#17660 ⟨a, b | aaaa=1, abbab=bb⟩

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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. b15 ⇒ b3
  2. bab14 ⇒ bab2
  3. b3ab ⇒ ab4
  4. ab2ab ⇒ b2
  5. ba2b2 ⇒ abab4
  6. b2(ab)2 ⇒ a2b2
  7. a3b2 ⇒ b2ab
  8. (ab)3b ⇒ bab12
  9. ba2bab2 ⇒ a2bab7
  10. a4 ⇒ 1
  11. a3bab2 ⇒ (ba)2b4 
# ab:aaaa=1,abbab=bb b/a
bbbbbbbbbbbbbbb=bbb
babbbbbbbbbbbbbb=babb
bbbab=abbbb
abbab=bb
baabb=ababbbb
bbabab=aabb
aaabb=bbab
abababb=babbbbbbbbbbbb
baababb=aababbbbbbb
aaaa=1
aaababb=bababbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)