〈a, b | aa=1, bbabbabb=a〉

Properties

• Infinite non-Abelian group

Completion parameters

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

Inverses of generators

• a^-1 = a
• b^-1 = bc²a
• c^-1 = c²

Complete rewriting system

1. a² ⇒ 1
2. c³ ⇒ 1
3. ab ⇒ cbc²a
4. acb ⇒ bac
5. b² ⇒ ac

Right Cayley graph (truncated)

Left Cayley graph (truncated)