#2171 ⟨a, b | aaababa=baa⟩

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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. a3(ca)2 ⇒ ca2
  2. a3cac2 ⇒ cac
  3. a3cbc ⇒ c2
  4. a3cacbc ⇒ cabc
  5. ba2 ⇒ aca
  6. bac ⇒ ac2
  7. bc2 ⇒ aca2cbc
  8. bca2 ⇒ (aca)2ca
  9. bcac ⇒ (aca)2c2
  10. a(ab)2 ⇒ c
  11. ac(ab)2 ⇒ bc
  12. b2c ⇒ ac2(ab)2
  13. babc ⇒ acbc
  14. (bc)2 ⇒ (aca)2c2(ab)2
  15. bcabc ⇒ (aca)2cbc 
# ab:aaababa=baa reversed:ac/b aabab=c frequency:5/2
aaacaca=caa
aaacacc=cac
aaacbc=cc
aaacacbc=cabc
baa=aca
bac=acc
bcc=acaacbc
bcaa=acaacaca
bcac=acaacacc
aabab=c
acabab=bc
bbc=accabab
babc=acbc
bcbc=acaacaccabab
bcabc=acaacacbc

Right Cayley graph (truncated)

Left Cayley graph (truncated)