〈a, b | aaaa=bbb, abab=1〉

Properties

• Finite non-Abelian group with 336 elements

Completion parameters

• Reduction order: left-to-right a/b

Inverses of generators

• a^-1 = a⁵⁵
• b^-1 = aba

Complete rewriting system

1. a⁵⁶ ⇒ 1
2. a⁴b ⇒ ba⁴
3. b² ⇒ aba⁵
4. bab ⇒ a⁵⁵
5. ba²b ⇒ a³ba⁴⁷
6. aba³b ⇒ ba³ba⁴³

Right Cayley graph

Left Cayley graph