# Dependent choice as a termination principle

## TL;DR

This paper presents a new formulation of the dependent choice axiom as an abstract termination principle, generalizing recursive path orderings to establish termination in rewrite systems.

## Contribution

It introduces a novel formulation of dependent choice as a termination principle and relates it to existing termination theorems.

## Key findings

- Multiple variants of the termination principle are considered
- The new formulation generalizes recursive path orderings
- Connections to established termination theorems are established

## Abstract

We introduce a new formulation of the axiom of dependent choice that can be viewed as an abstract termination principle, which generalises the recursive path orderings used to establish termination of rewrite systems. We consider several variants of our termination principle, and relate them to general termination theorems in the literature.