---
title: Termination orders for 3-dimensional rewriting
url: https://www.emergentmind.com/papers/0612083
type: paper
arxiv_id: '0612083'
arxiv_url: https://arxiv.org/abs/0612083
published: '2006-12-04'
categories:
- math.CT
- cs.LO
---

# Termination orders for 3-dimensional rewriting

## Abstract

This paper studies 3-polygraphs as a framework for rewriting on two-dimensional words. A translation of term rewriting systems into 3-polygraphs with explicit resource management is given, and the respective computational properties of each system are studied. Finally, a convergent 3-polygraph for the (commutative) theory of Z/2Z-vector spaces is given. In order to prove these results, it is explained how to craft a class of termination orders for 3-polygraphs.