〈a, b | aaab=a, bbbbb=b〉

Properties

• Finite non-commutative monoid with 45 elements

Completion parameters

• Reduction order: left-to-right a/b

Complete rewriting system

1. a⁹ ⇒ a
2. ab ⇒ a⁷
3. b⁵ ⇒ b

Idempotents

• 1
• a⁸
• ba²
• b²a⁴
• b³a⁶
• b⁴
• b⁴a⁸

Right Cayley graph

Left Cayley graph