#533 ⟨a, b | aabba=baa⟩

Up:Monoids with two generators and one relation
Prev:#532 ⟨a, b | aabba=abb⟩
Next:#534 ⟨a, b | aabba=bab⟩

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. ca ⇒ ac
  2. a2 ⇒ c
  3. c2de ⇒ dc
  4. cd2 ⇒ da
  5. d2c ⇒ cdea
  6. d2a ⇒ cde
  7. (cd)2e ⇒ (da)2
  8. dade ⇒ ead2
  9. dacde ⇒ ea
  10. (cde)2 ⇒ dea
  11. dcdea ⇒ cdeacde
  12. c(de)2a ⇒ deacde
  13. deacdea ⇒ c(de)2c
  14. dad2 ⇒ e
  15. cded2 ⇒ de
  16. dead2 ⇒ c(de)2
  17. dadcde ⇒ eda
  18. cdedcde ⇒ deda
  19. deadcde ⇒ cd(ed)2a
  20. d3ea ⇒ cdeadecde
  21. cdeadecdea ⇒ d3ec
  22. cdeaded2 ⇒ d3e
  23. cdeadedcde ⇒ d3eda
  24. cdeac(de)2cdea ⇒ d4ec
  25. cdeac(de)2d2 ⇒ d4e
  26. d5e ⇒ cde(ade)2d2
  27. cdeacd(ed)2cde ⇒ d4eda
  28. bc ⇒ cd
  29. be ⇒ ed
  30. bac ⇒ cda
  31. bae ⇒ ced2
  32. bdc ⇒ (da)2
  33. badc ⇒ cea
  34. bda ⇒ dad
  35. bada ⇒ ce
  36. bde ⇒ daed2
  37. bade ⇒ cead4
  38. bd2e ⇒ daead4
  39. bad2e ⇒ ceaded2
  40. bd3e ⇒ daeaded2
  41. bad3e ⇒ ceac(de)2d2
  42. bd4e ⇒ daeac(de)2d2
  43. bad4e ⇒ ce(ade)2d2
  44. b2a ⇒ d 
# ab:aabba=baa reversed:cae/d/b aa=c,bba=d,bdad=e frequency:2/0,3/2,4/1
ca=ac
aa=c
ccde=dc
cdd=da
ddc=cdea
dda=cde
cdcde=dada
dade=eadd
dacde=ea
cdecde=dea
dcdea=cdeacde
cdedea=deacde
deacdea=cdedec
dadd=e
cdedd=de
deadd=cdede
dadcde=eda
cdedcde=deda
deadcde=cdededa
dddea=cdeadecde
cdeadecdea=dddec
cdeadedd=ddde
cdeadedcde=dddeda
cdeacdedecdea=ddddec
cdeacdededd=dddde
ddddde=cdeadeadedd
cdeacdededcde=ddddeda
bc=cd
be=ed
bac=cda
bae=cedd
bdc=dada
badc=cea
bda=dad
bada=ce
bde=daedd
bade=ceadddd
bdde=daeadddd
badde=ceadedd
bddde=daeadedd
baddde=ceacdededd
bdddde=daeacdededd
badddde=ceadeadedd
bba=d

Right Cayley graph (truncated)

Left Cayley graph (truncated)