#22860 ⟨a, b | aaa=1, bbbbb=aba⟩

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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. c3d ⇒ c
  3. c2d2 ⇒ d
  4. cac2d ⇒ ca
  5. da ⇒ cacd2
  6. c3a ⇒ ac3
  7. ca2c2d ⇒ ca2
  8. (ca)2 ⇒ a2c8
  9. c2a2 ⇒ (ac)2d3
  10. a3 ⇒ 1
  11. bc2d ⇒ b
  12. bac2d ⇒ ba
  13. ba2c2d ⇒ ba2
  14. cb ⇒ bc
  15. db ⇒ bd
  16. ab ⇒ b(ac)2d3
  17. b2 ⇒ c 
# ab:aaa=1,bbbbb=aba cd/a/b bb=c,aaccaaccaa=d frequency:2/1,10/0
dc=cd
cccd=c
ccdd=d
caccd=ca
da=cacdd
ccca=accc
caaccd=caa
caca=aacccccccc
ccaa=acacddd
aaa=1
bccd=b
baccd=ba
baaccd=baa
cb=bc
db=bd
ab=bacacddd
bb=c

Right Cayley graph (truncated)

Left Cayley graph (truncated)