〈a, b | abababbbba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right d/b/ca
• Auxiliary generator aa=c
• Auxiliary generator ba=d

Inverses of generators

• a^-1 = d²b³d
• b^-1 = cd²b³
• c^-1 = d²b⁴
• d^-1 = cd²b³d³b³

Complete rewriting system

1. d³b³d ⇒ b
2. d³b⁴ ⇒ bd²b³d
3. cd²b⁴ ⇒ 1
4. dc ⇒ cd²(d³b²)²d
5. bc ⇒ cd⁵b²d³b³
6. a ⇒ cd²b³d