〈a, b | aaaa=1, bbabb=a〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a³
• b^-1 = ba²ca
• c^-1 = a²c

Complete rewriting system

1. c² ⇒ a²
2. ca² ⇒ a²c
3. a⁴ ⇒ 1
4. cb ⇒ aba³c
5. cab ⇒ a²ba²ca
6. b² ⇒ a³c

Right Cayley graph (truncated)

Left Cayley graph (truncated)