#5741 ⟨a, b | aabbaa=babab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

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
#RuleProof
1. a2b2a2 ⇒ b(ab)2 [1]
2. (ba)2b3a2 ⇒ a2b3(ab)2 [2]
3. (ba)3b2a2 ⇒ a2b2(ab)3 [3]
# ab:aabbaa=babab ab
aabbaa=babab
bababbbaa=aabbbabab
babababbaa=aabbababab

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102273⟨a, b | aabbbaa=bab⟩Infinite cancellative non-commutative monoid