#2522 ⟨a, b | aabbaa=aaab⟩

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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. cba2 ⇒ ac
  2. acab ⇒ cbc
  3. a3b ⇒ c
  4. cb2a2 ⇒ cab
  5. c(ab)2 ⇒ cb2c
  6. acb2c ⇒ cbcab
  7. aca2b ⇒ cbac
  8. a2b2c ⇒ cab
  9. cbacbc ⇒ ac2ab
  10. cab3c ⇒ cb2cab
  11. cab2a2 ⇒ ca2b
  12. caba2b ⇒ cb2ac
  13. ca(ab)2 ⇒ cab2c
  14. acb2ac ⇒ cbca2b
  15. a2b2ac ⇒ ca2b
  16. a2b2a2 ⇒ c
  17. cb2acbc ⇒ (cab)2
  18. c(bac)2 ⇒ ac2a2b
  19. cab3ac ⇒ cb2ca2b
  20. cab3a2 ⇒ cb2c
  21. ca2b3c ⇒ cab2cab
  22. c(a2b)2 ⇒ cab2ac
  23. cb(bac)2 ⇒ cabca2b
  24. cab2acbc ⇒ ca2bcab
  25. ca2b3ac ⇒ cab2ca2b
  26. ca2b3a2 ⇒ cab2c
  27. cab(bac)2 ⇒ (ca2b)2 
# ab:aabbaa=aaab bca aaab=c magic:0
cbaa=ac
acab=cbc
aaab=c
cbbaa=cab
cabab=cbbc
acbbc=cbcab
acaab=cbac
aabbc=cab
cbacbc=accab
cabbbc=cbbcab
cabbaa=caab
cabaab=cbbac
caabab=cabbc
acbbac=cbcaab
aabbac=caab
aabbaa=c
cbbacbc=cabcab
cbacbac=accaab
cabbbac=cbbcaab
cabbbaa=cbbc
caabbbc=cabbcab
caabaab=cabbac
cbbacbac=cabcaab
cabbacbc=caabcab
caabbbac=cabbcaab
caabbbaa=cabbc
cabbacbac=caabcaab

Right Cayley graph (truncated)

Left Cayley graph (truncated)