〈a, b | aaaa=a, aaba=b〉

Properties

• Infinite commutative monoid
• Isomorphic to commutative presentation: 〈a, b | 4b=b, a+3b=a〉
• Grothendieck group is ℤ₃ ⊕ ℤ

Completion parameters

• Reduction order: left-to-right ab

Complete rewriting system

1. ba ⇒ ab
2. a⁴ ⇒ a
3. a³b ⇒ b

Right Cayley graph (truncated)