2024-03-29T14:48:46Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00028615
2023-01-16T04:21:35Z
312:313:314
Conditions for confluence of innermost terminating term rewriting systems
Ishizuki, Sayaka
93693
Oyamaguchi, Michio
93694
Sakai, Masahiko
93695
Confluence
Innermost termination
Term rewriting systems
Decidability
This paper presents a counterexample for the open conjecture whether innermost joinability of all critical pairs ensures confluence of innermost terminating term rewriting systems. We then show that innermost joinability of all normalized instances of the critical pairs is a necessary and sufficient condition. Using this condition, we give a decidable sufficient condition for confluence of innermost terminating systems. Finally, we enrich the condition by introducing the notion of left-stable rules. As a corollary, confluence of innermost terminating left-weakly-shallow TRSs is shown to be decidable.
ファイル公開:2020/08/01
journal article
Springer
2019-08
application/pdf
Applicable Algebra in Engineering, Communication and Computing
4
30
349
360
0938-1279
1432-0622
https://nagoya.repo.nii.ac.jp/record/28615/files/aaecc2018.pdf
eng
https://doi.org/10.1007/s00200-018-0377-8
“This is a post-peer-review, pre-copyedit version of an article published in [Applicable Algebra in Engineering, Communication and Computing]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00200-018-0377-8”.