#19836 ⟨a, b | aaa=a, babb=aba⟩

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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. bab6 ⇒ bab2
  2. aba ⇒ bab2
  3. (ab2)2 ⇒ bab3a
  4. bab3ab4 ⇒ bab3a
  5. (bab4)2 ⇒ bab5a
  6. a3 ⇒ a
  7. bab2a2 ⇒ bab2
  8. bab4a2 ⇒ bab4
  9. b(b3a)3 ⇒ a(b3a)2
  10. (b5a)2b3a ⇒ bab5ab3a
  11. b(b4a)2b5a ⇒ bab4ab5a
  12. bab3a2b2 ⇒ a(b3a)2
  13. (b5a)2ab2 ⇒ bab5a2b2
  14. a(b3ab)2b ⇒ (b3a)3
  15. bab5a2b6 ⇒ bab5a2b2
  16. a2(b3a)2 ⇒ bab5a2b2
  17. a(b3a)3 ⇒ bab5a2b3a
  18. ab(b2ab3)2a ⇒ (b4a)2b5a
  19. ab4ab5ab3a ⇒ b3ab5a2b2
  20. b(ab5a)2 ⇒ (b3a)3
  21. (ab4)3ba ⇒ b(b2ab3)2a
  22. ab3ab5a2b2 ⇒ b4ab5ab3a
  23. ab4ab5a2b2 ⇒ b3ab5a2b3a
  24. bab5a2b4ab2 ⇒ bab4ab5a
  25. bab5a2b3ab4 ⇒ bab5a2b3a
  26. bab3(b2a2)2 ⇒ bab5a2b2
  27. bab(b4a2)2 ⇒ bab5a2b4
  28. bab4(ba2b2)2 ⇒ b(b2ab3)2a 
# ab:aaa=a,babb=aba reversed:b/a
babbbbbb=babb
aba=babb
abbabb=babbba
babbbabbbb=babbba
babbbbbabbbb=babbbbba
aaa=a
babbaa=babb
babbbbaa=babbbb
bbbbabbbabbba=abbbabbba
bbbbbabbbbbabbba=babbbbbabbba
bbbbbabbbbabbbbba=babbbbabbbbba
babbbaabb=abbbabbba
bbbbbabbbbbaabb=babbbbbaabb
abbbabbbbabb=bbbabbbabbba
babbbbbaabbbbbb=babbbbbaabb
aabbbabbba=babbbbbaabb
abbbabbbabbba=babbbbbaabbba
abbbabbbbbabbba=bbbbabbbbabbbbba
abbbbabbbbbabbba=bbbabbbbbaabb
babbbbbaabbbbba=bbbabbbabbba
abbbbabbbbabbbbba=bbbabbbbbabbba
abbbabbbbbaabb=bbbbabbbbbabbba
abbbbabbbbbaabb=bbbabbbbbaabbba
babbbbbaabbbbabb=babbbbabbbbba
babbbbbaabbbabbbb=babbbbbaabbba
babbbbbaabbaa=babbbbbaabb
babbbbbaabbbbaa=babbbbbaabbbb
babbbbbaabbbaabb=bbbabbbbbabbba

Right Cayley graph (truncated)

Left Cayley graph (truncated)