〈a, b | ababbbabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = adc
• b^-1 = aba²d
• c^-1 = a²d
• d^-1 = ca²

Complete rewriting system

1. acd ⇒ cda
2. cda² ⇒ 1
3. da²c ⇒ 1
4. bc ⇒ d²a²ba
5. bd ⇒ cdada²dcba
6. ba² ⇒ da⁴cb
7. bac ⇒ cab
8. bad ⇒ c²b
9. bab ⇒ c