#22279 ⟨a, b | aaa=1, abbabb=ba⟩

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Properties

Element profile

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. b10 ⇒ b
  2. b9ab ⇒ ab
  3. ab9 ⇒ b9a
  4. aba ⇒ b4ab3
  5. ab2a ⇒ bab7
  6. ab4a ⇒ b2ab8
  7. ab5a ⇒ b6ab5
  8. a2b ⇒ b3ab7a
  9. ab3ab ⇒ b(b6a)2
  10. ab7ab ⇒ b5ab3a
  11. ab6ab3 ⇒ bab8a
  12. ab8ab3 ⇒ b2a2
  13. a3 ⇒ 1
  14. ab3a2 ⇒ b5ab
  15. ab6a2 ⇒ (b5ab)2
  16. ab7a2 ⇒ b8ab2
  17. ab8a2 ⇒ b7ab4 
# ab:aaa=1,abbabb=ba reversed:b/a
bbbbbbbbbb=b
bbbbbbbbbab=ab
abbbbbbbbb=bbbbbbbbba
aba=bbbbabbb
abba=babbbbbbb
abbbba=bbabbbbbbbb
abbbbba=bbbbbbabbbbb
aab=bbbabbbbbbba
abbbab=bbbbbbbabbbbbba
abbbbbbbab=bbbbbabbba
abbbbbbabbb=babbbbbbbba
abbbbbbbbabbb=bbaa
aaa=1
abbbaa=bbbbbab
abbbbbbaa=bbbbbabbbbbbab
abbbbbbbaa=bbbbbbbbabb
abbbbbbbbaa=bbbbbbbabbbb

Right Cayley graph

Left Cayley graph