〈a, b | abab=1, aabaa=b〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right c/ab
• Auxiliary generator ba=c

Inverses of generators

• a^-1 = cb
• b^-1 = ac
• c^-1 = c

Complete rewriting system

1. c² ⇒ 1
2. acb ⇒ 1
3. ba ⇒ c
4. b² ⇒ (ca)²
5. bcb ⇒ a²c
6. a²ca ⇒ b
7. aca² ⇒ cbc
8. bca² ⇒ a²bc
9. b(ca)² ⇒ (ca)²b

Right Cayley graph (truncated)

Left Cayley graph (truncated)