〈a, b | aaabaabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = bda
• b^-1 = a²c²
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. cd ⇒ 1
2. dc ⇒ 1
3. db ⇒ cbc
4. c²b ⇒ bd
5. ab ⇒ bdac
6. ca² ⇒ a²d²
7. da² ⇒ a²c²
8. ba² ⇒ d²