〈a, b | abbbba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = ad
• b^-1 = b³c
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. a² ⇒ c
2. ca ⇒ ac
3. cb ⇒ bc
4. cd ⇒ 1
5. da ⇒ ad
6. db ⇒ bd
7. dc ⇒ 1
8. b⁴ ⇒ d