#23303 ⟨a, b | aaa=1, baba=abbb⟩

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Properties

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 ⇒ b7
  2. ab7 ⇒ b8
  3. bab4 ⇒ b9
  4. b5ab2 ⇒ b8
  5. b6ab ⇒ b8
  6. b7a ⇒ b8
  7. ba2b3 ⇒ ab4a
  8. (ba)2 ⇒ ab3
  9. b(ab2)2 ⇒ b7
  10. bab3ab ⇒ b7
  11. (b2a)2b ⇒ b7
  12. b5a2b ⇒ b8
  13. a3 ⇒ 1
  14. a(ab)2 ⇒ b3a2
  15. ab3a2 ⇒ bab
  16. ab6a2 ⇒ (bab)2
  17. b2a2b2ab ⇒ b8
  18. b4ab2a2b ⇒ b7
  19. ab4a2ba ⇒ ba2b2ab3
  20. b(b2a2)2 ⇒ a2b2ab
  21. b4(a2b)2 ⇒ b7
  22. (a2b)2bab3 ⇒ b4a2ba
  23. (ba2)2b2ab ⇒ b7 
# ab:aaa=1,baba=abbb b/a
bbbbbbbbbb=bbbbbbb
abbbbbbb=bbbbbbbb
babbbb=bbbbbbbbb
bbbbbabb=bbbbbbbb
bbbbbbab=bbbbbbbb
bbbbbbba=bbbbbbbb
baabbb=abbbba
baba=abbb
babbabb=bbbbbbb
babbbab=bbbbbbb
bbabbab=bbbbbbb
bbbbbaab=bbbbbbbb
aaa=1
aabab=bbbaa
abbbaa=bab
abbbbbbaa=babbab
bbaabbab=bbbbbbbb
bbbbabbaab=bbbbbbb
abbbbaaba=baabbabbb
bbbaabbaa=aabbab
bbbbaabaab=bbbbbbb
aabaabbabbb=bbbbaaba
baabaabbab=bbbbbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)