〈a, b | abba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right abcd
• Auxiliary generator aa=c
• Auxiliary generator bb=d

Inverses of generators

• a^-1 = ad
• b^-1 = bc
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. a² ⇒ c
2. b² ⇒ d
3. ca ⇒ ac
4. cb ⇒ bc
5. cd ⇒ 1
6. da ⇒ ad
7. db ⇒ bd
8. dc ⇒ 1