〈a, b | abbababbba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right cbe/da
• Auxiliary generator bb=c
• Auxiliary generator aa=d
• Auxiliary generator ab=e

Inverses of generators

• a^-1 = ebe²c
• b^-1 = dce²b
• c^-1 = dce²
• d^-1 = ce²c
• e^-1 = dce(eb)²e²c

Complete rewriting system

1. bc ⇒ cb
2. b² ⇒ c
3. ebe²c² ⇒ ce²ceb
4. ebe²cb ⇒ ce²ce
5. ebe²ce ⇒ b
6. dce²c ⇒ 1
7. cd ⇒ dce²(bebe²)²
8. bd ⇒ dce(e²b)²ebe²
9. ed ⇒ d(ebe²)²bebe²
10. a ⇒ debe²c