#1314 ⟨a, b | aaaababaaa=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. ca ⇒ ac
  2. a7 ⇒ c
  3. dc ⇒ 1
  4. dac ⇒ a
  5. da2c ⇒ a2
  6. da3c ⇒ a3
  7. da4c ⇒ a4
  8. da5c ⇒ a5
  9. da6c ⇒ a6
  10. ad ⇒ da
  11. cd ⇒ 1
  12. cb ⇒ aba6
  13. a6b ⇒ ba6
  14. db ⇒ a5bd2a2
  15. dab ⇒ bda
  16. da2b ⇒ abda
  17. da3b ⇒ a2bda
  18. da4b ⇒ a3bda
  19. da5b ⇒ a4bda
  20. bab ⇒ d 
# ab:aaaababaaa=1 ac/d/b aaaaaaa=c,bab=d magic:0
ca=ac
aaaaaaa=c
dc=1
dac=a
daac=aa
daaac=aaa
daaaac=aaaa
daaaaac=aaaaa
daaaaaac=aaaaaa
ad=da
cd=1
cb=abaaaaaa
aaaaaab=baaaaaa
db=aaaaabddaa
dab=bda
daab=abda
daaab=aabda
daaaab=aaabda
daaaaab=aaaabda
bab=d

Right Cayley graph (truncated)

Left Cayley graph (truncated)