#1774 ⟨a, b | abaabbaba=b⟩

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  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. aba2b3 ⇒ (bab)2a [2]
2. aba(ab2)2 ⇒ b2a2b(ba)2 [3]
3. aba2b(ba)2 ⇒ b [1]
# ab:abaabbaba=b ba
abaabbb=babbaba
abaabbabb=bbaabbaba
abaabbaba=b

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
9815⟨a, b | aabbaaba=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

2 unique, 2 total

Σ#PresentationDescriptionRelated
91234⟨a, b | aabba=babb⟩Infinite cancellative non-commutative monoid
115376⟨a, b | ababbba=babb⟩Infinite cancellative non-commutative monoid