#23325 ⟨a, b | aaa=1, bbbb=abab⟩

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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. b30 ⇒ b6
  2. bab27 ⇒ bab3
  3. b2ab26 ⇒ b2ab2
  4. b4ab ⇒ ab5
  5. a2b4 ⇒ bab
  6. (ab)2 ⇒ b4
  7. (ab2)2 ⇒ b3ab5
  8. (bab)2 ⇒ ab8
  9. bab3ab ⇒ ab3ab8
  10. a3 ⇒ 1
  11. a2b3ab2 ⇒ b2ab23 
# ab:aaa=1,bbbb=abab b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbbbb
babbbbbbbbbbbbbbbbbbbbbbbbbbb=babbb
bbabbbbbbbbbbbbbbbbbbbbbbbbbb=bbabb
bbbbab=abbbbb
aabbbb=bab
abab=bbbb
abbabb=bbbabbbbb
babbab=abbbbbbbb
babbbab=abbbabbbbbbbb
aaa=1
aabbbabb=bbabbbbbbbbbbbbbbbbbbbbbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)