#2087 ⟨a, b | abbbaaab=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. (cd)3b ⇒ d
  2. cd(cdc)2dbc ⇒ db
  3. (cd)2(c(cd)2)2bd ⇒ d2(cd)2b
  4. (c(cd)2)2(c2d)2cdbc2 ⇒ dcb
  5. db2 ⇒ (cd)2bc
  6. dbd(cd)2b ⇒ cd(cdc)2dbd
  7. dcbd(cd)2b ⇒ (c(cd)2)2(c2d)2cdbcd
  8. d2cdbcb ⇒ cd(cdc)2d((c2d)2cd)2bc2
  9. c(cd)2bcb ⇒ bc
  10. d(cd)2bcb ⇒ (cd)2c2d(cdc)3dbc2
  11. d2((cd)2b)2 ⇒ cd((cdc)2dc)2(cd)2bd
  12. cd(cdc)2(db)2 ⇒ dbd(cdc)2dbc
  13. cd(cdc)2dbdcb ⇒ db(cd)2c2d(cdc)3dbc2
  14. cd(cdc)2dbd2(cd)2b ⇒ dbdcd(c(cd)2)2bd
  15. (c(cd)2)2(c2d)2(cdb)2 ⇒ dcbd(cdc)2dbc
  16. (c(cd)2)2(c2d)2cdbdcb ⇒ dcbdcdc2d(cdc)3dbc2
  17. (c(cd)2)2(c2d)2cdbcdcb ⇒ dcb(cd)2c2d(cdc)3dbc2
  18. (c(cd)2)2(c2d)2cdbcd2(cd)2b ⇒ dcbdcd(c(cd)2)2bd
  19. dbdcdbcb ⇒ (cd)2((c2d)2cd)2bc2
  20. db(cd)2bcb ⇒ cd(cdc)3dbc2
  21. dcbdcdbcb ⇒ (c(cd)2)2(c2d)3cdbc2
  22. dcb(cd)2bcb ⇒ c2d(cdc2d)2bc2
  23. d(dc)2(dbc)2b ⇒ cd(cdc)2d((c2d)2cd)3bc2
  24. ab2 ⇒ c
  25. ca ⇒ abcdb
  26. da ⇒ cd2
  27. ba ⇒ cdb 
# ab:abbbaaab=ba cd/b/a abb=c,baaa=d frequency:3/1,4/6
cdcdcdb=d
cdcdccdcdbc=db
cdcdccdcdccdcdbd=ddcdcdb
ccdcdccdcdccdccdcdbcc=dcb
dbb=cdcdbc
dbdcdcdb=cdcdccdcdbd
dcbdcdcdb=ccdcdccdcdccdccdcdbcd
ddcdbcb=cdcdccdcdccdccdcdccdccdcdbcc
ccdcdbcb=bc
dcdcdbcb=cdcdccdcdccdccdcdbcc
ddcdcdbcdcdb=cdcdccdcdccdccdcdccdcdbd
cdcdccdcdbdb=dbdcdccdcdbc
cdcdccdcdbdcb=dbcdcdccdcdccdccdcdbcc
cdcdccdcdbddcdcdb=dbdcdccdcdccdcdbd
ccdcdccdcdccdccdcdbcdb=dcbdcdccdcdbc
ccdcdccdcdccdccdcdbdcb=dcbdcdccdcdccdccdcdbcc
ccdcdccdcdccdccdcdbcdcb=dcbcdcdccdcdccdccdcdbcc
ccdcdccdcdccdccdcdbcddcdcdb=dcbdcdccdcdccdcdbd
dbdcdbcb=cdcdccdccdcdccdccdcdbcc
dbcdcdbcb=cdcdccdccdcdbcc
dcbdcdbcb=ccdcdccdcdccdccdccdcdbcc
dcbcdcdbcb=ccdcdccdcdccdbcc
ddcdcdbcdbcb=cdcdccdcdccdccdcdccdccdcdccdccdcdbcc
abb=c
ca=abcdb
da=cdd
ba=cdb

Right Cayley graph (truncated)

Left Cayley graph (truncated)