〈a, b | abbaaabaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: right-to-left bdc/a
• Auxiliary generator aa=c
• Auxiliary generator abbca=d

Inverses of generators

• a^-1 = abdb
• b^-1 = dbc
• c^-1 = bdb
• d^-1 = bcb

Complete rewriting system

1. dbc ⇒ cbd
2. cbdb ⇒ 1
3. bcbd ⇒ 1
4. ad ⇒ cb²ca
5. ac ⇒ ca
6. ab² ⇒ d(bdb)²a
7. abd ⇒ (cb)²ab
8. abc ⇒ b(dcb)²cbab
9. a² ⇒ c