〈a, b | abaaaabaab=1〉

Properties

• Infinite non-Abelian group

Completion parameters

• Reduction order: right-to-left dc/ab
• Auxiliary generator aba=c
• Auxiliary generator aa=d

Inverses of generators

• a^-1 = bc²d
• b^-1 = (c²d)²c
• c^-1 = b(c²d)²
• d^-1 = bc⁴dc

Complete rewriting system

1. dcdc² ⇒ cdc²d
2. d²c³dc² ⇒ cdc³dcd
3. (cdc²)² ⇒ d
4. a ⇒ cdc²
5. d²c²b ⇒ cdc²
6. d(dc²)²b ⇒ cdc³dc
7. c(dc²)²b ⇒ 1
8. bd ⇒ dc²(cdc⁴)²b
9. bc ⇒ cdc⁶b