〈a, b | ababaaabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: right-to-left d/e/b/c/a
• Auxiliary generator abaaa=c
• Auxiliary generator cbba=d
• Auxiliary generator bd=e

Inverses of generators

• a^-1 = e
• b^-1 = cde²d
• c^-1 = de³
• d^-1 = cde²ded²e²
• e^-1 = cde²

Complete rewriting system

1. de²d²ed ⇒ e
2. e³d²ed ⇒ de²d²e²
3. b ⇒ de²d²e
4. e³dc ⇒ 1
5. cd ⇒ ded³ed(ed²)²c
6. ce ⇒ e(ed²)²c
7. a ⇒ e²dc