〈a, b | abababbaba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right cd/ba
• Auxiliary generator ba=c
• Auxiliary generator bcca=d

Inverses of generators

• a^-1 = c²bc²
• b^-1 = acd
• c^-1 = cd
• d^-1 = c²

Complete rewriting system

1. dc ⇒ cd
2. c²d ⇒ 1
3. db ⇒ cbc²
4. c³b ⇒ bd
5. da ⇒ ac³
6. c²a ⇒ acd²
7. ba ⇒ c
8. ac²b ⇒ d