#22841 ⟨a, b | aaa=1, babab=abb⟩

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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. b7 ⇒ b4
  2. bab6 ⇒ bab3
  3. b2ab5 ⇒ b2ab2
  4. b3ab ⇒ ab4
  5. abab3 ⇒ b2ab4
  6. ba2b2 ⇒ ab2ab
  7. b(ab)2 ⇒ ab2
  8. (b2a)2b ⇒ a2b5
  9. a3 ⇒ 1
  10. a(ab2)2 ⇒ bab4
  11. ab(ab2)2 ⇒ bab2ab4
  12. ba2bab2 ⇒ a(bab)2 
# ab:aaa=1,babab=abb b/a
bbbbbbb=bbbb
babbbbbb=babbb
bbabbbbb=bbabb
bbbab=abbbb
ababbb=bbabbbb
baabb=abbab
babab=abb
bbabbab=aabbbbb
aaa=1
aabbabb=babbbb
ababbabb=babbabbbb
baababb=ababbab

Right Cayley graph (truncated)

Left Cayley graph (truncated)