〈a, b | abba=b, baaab=a〉

Properties

• Finite non-commutative monoid with 49 elements

Completion parameters

• Reduction order: left-to-right a/b

Complete rewriting system

1. a⁹ ⇒ a
2. ba⁸ ⇒ b
3. a⁴b ⇒ ba⁴
4. b² ⇒ a³ba³
5. ba²b ⇒ aba
6. ba³b ⇒ a
7. (ab)² ⇒ baba⁷

Idempotents

• 1
• a⁸

Right Cayley graph

Left Cayley graph