〈a, b | ababba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = bd
• b^-1 = ac²
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. cd ⇒ 1
2. dc ⇒ 1
3. ca ⇒ ad²
4. da ⇒ ac²
5. db ⇒ cbc
6. c²b ⇒ bd
7. ab ⇒ c
8. ba ⇒ d²