〈a, b | aaaa=a, aabab=a〉

Properties

• Infinite non-commutative monoid

Completion parameters

• Reduction order: left-to-right acb
• Auxiliary generator baaa=c

Complete rewriting system

1. ab ⇒ ac
2. cb ⇒ c²
3. ba ⇒ ca
4. a⁴ ⇒ a
5. (ac)² ⇒ a³
6. ca³ ⇒ c
7. c²ac ⇒ ca²

Right Cayley graph (truncated)

Left Cayley graph (truncated)