#19268 ⟨a, b | aaa=a, ababa=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. a3 ⇒ a
  2. a2b2 ⇒ b2
  3. b2a2 ⇒ b2
  4. b3a ⇒ ab3
  5. a(ba)2 ⇒ b2
  6. abab3 ⇒ b2ab2
  7. (ab2)2 ⇒ bab3
  8. (b2a)2 ⇒ ab4 
# ab:aaa=a,ababa=bb ab
aaa=a
aabb=bb
bbaa=bb
bbba=abbb
ababa=bb
ababbb=bbabb
abbabb=babbb
bbabba=abbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)