#1459 ⟨a, b | aabbbaaabb=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. ea2 ⇒ 1
  2. ae ⇒ ea
  3. aded2 ⇒ d(ed)2a3
  4. a2d(ed)2 ⇒ da(de)2a
  5. edaded ⇒ d(ed)2a
  6. e(ad)2ed ⇒ ad(ed)2a
  7. ead(ed)2 ⇒ ded2e2a
  8. ed2(ed)2 ⇒ d(ed)2ade2a
  9. ead2(ed)2 ⇒ ad(ed)2ade2a
  10. d2(ed)2ad ⇒ a2
  11. edad2(ed)2 ⇒ d(ed)2a2(de)2a
  12. eadad2(ed)2 ⇒ ad(ed)2a2(de)2a
  13. c ⇒ (de)2
  14. b ⇒ de 
# ab:aabbbaaabb=1 a/e/d/cb bb=c,baa=d,cdac=e frequency:2/0,3/2,4/0
eaa=1
ae=ea
adedd=dededaaa
aadeded=dadedea
edaded=dededa
eadaded=adededa
eadeded=deddeea
eddeded=dededadeea
eaddeded=adededadeea
ddededad=aa
edaddeded=dededaadedea
eadaddeded=adededaadedea
c=dede
b=de

Right Cayley graph (truncated)

Left Cayley graph (truncated)