〈a, b | abaabbba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = bdca
• b^-1 = bd²
• c^-1 = d²
• d^-1 = dc

Complete rewriting system

1. cd ⇒ dc
2. d²c ⇒ 1
3. cb ⇒ bc
4. d²b ⇒ bd²
5. b² ⇒ c
6. ab ⇒ bdcad
7. adb ⇒ dbd²ac
8. a² ⇒ dbd²