#922 ⟨a, b | aaabbba=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. cb3 ⇒ cacbc
  2. ab2 ⇒ c
  3. cacb2 ⇒ (cb)2a
  4. ca(cb)2 ⇒ cbacbc
  5. cacba ⇒ cb
  6. a2cbc ⇒ cb
  7. (cb)2ab ⇒ c(ac)2bc
  8. cbacb2 ⇒ cb2cba
  9. cba(cb)2 ⇒ cb2acbc
  10. (cba)2 ⇒ cb2
  11. abacbc ⇒ cb2
  12. a2cb2 ⇒ abcba
  13. a2cba ⇒ ab
  14. cb2cbab ⇒ cb(ac)2bc
  15. cb2acb2 ⇒ cacbc2ba
  16. cb2a(cb)2 ⇒ c(acbc)2
  17. cb2acba ⇒ cacbc
  18. cbacbcab ⇒ c(ac)3bc
  19. abcbab ⇒ a(ac)2bc
  20. cacbc2bab ⇒ cb2(ac)2bc
  21. abacb2 ⇒ c2ba
  22. abacba ⇒ c
  23. ab(ac)2bc ⇒ c2bab
  24. cac(acbc)2 ⇒ (cb)3b
  25. a(ac)3bc ⇒ cb2ab
  26. c(ac)4bc ⇒ c(bc)2ab
  27. cb2acbcab ⇒ cb(ac)3bc
  28. cbacbc2bab ⇒ cacbc(ac)2bc
  29. cbac(acbc)2 ⇒ cb(bc)2b2
  30. cb(ac)4bc ⇒ cb(bc)2ab
  31. ca(cbca)2b ⇒ cb2(ac)3bc
  32. ab(ac)3bc ⇒ cacbcab
  33. c((ac)2bc)2 ⇒ (cb)2c2bab
  34. a2c(acbc)2 ⇒ a(bc)2b2
  35. a(ac)4bc ⇒ a(bc)2ab
  36. cb2acbc2bab ⇒ cbacbc(ac)2bc
  37. cb2ac(acbc)2 ⇒ ca(cbc)2b2
  38. cb2(ac)4bc ⇒ ca(cbc)2ab
  39. cba(cbca)2b ⇒ cacbc(ac)3bc
  40. cb((ac)2bc)2 ⇒ cb2cbc2bab
  41. ab(ac)4bc ⇒ c2bcab
  42. c(ac)2bc(ac)3bc ⇒ cb(cbca)2b
  43. a((ac)2bc)2 ⇒ abcbc2bab
  44. cb2a(cbca)2b ⇒ cbacbc(ac)3bc
  45. cb2((ac)2bc)2 ⇒ cacb(c2b)2ab
  46. cb(ac)2bc(ac)3bc ⇒ cb2(cbca)2b
  47. a(ac)2bc(ac)3bc ⇒ ab(cbca)2b
  48. cb2(ac)2bc(ac)3bc ⇒ cacbc(cbca)2b 
# ab:aaabbba=ab c/ba abb=c frequency:3/1
cbbb=cacbc
abb=c
cacbb=cbcba
cacbcb=cbacbc
cacba=cb
aacbc=cb
cbcbab=cacacbc
cbacbb=cbbcba
cbacbcb=cbbacbc
cbacba=cbb
abacbc=cbb
aacbb=abcba
aacba=ab
cbbcbab=cbacacbc
cbbacbb=cacbccba
cbbacbcb=cacbcacbc
cbbacba=cacbc
cbacbcab=cacacacbc
abcbab=aacacbc
cacbccbab=cbbacacbc
abacbb=ccba
abacba=c
abacacbc=ccbab
cacacbcacbc=cbcbcbb
aacacacbc=cbbab
cacacacacbc=cbcbcab
cbbacbcab=cbacacacbc
cbacbccbab=cacbcacacbc
cbacacbcacbc=cbbcbcbb
cbacacacacbc=cbbcbcab
cacbcacbcab=cbbacacacbc
abacacacbc=cacbcab
cacacbcacacbc=cbcbccbab
aacacbcacbc=abcbcbb
aacacacacbc=abcbcab
cbbacbccbab=cbacbcacacbc
cbbacacbcacbc=cacbccbcbb
cbbacacacacbc=cacbccbcab
cbacbcacbcab=cacbcacacacbc
cbacacbcacacbc=cbbcbccbab
abacacacacbc=ccbcab
cacacbcacacacbc=cbcbcacbcab
aacacbcacacbc=abcbccbab
cbbacbcacbcab=cbacbcacacacbc
cbbacacbcacacbc=cacbccbccbab
cbacacbcacacacbc=cbbcbcacbcab
aacacbcacacacbc=abcbcacbcab
cbbacacbcacacacbc=cacbccbcacbcab

Right Cayley graph (truncated)

Left Cayley graph (truncated)