〈a, b | aaaa=a, baab=a〉

Properties

• Infinite non-commutative monoid

Completion parameters

• Reduction order: left-to-right ac/b
• Auxiliary generator abaaa=c

Complete rewriting system

1. cac ⇒ a²
2. a⁴ ⇒ a
3. a³c ⇒ c
4. ca³ ⇒ c
5. ba ⇒ a²ca
6. bc ⇒ a²c²
7. ab ⇒ c
8. cb ⇒ ca²c

Right Cayley graph (truncated)

Left Cayley graph (truncated)