〈a, b | aabbabaaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right bdc/a
• Auxiliary generator aaa=c
• Auxiliary generator aabba=d

Inverses of generators

• a^-1 = a²bdb
• b^-1 = dbc
• c^-1 = bdb
• d^-1 = bcb

Complete rewriting system

1. cbd ⇒ dbc
2. bdbc ⇒ 1
3. dbcb ⇒ 1
4. ca ⇒ ac
5. b²a ⇒ a(bd)²
6. dba ⇒ babcb
7. da² ⇒ a²b²c
8. cba² ⇒ babcba(dbc)²
9. a³ ⇒ c