We show, under some assumption on the signature, that the 9 8 fragment of the theory of a lexicographic path ordering is undecidable, both in the partial and in the total precedence cases. Our result implies in particular that the simpli cation rule of ordered completion is undecidable.
Comon and Treinen show the first-order theory of lexicographic path ordering is undecidable REF .
The First-Order Theory of Lexicographic Path Orderings is Undecidable
Theoretical Computer Science
Mathematics Computer Science