〈a, b | abaaaabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right acd/b
• Auxiliary generator baa=c
• Auxiliary generator aab=d

Inverses of generators

• a^-1 = bc²a
• b^-1 = a²cd
• c^-1 = cd
• d^-1 = c²

Complete rewriting system

1. dc ⇒ cd
2. c²d ⇒ 1
3. da² ⇒ a²c
4. c²a² ⇒ a²cd
5. ba² ⇒ c
6. ab ⇒ bc²ad
7. cb ⇒ bd
8. db ⇒ bc⁴