#19271 ⟨a, b | aaa=a, ababb=ba⟩

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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 ⇒ a
  2. a2ba ⇒ ba
  3. bab2 ⇒ aba
  4. a2b2a ⇒ b2a
  5. ba2b2 ⇒ b3a2
  6. (ba)3 ⇒ ab3a2
  7. ab(ba)2 ⇒ b2aba2
  8. b3aba ⇒ ab2a2
  9. a2b3a ⇒ b3a
  10. ab4a ⇒ b4a2
  11. b5a ⇒ ba 
# ab:aaa=a,ababb=ba reversed:ab
aaa=a
aaba=ba
babb=aba
aabba=bba
baabb=bbbaa
bababa=abbbaa
abbaba=bbabaa
bbbaba=abbaa
aabbba=bbba
abbbba=bbbbaa
bbbbba=ba

Right Cayley graph (truncated)

Left Cayley graph (truncated)