#2723 ⟨a, b | abbba=abbab⟩

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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. cab ⇒ cba
  2. c2b ⇒ cbc
  3. cbab ⇒ ab2c
  4. cbca ⇒ cbac
  5. c3a ⇒ c2ac
  6. ab2ab ⇒ ab3a
  7. ab2cb ⇒ ab3c
  8. cba2b ⇒ ab2ca
  9. cbacb ⇒ ab2c2
  10. (cb)2a ⇒ ab2c2
  11. cbc2a ⇒ cbac2
  12. c2a2b ⇒ cbaca
  13. c2acb ⇒ cbac2
  14. ab3ab2 ⇒ c
  15. ab3cba ⇒ ab3abc
  16. ab3c2a ⇒ ab3cac
  17. ab3(ab)2 ⇒ ca
  18. ab3abcb ⇒ c2
  19. ab3ca2b ⇒ ab3abca
  20. ab3cacb ⇒ ab3abc2 
# ab:abbba=abbab bac abbbabb=c frequency:7/0
cab=cba
ccb=cbc
cbab=abbc
cbca=cbac
ccca=ccac
abbab=abbba
abbcb=abbbc
cbaab=abbca
cbacb=abbcc
cbcba=abbcc
cbcca=cbacc
ccaab=cbaca
ccacb=cbacc
abbbabb=c
abbbcba=abbbabc
abbbcca=abbbcac
abbbabab=ca
abbbabcb=cc
abbbcaab=abbbabca
abbbcacb=abbbabcc

Right Cayley graph (truncated)

Left Cayley graph (truncated)