〈a, b | aaa=1, abbaabba=1〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a²
• b^-1 = ba²ca²
• c^-1 = a²ca²

Complete rewriting system

1. a³ ⇒ 1
2. ca²c ⇒ a
3. cb ⇒ bc
4. ca²b ⇒ aba²ca²
5. b² ⇒ c

Right Cayley graph (truncated)

Left Cayley graph (truncated)