On algorithmic decidability of the square-free word problem relative to a system of two defining relations

TL;DR

This paper proves that determining whether a word is square-free relative to a system of two defining relations is a decidable problem, advancing understanding in formal language theory.

Contribution

It establishes the decidability of the square-free word problem for systems with two defining relations, a previously unresolved question.

Findings

The problem is decidable for systems with two defining relations.

Provides a formal proof of decidability.

Enhances theoretical understanding of word problems in formal languages.

Abstract

The square-free word problem relative to a system of two defining relations is decidable.