#2073 ⟨a, b | abbaaaab=ba⟩

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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. ad2c ⇒ d
  2. ca(dc)3 ⇒ ad
  3. da(dc)4 ⇒ ad3
  4. c2a(dc)2(cd)3c2 ⇒ acd
  5. a2d ⇒ ca(dc)2
  6. ad2ad ⇒ da(dc)3
  7. acadc ⇒ ca
  8. ad2acd ⇒ dca(dc)2(cd)3c2
  9. acad2 ⇒ c2adcdc2(dc)3
  10. adad3 ⇒ da(dc)3c(dc)3
  11. ada(dc)3 ⇒ cad(cd)2ad
  12. acda(dc)3 ⇒ c2adcdc2(dc)3ad
  13. ad3a(dc)3 ⇒ dad(cd)3ad
  14. ac2a(dc)2d2 ⇒ c2a(dcdc2)2(dc)3
  15. (adc)2dc(cd)3c2 ⇒ cad(cd)2acd
  16. acda(dc)2(cd)3c2 ⇒ c2a(dc)2(cd)3acd
  17. acdca(dc)2(cd)3c2 ⇒ c2adcdc2(dc)3acd
  18. ad3ca(dc)2(cd)3c2 ⇒ dad(cd)3acd
  19. ac(ad)2 ⇒ c2ad(cdc)2dc
  20. ac2ad(cd)2ad ⇒ c2a(dc)2(c(dc)2)2
  21. acadacd ⇒ c2adc(cd)3c2
  22. ac2ad(cd)2acd ⇒ c2ad(cdc)3dcdc2
  23. ac2a(dc)2ad3 ⇒ c2a(dcdc2)3(dc)3
  24. a3b ⇒ c
  25. bc ⇒ ada2b
  26. bd ⇒ ad3c
  27. ba ⇒ ad 
# ab:abbaaaab=ba reversed:cd/a/b aaab=c,bbac=d frequency:4/0,4/4
addc=d
cadcdcdc=ad
dadcdcdcdc=addd
ccadcdccdcdcdcc=acd
aad=cadcdc
addad=dadcdcdc
acadc=ca
addacd=dcadcdccdcdcdcc
acadd=ccadcdccdcdcdc
adaddd=dadcdcdccdcdcdc
adadcdcdc=cadcdcdad
acdadcdcdc=ccadcdccdcdcdcad
adddadcdcdc=dadcdcdcdad
accadcdcdd=ccadcdccdcdccdcdcdc
adcadcdccdcdcdcc=cadcdcdacd
acdadcdccdcdcdcc=ccadcdccdcdcdacd
acdcadcdccdcdcdcc=ccadcdccdcdcdcacd
adddcadcdccdcdcdcc=dadcdcdcdacd
acadad=ccadcdccdcdc
accadcdcdad=ccadcdccdcdccdcdc
acadacd=ccadccdcdcdcc
accadcdcdacd=ccadcdccdccdcdcdcc
accadcdcaddd=ccadcdccdcdccdcdccdcdcdc
aaab=c
bc=adaab
bd=adddc
ba=ad

Right Cayley graph (truncated)

Left Cayley graph (truncated)