#17137 ⟨a, b | aaaa=1, abbbba=b⟩

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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. cd2 ⇒ d
  2. dc ⇒ cd
  3. c2d ⇒ c
  4. bcd ⇒ b
  5. db ⇒ bd
  6. cb ⇒ bc
  7. b2 ⇒ c
  8. dacd ⇒ da
  9. d5a ⇒ ad5
  10. ca ⇒ d4ac5
  11. cda ⇒ acd
  12. ba ⇒ d2abc2
  13. bda ⇒ d3abc2
  14. bd2a ⇒ d4abc2
  15. bd3a ⇒ abd3
  16. bd4a ⇒ dabd3
  17. ad3a ⇒ bd5
  18. da2cd ⇒ da2
  19. d2a2 ⇒ adac2
  20. d3ada ⇒ a2d7
  21. a3d ⇒ d3abc3
  22. a3c ⇒ d3abc5
  23. a3b ⇒ d3ac5
  24. a(da)2 ⇒ d2abd5
  25. da3 ⇒ d4abc4
  26. a4 ⇒ 1 
# ab:aaaa=1,abbbba=b d/c/b/a bb=c,abcabcabcab=d frequency:2/1,11/0
cdd=d
dc=cd
ccd=c
bcd=b
db=bd
cb=bc
bb=c
dacd=da
ddddda=addddd
ca=ddddaccccc
cda=acd
ba=ddabcc
bda=dddabcc
bdda=ddddabcc
bddda=abddd
bdddda=dabddd
addda=bddddd
daacd=daa
ddaa=adacc
dddada=aaddddddd
aaad=dddabccc
aaac=dddabccccc
aaab=dddaccccc
adada=ddabddddd
daaa=ddddabcccc
aaaa=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)