〈a, b | abababba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = bd
• b^-1 = ac³
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. dc ⇒ 1
2. cd ⇒ 1
3. ca ⇒ ad³
4. da ⇒ ac³
5. c³b ⇒ bd
6. db ⇒ c²bc
7. ab ⇒ c
8. ba ⇒ d³