〈a, b | aaabb=1, abbaa=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right bac
• Auxiliary generator bb=c

Inverses of generators

• a^-1 = a²c
• b^-1 = ba³
• c^-1 = a³

Complete rewriting system

1. b² ⇒ c
2. cb ⇒ bc
3. ca ⇒ ac
4. a³b ⇒ ba³
5. a³c ⇒ 1

Right Cayley graph (truncated)

Left Cayley graph (truncated)