1995
*
Lecture Notes in Computer Science
*

Some (largely syntactic) sufficient conditions are given here for the union

doi:10.1007/3-540-60381-6_6
fatcat:2cpjqo6k6nhetdb7nhuf2kxm2u
*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. ...##
###
When are two rewrite systems more than none?
[chapter]

1997
*
Lecture Notes in Computer Science
*

We present some old and new su cient conditions under which

doi:10.1007/bfb0029947
fatcat:g7qrw35qljgy5dzqo7zxh4t45u
*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*. ...##
###
From Conditional to Unconditional Rewriting
[chapter]

2005
*
Lecture Notes in Computer Science
*

An automated technique to translate conditional

doi:10.1007/978-3-540-31959-7_13
fatcat:iirh3zqu4jfcteosiw4rwk64oe
*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. ...
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