〈a, b | aabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a²d
• b^-1 = bc
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. b² ⇒ d
2. ca ⇒ ac
3. cb ⇒ bc
4. cd ⇒ 1
5. da ⇒ ad
6. db ⇒ bd
7. dc ⇒ 1
8. a³ ⇒ c