〈a, b | aaa=1, babaabb=a〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right c/ab
• Auxiliary generator aab=c

Inverses of generators

• a^-1 = a²
• b^-1 = ca²c²
• c^-1 = c³

Complete rewriting system

1. c⁴ ⇒ 1
2. c²a ⇒ ac²
3. b ⇒ ac
4. a³ ⇒ 1

Right Cayley graph (truncated)

Left Cayley graph (truncated)