#1875 ⟨a, b | aaaabbba=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. b2a ⇒ c
  2. cb3 ⇒ c2a2bc
  3. c2a2bca ⇒ cbc
  4. ca3bc ⇒ cb
  5. c2a2bcb ⇒ cbca2bc
  6. c2a2b2c ⇒ c(bca)2
  7. ab3 ⇒ aca2bc
  8. aca2bca ⇒ abc
  9. cbca2bca ⇒ cb2c
  10. a4bc ⇒ ab
  11. c(ca2)2bc2 ⇒ cbcabcba
  12. cba3bc ⇒ cb2
  13. aca2bcb ⇒ abca2bc
  14. ca3b2c ⇒ cba2bca
  15. aca2b2c ⇒ a(bca)2
  16. cbca2bcb ⇒ cb2ca2bc
  17. cbca2b2c ⇒ cb(bca)2
  18. (abca)2 ⇒ ab2c
  19. cb2ca2bca ⇒ c2a2bc2
  20. ca3ca2bc2 ⇒ cba2bcba
  21. a(ca2)2bc2 ⇒ (abc)2ba
  22. cb(ca2)2bc2 ⇒ cb2cabcba
  23. aba3bc ⇒ ab2
  24. a4b2c ⇒ aba2bca
  25. cba3b2c ⇒ c2abca
  26. abca2bcb ⇒ ab2ca2bc
  27. abca2b2c ⇒ ab(bca)2
  28. cb2ca2bcb ⇒ (c2a2b)2c
  29. cb2ca2b2c ⇒ c2a2bc2abca
  30. ab2ca2bca ⇒ aca2bc2
  31. a4ca2bc2 ⇒ aba2bcba
  32. cba3ca2bc2 ⇒ c2abcba
  33. ab(ca2)2bc2 ⇒ ab2cabcba
  34. cb2(ca2)2bc2 ⇒ c2a2bc2abcba
  35. aba3b2c ⇒ acabca
  36. ab2ca2bcb ⇒ a(ca2bc)2
  37. ab2ca2b2c ⇒ aca2bc2abca
  38. aba3ca2bc2 ⇒ acabcba
  39. ab2(ca2)2bc2 ⇒ aca2bc2abcba 
# ab:aaaabbba=ab reversed:c/ab bba=c frequency:3/0
bba=c
cbbb=ccaabc
ccaabca=cbc
caaabc=cb
ccaabcb=cbcaabc
ccaabbc=cbcabca
abbb=acaabc
acaabca=abc
cbcaabca=cbbc
aaaabc=ab
ccaacaabcc=cbcabcba
cbaaabc=cbb
acaabcb=abcaabc
caaabbc=cbaabca
acaabbc=abcabca
cbcaabcb=cbbcaabc
cbcaabbc=cbbcabca
abcaabca=abbc
cbbcaabca=ccaabcc
caaacaabcc=cbaabcba
acaacaabcc=abcabcba
cbcaacaabcc=cbbcabcba
abaaabc=abb
aaaabbc=abaabca
cbaaabbc=ccabca
abcaabcb=abbcaabc
abcaabbc=abbcabca
cbbcaabcb=ccaabccaabc
cbbcaabbc=ccaabccabca
abbcaabca=acaabcc
aaaacaabcc=abaabcba
cbaaacaabcc=ccabcba
abcaacaabcc=abbcabcba
cbbcaacaabcc=ccaabccabcba
abaaabbc=acabca
abbcaabcb=acaabccaabc
abbcaabbc=acaabccabca
abaaacaabcc=acabcba
abbcaacaabcc=acaabccabcba

Right Cayley graph (truncated)

Left Cayley graph (truncated)