#12545 ⟨a, b | abab=ba, bbbb=b⟩

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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. b4 ⇒ b
  2. bab3 ⇒ ba
  3. aba ⇒ bab2
  4. ba2 ⇒ (ab2)2
  5. (b2a)2 ⇒ ab3ab
  6. a2b2a ⇒ (bab)2
  7. a3b3a ⇒ b3a 
# ab:abab=ba,bbbb=b b/a
bbbb=b
babbb=ba
aba=babb
baa=abbabb
bbabba=abbbab
aabba=babbab
aaabbba=bbba

Right Cayley graph (truncated)

Left Cayley graph (truncated)