〈a, b | aaaa=1, babab=a〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: left-to-right ab

Inverses of generators

• a^-1 = a³
• b^-1 = a³(ba)²

Complete rewriting system

1. ba² ⇒ a²b
2. a⁴ ⇒ 1
3. b(ab)² ⇒ a

Right Cayley graph (truncated)

Left Cayley graph (truncated)