#17663 ⟨a, b | aaaa=1, abbba=bb⟩

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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. db ⇒ bd
  2. cd ⇒ bd2
  3. dc ⇒ bd2
  4. b2d2 ⇒ d
  5. cbd ⇒ d
  6. b2c ⇒ b3d
  7. cb2 ⇒ b3d
  8. b4d ⇒ b2
  9. dac ⇒ dabd
  10. dab2d ⇒ da
  11. dabc ⇒ da
  12. dab3d ⇒ dab
  13. d5a ⇒ ad5
  14. bad ⇒ d2ab3
  15. babd ⇒ d2ab4
  16. bab2 ⇒ d2ab7
  17. bda ⇒ d3ab5
  18. bd2a ⇒ d4ab5
  19. bd3a ⇒ abd3
  20. bd4a ⇒ dabd3
  21. cad ⇒ d3ab3
  22. cabd ⇒ d3ab4
  23. cab2 ⇒ d3ab7
  24. b2a ⇒ d4ab10
  25. cba ⇒ abc
  26. ada ⇒ bd2
  27. da2c ⇒ da2bd
  28. da2b2d ⇒ da2
  29. da2bc ⇒ da2
  30. da2b3d ⇒ da2b
  31. dad2a ⇒ a2d4
  32. daba ⇒ a2bd2
  33. d4a2 ⇒ ad2ad
  34. ba2d ⇒ d2a2b3
  35. ba2bd ⇒ d2a2b4
  36. ba2b2 ⇒ d2a2b7
  37. ca2d ⇒ d3a2b3
  38. ca2bd ⇒ d3a2b4
  39. ca2c ⇒ d3a2b4
  40. ca2b2 ⇒ d3a2b7
  41. a3d ⇒ dab
  42. a3bd ⇒ dab2
  43. a3b2 ⇒ dab5
  44. da3 ⇒ d2ab3
  45. da2ba ⇒ da2d2ab5
  46. ba3c ⇒ d3ab7
  47. (ba)3 ⇒ a3c
  48. ca3 ⇒ (ab)3
  49. a4 ⇒ 1 
# ab:aaaa=1,abbba=bb d/bc/a abababa=c,bbcccc=d frequency:7/0,6/0
db=bd
cd=bdd
dc=bdd
bbdd=d
cbd=d
bbc=bbbd
cbb=bbbd
bbbbd=bb
dac=dabd
dabbd=da
dabc=da
dabbbd=dab
ddddda=addddd
bad=ddabbb
babd=ddabbbb
babb=ddabbbbbbb
bda=dddabbbbb
bdda=ddddabbbbb
bddda=abddd
bdddda=dabddd
cad=dddabbb
cabd=dddabbbb
cabb=dddabbbbbbb
bba=ddddabbbbbbbbbb
cba=abc
ada=bdd
daac=daabd
daabbd=daa
daabc=daa
daabbbd=daab
dadda=aadddd
daba=aabdd
ddddaa=addad
baad=ddaabbb
baabd=ddaabbbb
baabb=ddaabbbbbbb
caad=dddaabbb
caabd=dddaabbbb
caac=dddaabbbb
caabb=dddaabbbbbbb
aaad=dab
aaabd=dabb
aaabb=dabbbbb
daaa=ddabbb
daaba=daaddabbbbb
baaac=dddabbbbbbb
bababa=aaac
caaa=ababab
aaaa=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)