On ground word problem of term equation systems

TL;DR

This paper introduces improved semi-decision procedures for solving the ground word problem in variable preserving and general term equation systems, ensuring correctness.

Contribution

It presents natural enhancements over existing trivial procedures for the ground word problem, with proven correctness.

Findings

Procedures are semi-decision methods for the ground word problem.

The new procedures are natural improvements over trivial methods.

Correctness of the procedures is formally proven.

Abstract

We give semi-decision procedures for the ground word problem of variable preserving term equation systems and term equation systems. They are natural improvements of two well known trivial semi-decision procedures. We show the correctness of our procedures.