〈a, b | aaa=a, aaba=ba〉

Properties

• Infinite non-commutative monoid

Completion parameters

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

Complete rewriting system

1. ab ⇒ ac
2. ba ⇒ ca
3. bc ⇒ c²
4. a³ ⇒ a
5. a²c ⇒ c

Right Cayley graph (truncated)

Left Cayley graph (truncated)