〈a, b | aabbbaaabb=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right a/e/d/cb
• Auxiliary generator bb=c
• Auxiliary generator baa=d
• Auxiliary generator cdac=e

Inverses of generators

• a^-1 = ea
• b^-1 = d²(ed)²a
• c^-1 = daded
• d^-1 = d(ed)²ade
• e^-1 = a²

Complete rewriting system

1. ea² ⇒ 1
2. ae ⇒ ea
3. aded² ⇒ d(ed)²a³
4. a²d(ed)² ⇒ da(de)²a
5. edaded ⇒ d(ed)²a
6. e(ad)²ed ⇒ ad(ed)²a
7. ead(ed)² ⇒ ded²e²a
8. ed²(ed)² ⇒ d(ed)²ade²a
9. ead²(ed)² ⇒ ad(ed)²ade²a
10. d²(ed)²ad ⇒ a²
11. edad²(ed)² ⇒ d(ed)²a²(de)²a
12. eadad²(ed)² ⇒ ad(ed)²a²(de)²a
13. c ⇒ (de)²
14. b ⇒ de