〈a, b | aaaabbabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right ad/cb
• Auxiliary generator abb=c
• Auxiliary generator acc=d

Inverses of generators

• a^-1 = a²d
• b^-1 = ca⁵b
• c^-1 = ca⁴
• d^-1 = a³

Complete rewriting system

1. da ⇒ ad
2. a³d ⇒ 1
3. dc ⇒ aca²d²
4. a⁴c ⇒ ca⁴
5. c² ⇒ a²d²
6. bc ⇒ ca⁵bad²
7. ba³c ⇒ a³ca²d²ba⁴
8. b² ⇒ a³ca²d²