#995 ⟨a, b | abbaaab=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)2 ⇒ ad
  3. da(dc)3 ⇒ ad3
  4. c2adc(cd)2c2 ⇒ acd
  5. a2d ⇒ cadc
  6. ad2ad ⇒ da(dc)2
  7. acadc ⇒ ca
  8. ad2acd ⇒ dcadc(cd)2c2
  9. acad2 ⇒ c2adc2(dc)2
  10. adad3 ⇒ dad(cdc)2dc
  11. ada(dc)2 ⇒ cadcdad
  12. acda(dc)2 ⇒ c2adc2(dc)2ad
  13. ad3a(dc)2 ⇒ dad(cd)2ad
  14. ac2adcd2 ⇒ c2a(dc2)2(dc)2
  15. (adc)2(cd)2c2 ⇒ cadcdacd
  16. acdadc(cd)2c2 ⇒ c2adc(cd)2acd
  17. acdcadc(cd)2c2 ⇒ c2adc2(dc)2acd
  18. ad3cadc(cd)2c2 ⇒ dad(cd)2acd
  19. ac(ad)2 ⇒ c2adc2dc
  20. ac2adcdad ⇒ c2ad(c2d)2c
  21. acadacd ⇒ c2a(cd)2c2
  22. ac2adcdacd ⇒ c2adc3dcdc2
  23. ac(cad)2d2 ⇒ c2a(dc2)3(dc)2
  24. a2b ⇒ c
  25. bc ⇒ adab
  26. bd ⇒ ad3c
  27. ba ⇒ ad 
# ab:abbaaab=ba reversed:cd/a/b aab=c,bbac=d frequency:3/0,4/3
addc=d
cadcdc=ad
dadcdcdc=addd
ccadccdcdcc=acd
aad=cadc
addad=dadcdc
acadc=ca
addacd=dcadccdcdcc
acadd=ccadccdcdc
adaddd=dadcdccdcdc
adadcdc=cadcdad
acdadcdc=ccadccdcdcad
adddadcdc=dadcdcdad
accadcdd=ccadccdccdcdc
adcadccdcdcc=cadcdacd
acdadccdcdcc=ccadccdcdacd
acdcadccdcdcc=ccadccdcdcacd
adddcadccdcdcc=dadcdcdacd
acadad=ccadccdc
accadcdad=ccadccdccdc
acadacd=ccacdcdcc
accadcdacd=ccadcccdcdcc
accadcaddd=ccadccdccdccdcdc
aab=c
bc=adab
bd=adddc
ba=ad

Right Cayley graph (truncated)

Left Cayley graph (truncated)