#1234 ⟨a, b | aabba=babb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a2b2a ⇒ bab2 [1]
2. a2b3ab2 ⇒ ba(b2a)2 [2]
# ab:aabba=babb ba
aabba=babb
aabbbabb=babbabba

Other submonoids of same group

4 unique, 4 total

Σ#PresentationDescriptionRelated
9815⟨a, b | aabbaaba=b⟩Infinite cancellative non-commutative monoid
101774⟨a, b | abaabbaba=b⟩Infinite cancellative non-commutative monoid
102266⟨a, b | aabbaba=bab⟩Infinite cancellative non-commutative monoid
113583⟨a, b | aababaaaba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
115376⟨a, b | ababbba=babb⟩Infinite cancellative non-commutative monoid