〈a, b | ababbabaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = bc²d
• b^-1 = dad
• c^-1 = c²d
• d^-1 = c³

Complete rewriting system

1. dc ⇒ cd
2. c³d ⇒ 1
3. d²a ⇒ ac⁹
4. ca ⇒ dad²
5. cda ⇒ ac³
6. db ⇒ bc²
7. c³b ⇒ bcd
8. ab ⇒ c
9. bda ⇒ c³