On the ground reducibility problem for word rewriting systems with variables
Abstract
Given a word rewriting system with variables R and a word with variables w the question we are interested in is whether all the instances of w obtained by substituting its variables by non-empty words are reducible by R. We prove this problem to be generally undecidable even for a very simple word w, namely axa where a is a letter and x a variable. When R is left-linear, the question is decidable for arbitrary (linear or non-linear).