〈a, b | ba=ab, bbb=aaa〉

Properties

• Infinite commutative monoid
• Isomorphic to commutative presentation: 〈a, b | 3a=3b〉
• Grothendieck group is ℤ₃ ⊕ ℤ

Completion parameters

• Reduction order: left-to-right ab

Complete rewriting system

1. ba ⇒ ab
2. b³ ⇒ a³

Right Cayley graph (truncated)