The word problem for free partially commutative groups
Journal of Symbolic Computation
String-rewriting systems
A finiteness condition for rewriting systems
Theoretical Computer Science
Journal of Symbolic Computation
Semigroups and Combinatorial Applications
Semigroups and Combinatorial Applications
String rewriting and homology of monoids
Mathematical Structures in Computer Science
Complete involutive rewriting systems
Journal of Symbolic Computation
The q-theory of Finite Semigroups
The q-theory of Finite Semigroups
String rewriting for double coset systems
Journal of Symbolic Computation
Finite complete rewriting systems for regular semigroups
Theoretical Computer Science
Homotopy bases and finite derivation type for Schützenberger groups of monoids
Journal of Symbolic Computation
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We give an example of a monoid with finitely many left and right ideals, all of whose Schutzenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation type, but such that the monoid itself does not have finite derivation type, and therefore does not admit a presentation by a finite complete rewriting system. The example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type. Specifically it allows us to construct two finitely generated monoids M and N with isometric Cayley graphs, where N has finite derivation type (respectively, admits a presentation by a finite complete rewriting system) but M does not. This contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi-isometry invariant. The same example is also used to show that neither of these two properties is preserved under finite Green index extensions.