〈a, b | aab=ba, bbbbbb=1〉

Properties

• Finite non-commutative monoid with 384 elements

Completion parameters

• Reduction order: right-to-left a/b

Complete rewriting system

1. a⁶⁴ ⇒ a
2. ba ⇒ a²b
3. b⁶ ⇒ 1

Idempotents

• 1
• a⁶³

Right Cayley graph

Left Cayley graph