〈a, b | aababaaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: right-to-left c/a/b
• Auxiliary generator aba=c

Inverses of generators

• a^-1 = bc²a
• b^-1 = (ac)²
• c^-1 = baca

Complete rewriting system

1. cac² ⇒ a
2. a²c² ⇒ (ca)²
3. (ca)²b ⇒ 1
4. a²cab ⇒ cac
5. bc ⇒ c⁴b
6. ba ⇒ ac⁶b