〈a, b | abaaaaabab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: right-to-left c/d/ab
• Auxiliary generator aaaaa=c
• Auxiliary generator babab=d

Inverses of generators

• a^-1 = a⁴d
• b^-1 = a²c³bcbd³
• c^-1 = d
• d^-1 = c

Complete rewriting system

1. cd ⇒ 1
2. dc ⇒ 1
3. ac ⇒ ca
4. ad ⇒ da
5. bc⁴ ⇒ c⁴b
6. bd ⇒ d⁴bc³
7. ab ⇒ d³bc³a
8. b(cb)² ⇒ a³
9. a⁵ ⇒ c