#22808 ⟨a, b | aaa=1, abbab=bba⟩

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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. b5 ⇒ b2
  2. b2ab3 ⇒ b2a
  3. b3a ⇒ ab3
  4. ab2a ⇒ b2ab2
  5. (ba)2b2 ⇒ abab3
  6. b2a2b3 ⇒ b2a2
  7. b(ba)2 ⇒ abab2
  8. a3 ⇒ 1
  9. a2bab2 ⇒ b2a2
  10. aba2b2 ⇒ ba2b4
  11. b2a2ba ⇒ ba2b4 
# ab:aaa=1,abbab=bba b/a
bbbbb=bb
bbabbb=bba
bbba=abbb
abba=bbabb
bababb=ababbb
bbaabbb=bbaa
bbaba=ababb
aaa=1
aababb=bbaa
abaabb=baabbbb
bbaaba=baabbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)