#14293 ⟨a, b | abba=b, aaaaaa=1⟩

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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. dc ⇒ cd
  2. c3d3 ⇒ c
  3. c2d4 ⇒ d
  4. bc2d3 ⇒ b
  5. cb ⇒ bc
  6. cdb ⇒ dbc
  7. cd2b ⇒ d2bc
  8. d3b ⇒ bd3
  9. (db)2 ⇒ b2cd2
  10. d2b2 ⇒ bdbcd4
  11. b3 ⇒ c
  12. ca ⇒ ac
  13. da ⇒ a(bdb)2cd4
  14. ba ⇒ abdb2
  15. a2c ⇒ b2db2
  16. a2d ⇒ b2db2cd4
  17. a2b ⇒ b2d
  18. a6 ⇒ 1 
# ab:abba=b,aaaaaa=1 cd/b/a bbb=c,abababa=d frequency:3/1,7/0
dc=cd
cccddd=c
ccdddd=d
bccddd=b
cb=bc
cdb=dbc
cddb=ddbc
dddb=bddd
dbdb=bbcdd
ddbb=bdbcdddd
bbb=c
ca=ac
da=abdbbdbcdddd
ba=abdbb
aac=bbdbb
aad=bbdbbcdddd
aab=bbd
aaaaaa=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)