〈a, b | aaabbabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a²d
• b^-1 = aca⁴b
• c^-1 = aca⁴
• d^-1 = a³

Complete rewriting system

1. da ⇒ ad
2. a³d ⇒ 1
3. dc ⇒ cd
4. a³c ⇒ ca³
5. cac ⇒ a²d²
6. bc ⇒ cb
7. bac ⇒ aca⁴ba²d²
8. b² ⇒ c