#1678 ⟨a, b | aabaababa=b⟩

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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. (a2b)2ab2 ⇒ b(aba)2ba [2]
2. (a2b)2aba ⇒ b [1]
# ab:aabaababa=b ba
aabaababb=babaababa
aabaababa=b

Other submonoids of same group

4 unique, 9 total

Σ#PresentationDescriptionRelated
8382⟨a, b | aababba=b⟩Infinite cancellative non-commutative monoid
8592⟨a, b | babb=abaa⟩Infinite cancellative non-commutative monoid
101408⟨a, b | aabaababba=1⟩Infinite non-Abelian group5 iso
102612⟨a, b | ababba=bbab⟩Infinite cancellative non-commutative monoid