#10660 ⟨a, b | aaaa=bab, bbbb=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. da4 ⇒ a
  2. ad ⇒ da
  3. d2a3 ⇒ d
  4. abda3 ⇒ ab
  5. a5b ⇒ ba5
  6. db ⇒ a2bd2a
  7. dab ⇒ a3bd2a
  8. da2b ⇒ a4bd2a
  9. da3b ⇒ bda3
  10. ca ⇒ abd
  11. cd ⇒ abd3a2
  12. ac ⇒ a2bd2a2
  13. dc ⇒ a3bd3
  14. bab ⇒ a4
  15. ab2da3 ⇒ ab2
  16. aba2b ⇒ b2a9
  17. a4b2 ⇒ ba2bd2a2
  18. bc ⇒ 1
  19. cb ⇒ 1
  20. c2 ⇒ b2
  21. b3 ⇒ c 
# ab:aaaa=bab,bbbb=1 a/d/bc bbb=c,caaacaaacaaac=d frequency:3/1,13/0
daaaa=a
ad=da
ddaaa=d
abdaaa=ab
aaaaab=baaaaa
db=aabdda
dab=aaabdda
daab=aaaabdda
daaab=bdaaa
ca=abd
cd=abdddaa
ac=aabddaa
dc=aaabddd
bab=aaaa
abbdaaa=abb
abaab=bbaaaaaaaaa
aaaabb=baabddaa
bc=1
cb=1
cc=bb
bbb=c

Right Cayley graph (truncated)

Left Cayley graph (truncated)