〈a, b | aabbba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a²d
• b^-1 = b²c
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. ca ⇒ ac
2. cb ⇒ bc
3. cd ⇒ 1
4. da ⇒ ad
5. db ⇒ bd
6. dc ⇒ 1
7. a³ ⇒ c
8. b³ ⇒ d