#2068 ⟨a, b | ababbbba=ab⟩

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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. ac2a ⇒ ac
  2. c3a ⇒ c2
  3. abac ⇒ ab
  4. abca ⇒ ab
  5. abc2a ⇒ abc
  6. cbac ⇒ cb
  7. cbca ⇒ cb
  8. cbc2a ⇒ cbc
  9. ac2b ⇒ abc2
  10. c3b ⇒ cbc2
  11. ab2ac ⇒ ab2
  12. ab2ca ⇒ ab2
  13. ab2c2a ⇒ ab2c
  14. abcb ⇒ (ab)2c2
  15. abc2b ⇒ ab2c2
  16. cb2ac ⇒ cb2
  17. cb2ca ⇒ cb2
  18. cb2c2a ⇒ cb2c
  19. (cb)2 ⇒ cbabc2
  20. cbc2b ⇒ cb2c2
  21. ab3ac ⇒ ab3
  22. ab3ca ⇒ ab3
  23. ab3c2a ⇒ ab3c
  24. ab2cb ⇒ ab2abc2
  25. ab2c2b ⇒ ab3c2
  26. cb3ac ⇒ cb3
  27. cb3ca ⇒ cb3
  28. cb3c2a ⇒ cb3c
  29. cb2cb ⇒ cb2abc2
  30. cb2c2b ⇒ cb3c2
  31. b4a ⇒ c
  32. ab4 ⇒ ac2
  33. ab3cb ⇒ ab3abc2
  34. ab3c2b ⇒ ac4
  35. cb4 ⇒ c3
  36. cb3cb ⇒ cb3abc2
  37. cb3c2b ⇒ c5 
# ab:ababbbba=ab ac/b bbbba=c frequency:5/0
acca=ac
ccca=cc
abac=ab
abca=ab
abcca=abc
cbac=cb
cbca=cb
cbcca=cbc
accb=abcc
cccb=cbcc
abbac=abb
abbca=abb
abbcca=abbc
abcb=ababcc
abccb=abbcc
cbbac=cbb
cbbca=cbb
cbbcca=cbbc
cbcb=cbabcc
cbccb=cbbcc
abbbac=abbb
abbbca=abbb
abbbcca=abbbc
abbcb=abbabcc
abbccb=abbbcc
cbbbac=cbbb
cbbbca=cbbb
cbbbcca=cbbbc
cbbcb=cbbabcc
cbbccb=cbbbcc
bbbba=c
abbbb=acc
abbbcb=abbbabcc
abbbccb=acccc
cbbbb=ccc
cbbbcb=cbbbabcc
cbbbccb=ccccc

Right Cayley graph (truncated)

Left Cayley graph (truncated)