#1932 ⟨a, b | aaabbbba=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. ab2 ⇒ c
  2. cb3 ⇒ cacb2c
  3. cacb2a ⇒ cb
  4. a2cb2c ⇒ cb
  5. c(ac)2b2c ⇒ cbcb2a
  6. cacb2cb ⇒ cbacb2c
  7. a2cb2a ⇒ ab
  8. cbacb2a ⇒ cb2
  9. a(ac)2b2c ⇒ abcb2a
  10. cb(ac)2b2c ⇒ (cb2)2a
  11. abacb2c ⇒ cb2
  12. c(acb)2bc ⇒ cbcb2ab
  13. cbacb2cb ⇒ cb2acb2c
  14. abacb2a ⇒ c
  15. (cb2a)2 ⇒ cacb2c
  16. ab(ac)2b2c ⇒ c2b2a
  17. cb2(ac)2b2c ⇒ cacb2c2b2a
  18. a(acb)2bc ⇒ abcb2ab
  19. c(bac)2b2c ⇒ (cb2)2ab
  20. cb2acb2cb ⇒ c(acb2c)2
  21. a(bac)2b2c ⇒ c2b2ab
  22. cb(bac)2b2c ⇒ cacb2c2b2ab 
# ab:aaabbbba=ab reversed:c/ab abb=c frequency:3/2
abb=c
cbbb=cacbbc
cacbba=cb
aacbbc=cb
cacacbbc=cbcbba
cacbbcb=cbacbbc
aacbba=ab
cbacbba=cbb
aacacbbc=abcbba
cbacacbbc=cbbcbba
abacbbc=cbb
cacbacbbc=cbcbbab
cbacbbcb=cbbacbbc
abacbba=c
cbbacbba=cacbbc
abacacbbc=ccbba
cbbacacbbc=cacbbccbba
aacbacbbc=abcbbab
cbacbacbbc=cbbcbbab
cbbacbbcb=cacbbcacbbc
abacbacbbc=ccbbab
cbbacbacbbc=cacbbccbbab

Right Cayley graph (truncated)

Left Cayley graph (truncated)