#1955 ⟨a, b | aabaabba=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. a2ba2c ⇒ ab
  2. caba2c ⇒ cb
  3. acba2ca ⇒ abc
  4. c2ba2ca ⇒ cbc
  5. b2a ⇒ c
  6. ab2c ⇒ (acba)2
  7. cb2c ⇒ c2ba2cba
  8. (a2b)2c ⇒ a(ca)2
  9. caba2bc ⇒ c(ca)2
  10. (ab)2a2c ⇒ ab2
  11. cbaba2c ⇒ cb2
  12. abcba2c ⇒ acba2cb
  13. (cb)2a2c ⇒ c2ba2cb
  14. ab3 ⇒ acba2c
  15. cb3 ⇒ c2ba2c
  16. (ab)2a2bc ⇒ ab(ca)2
  17. cbaba2bc ⇒ cb(ca)2
  18. abcba2bc ⇒ acba2c(ca)2
  19. (cb)2a2bc ⇒ c2ba2c(ca)2 
# ab:aabaabba=ab reversed:ac/b bba=c frequency:3/0
aabaac=ab
cabaac=cb
acbaaca=abc
ccbaaca=cbc
bba=c
abbc=acbaacba
cbbc=ccbaacba
aabaabc=acaca
cabaabc=ccaca
ababaac=abb
cbabaac=cbb
abcbaac=acbaacb
cbcbaac=ccbaacb
abbb=acbaac
cbbb=ccbaac
ababaabc=abcaca
cbabaabc=cbcaca
abcbaabc=acbaaccaca
cbcbaabc=ccbaaccaca

Right Cayley graph (truncated)

Left Cayley graph (truncated)