〈a, b | abbaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = bcd
• b^-1 = ac²
• c^-1 = cd
• d^-1 = c²

Complete rewriting system

1. dc ⇒ cd
2. c²d ⇒ 1
3. db ⇒ bc
4. c²b ⇒ bcd
5. ca ⇒ ad
6. da ⇒ ac⁴
7. ba ⇒ d
8. ab ⇒ c