〈a, b | abbababaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = db
• b^-1 = ad
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. cd ⇒ 1
2. dc ⇒ 1
3. d³a ⇒ ac²
4. ca ⇒ d²ad²
5. d²b ⇒ bc³
6. cb ⇒ dbd³
7. adb ⇒ 1
8. ba ⇒ c