〈a, b | aba=bb, aaaa=aa〉

Properties

• Infinite non-commutative monoid

Completion parameters

• Reduction order: left-to-right a/b

Complete rewriting system

1. a⁴ ⇒ a²
2. b² ⇒ aba
3. (ab)² ⇒ (ba)²
4. baba²b ⇒ (a²b)²a
5. baba³b ⇒ a(a²b)²a
6. ab(a²b)² ⇒ b(a²b)²a
7. aba²ba³b ⇒ ba(a²b)²a
8. (a³b)²a²ba ⇒ (aba²)²ba

Right Cayley graph (truncated)

Left Cayley graph (truncated)