Some undecidable termination problems for semi-Thue systems

Abstract

We show that the uniform termination problem is undecidable for length-preserving semi-Thue systems having 9 rules. We then give an explicit uniformly terminating semi-Thue system $\text{F}$ having 9 rules which is “universal with respect to termination problems” in some sense. It follows that there exists a fixed rule (u₀, v₀) such that $\text{F}$ ∪ {(u₀, v₀)} has 10 rules and undecidable termination problem.