English

Termination of Innermost-Terminating Right-Linear Overlay Term Rewrite Systems (Full Version)

Logic in Computer Science 2026-04-23 v1

Abstract

It has been shown that, regarding a terminating right-linear overlay term rewrite system (TRS), any rewrite sequence ending with a normal form can be simulated by the innermost reduction. In this paper, using this simulation property, we show that for a right-linear overlay TRS, there is no infinite minimal dependency-pair chain if and only if there is no infinite innermost minimal dependency-pair chain. This implies that a right-linear overlay TRS is terminating if and only if it is innermost terminating.

Cite

@article{arxiv.2604.20754,
  title  = {Termination of Innermost-Terminating Right-Linear Overlay Term Rewrite Systems (Full Version)},
  author = {Naoki Nishida},
  journal= {arXiv preprint arXiv:2604.20754},
  year   = {2026}
}

Comments

9 pages, full version of a submission to WST 2026

R2 v1 2026-07-01T12:30:48.793Z