#945 ⟨a, b | aababba=ab⟩

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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. a2bac ⇒ ab
  2. cabac ⇒ cb
  3. acbaca ⇒ abc
  4. c2baca ⇒ cbc
  5. b2a ⇒ c
  6. ab2c ⇒ a(cba)2
  7. cb2c ⇒ c(cba)2
  8. a(ab)2c ⇒ ac2a
  9. c(ab)2c ⇒ c3a
  10. a(ba)2c ⇒ ab2
  11. c(ba)2c ⇒ cb2
  12. abcbac ⇒ (acb)2
  13. (cb)2ac ⇒ c2bacb
  14. ab3 ⇒ acbac
  15. cb3 ⇒ c2bac
  16. (ab)3c ⇒ abc2a
  17. cb(ab)2c ⇒ cbc2a
  18. abcbabc ⇒ acbac3a
  19. (cb)2abc ⇒ c2bac3a 
# ab:aababba=ab reversed:ac/b bba=c frequency:3/0
aabac=ab
cabac=cb
acbaca=abc
ccbaca=cbc
bba=c
abbc=acbacba
cbbc=ccbacba
aababc=acca
cababc=ccca
ababac=abb
cbabac=cbb
abcbac=acbacb
cbcbac=ccbacb
abbb=acbac
cbbb=ccbac
abababc=abcca
cbababc=cbcca
abcbabc=acbaccca
cbcbabc=ccbaccca

Right Cayley graph (truncated)

Left Cayley graph (truncated)