〈a, b | aaabbabbaa=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a³d
• b^-1 = aca⁵b
• c^-1 = aca⁵
• d^-1 = a⁴

Complete rewriting system

1. ad ⇒ da
2. da⁴ ⇒ 1
3. cd ⇒ dc
4. ca⁴ ⇒ a⁴c
5. cac ⇒ d²a³
6. cb ⇒ bc
7. cab ⇒ d²a³ba⁵ca
8. b² ⇒ c