〈a, b | aaa=a, babbab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right ac/b
• Auxiliary generator bba=c

Inverses of generators

• a^-1 = a
• b^-1 = bac
• c^-1 = c

Complete rewriting system

1. a² ⇒ 1
2. c² ⇒ 1
3. cb ⇒ abac
4. cab ⇒ bca
5. b² ⇒ ca

Right Cayley graph (truncated)

Left Cayley graph (truncated)