#1122 ⟨a, b | ababba=aab⟩

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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. abab2a ⇒ a2b
  2. a(ab)3 ⇒ a3b3a
  3. a2(b2a)2 ⇒ a(ab)2
  4. a3b3aba ⇒ (a2b)2
  5. a2ba2b3a ⇒ a3b3a2b
  6. a3b3a2b2a ⇒ a(ab)2a2b
  7. a(ab)2a2b3a ⇒ a3b3a(ab)2 
# ab:ababba=aab ab
ababba=aab
aababab=aaabbba
aabbabba=aabab
aaabbbaba=aabaab
aabaabbba=aaabbbaab
aaabbbaabba=aababaab
aababaabbba=aaabbbaabab

Right Cayley graph (truncated)

Left Cayley graph (truncated)