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Termination for direct sums of left-linear complete term rewriting systems

1995
*
Journal of the ACM
*

A

doi:10.1145/227683.227689
fatcat:fbndklym5bdedbwtak7levgbxi
*term**rewriting**system*is called*complete*if it is confluent and*terminating*. ... We prove that*completeness**of*TRSs is a "modular" property (meaning that it stays preserved under*direct**sums*), provided the constituent TRSs are*left*-*linear*. ...*Termination**for*the*Direct**Sum*In this section, we will prove the main result, that is, the*termination*property*for*the*direct**sum*R b © P w*of**left*-*linear*and*complete*R b, R w. ...##
###
Termination for the direct sum of left-linear term rewriting systems
[chapter]

1989
*
Lecture Notes in Computer Science
*

It is shown that two

doi:10.1007/3-540-51081-8_127
fatcat:k55hqevomzc2jmuocusviibwti
*term**rewriting**systems*both are*left*-*linear*and*complete*if and only if the*direct**sum**of*these*systems*is so. ... A b s t r a c t The*direct**sum**of*two*term**rewriting**systems*is the union*of**systems*having disjoint sets*of*function symbols. ... Two*term**rewriting**systems*R0 and R1 are*left*-*linear*and*complete*iff the*direct**sum*R0 (~ R1 is so. ...##
###
Page 5759 of Mathematical Reviews Vol. , Issue 97I
[page]

1997
*
Mathematical Reviews
*

(NL-NIJM; Nijmegen)

*Termination**for**direct**sums**of**left*-*linear**complete**term**rewriting**systems*. (English summary) J. Assoc. Comput. Mach. 42 (1995), no. 6, 1275-1304. ... So*completeness**of*TRSs is a modular property that is, it is preserved under*direct**sums**of*TRSs—provided the underlying TRSs are*left*-*linear*. Peter R. J. ...##
###
Modular termination of r-consistent and left-linear term rewriting systems

1995
*
Theoretical Computer Science
*

A modular property

doi:10.1016/0304-3975(95)00080-g
fatcat:3a66qxq4jbao5jddrjxj3xyhre
*of**term**rewriting**systems*is one that holds;*for*the*direct**sum**of*two disjoint*term**rewriting**systems*iff it holds*for*every involved*term**rewriting**system*. ... Since confluence implies r-consistency, this constitutes a generalisation*of*the theorem*of*Toyama, Klop, and Barendregt on the modularity*of**termination**for*confluent and*left*-*linear**term**rewriting**systems*... Acknowledgements We thank Bernhard Gramlich, Jan Willem Klop and Enno Ohlebusch*for*valuable comments on a draft*of*this paper. ...##
###
Algebraic semantics and complexity of term rewriting systems
[chapter]

1989
*
Lecture Notes in Computer Science
*

*Termination*

*for*

*direct*

*sums*

*of*

*left*-

*linear*

*complete*

*term*

*rewrite*

*systems*. On the Church-Rosser property

*for*the

*direct*

*sum*

*of*

*term*

*rewriting*

*systems*. J. ACM, 34(1):128-143, 1987. V. van Oostrom. ... Decidability

*of*

*termination*

*for*semi-constructor TRSs,

*left*-

*linear*shallow TRSs and related

*systems*. ...

##
###
Page 2565 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

In this paper, the author shows that UN~ is modular

*for**left*-*linear**term**rewriting**systems*. ... The author shows that (i) decidability*of**termination*is not a modular property*for*finite*left*-*linear*monadic TRSs, (ii) decid- ability*of*confluence and decidability*of**completeness**of*(*left*- or right ...##
###
Modular term rewriting systems and the termination

1990
*
Information Processing Letters
*

Toyama

doi:10.1016/0020-0190(90)90221-i
fatcat:5po5kwbairc47dtvnnvxuu7464
*for*discussing the definitions ... The*direct**sum**of*two*term**rewriting**systems*(TRSs) [2, 8] R, and R, is confluent if R, and R, are confluent [lo] , but the*direct**sum*is not necessarily*terminating*even if R, and R, are*terminating*... [ll] ; that is,*termination*is not a "modular" [6] property*for*general*term**rewriting**systems*. ...##
###
On modularity in infinitary term rewriting

2006
*
Information and Computation
*

modularity

doi:10.1016/j.ic.2006.02.005
fatcat:42n4cgfrnzd7piktgzpocrzkiq
*of*top-*termination*and normalization*for**left*-*linear**systems*. ... We study modular properties in strongly convergent infinitary*term**rewriting*. ... Acknowledgments The author gratefully acknowledges the insightful comments*of*the referees and their contribution to the presentation*of*the paper. ...##
###
Computing with rewrite systems

1985
*
Information and Control
*

*Rewrite*

*systems*may be used

*for*straightforward computation by simplifying

*terms*. ...

*Term*-

*rewriting*

*systems*, that is, sets

*of*

*directed*equations, provide a paradigm

*of*computation with particularly simple syntax and semantics. ... discussions, and the referees

*for*their valuable suggestions. ...

##
###
Modular proofs for completeness of hierarchical term rewriting systems

1995
*
Theoretical Computer Science
*

A property P

doi:10.1016/0304-3975(95)00075-8
fatcat:hp5rkbjavnab3fj6fq3fuohbvu
*of**term**rewriting**systems*is modular if the following holds: two*rewriting**systems*~o and ~? ... Therefore, techniques employed in proving the modularity results*for**direct**sums*and constructor sharing*systems*are not applicable*for*hierarchical combinations. ... The author is grateful to the referees*for*many suggestions in improving the presentation very much. ...##
###
Primitive Rewriting
[chapter]

2005
*
Lecture Notes in Computer Science
*

It comes as no surprise that

doi:10.1007/11601548_10
fatcat:ndwwizgbe5gzzj2quk743cq3yy
*rewrite**systems*have the same computational power as the other basic models. 2 Moreover,*rewrite**systems*may be restricted in various ways, including*left*-*linearity*, orthogonality ... Another natural candidate*for*proofs regarding*term**rewriting*is Recursion Theory, a*direction*we promote in this contribution. ... Acknowledgement I thank the referees*for*their critical reading and constructive suggestions. ...##
###
Unique Normal Forms and Confluence of Rewrite Systems: Persistence

1995
*
International Joint Conference on Artificial Intelligence
*

We also prove the confluence

dblp:conf/ijcai/Verma95
fatcat:4kfkgy4jmjacvdzffqeb35urka
*of*the union (function symbols can be shared)*of*a nonlin ear*system*with a*left*-*linear**system*under fairly general conditions. ... In this paper, we study two funda mental concepts, uniqueness*of*normal forms and confluence,*for*nonlinear*systems*in the ab sence*of**termination*. ... Lemma 20 If the Ir-disjoint union R*of*a*left*-*linear**system*R 1 and any*system*R 2 is nonoverlapping and semi-*terminating*, then R is persistent. ...##
###
Page 3206 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

Standard or extended (i.e. modulo a theory)

*completion**of**term**rewriting**systems*may abort or succeed*for*a given input. ... 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. ...##
###
Modularity of simple termination of term rewriting systems with shared constructors

1992
*
Theoretical Computer Science
*

Ohuchi, Modularity

doi:10.1016/0304-3975(92)90015-8
fatcat:ak5g44my7rb6hko3o6hxxnkr5q
*of*simple*termination**of**term**rewriting**systems*with shared constructors, Theoretical Computer Science 103 (1992) 273-282. ... A*term**rewriting**system*is simply*terminating*if there exists a simplification ordering showing its*termination*. ... Toyama and anonymous referees*for*their helpful comments. This work is partially supported by the Grants from Ministry*of*Education, Science and Culture*of*Japan, #02249104 and #01460253. ...##
###
Page 5013 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

*of*r-consistent and

*left*-

*linear*

*term*

*rewriting*

*systems*. ... Summary: “A modular property

*of*

*term*

*rewriting*

*systems*is one that holds

*for*the

*direct*

*sum*

*of*two disjoint

*term*

*rewriting*

*systems*iff it holds

*for*every involved

*term*

*rewriting*

*system*. ...

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