#2573 ⟨a, b | abaaab=baba⟩

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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. cba ⇒ bac [4]
2. caba ⇒ aba3c [6]
3. ca2b ⇒ bc [7]
4. ca3b ⇒ aba2c [5]
5. (ba)2 ⇒ c [2]
6. aba3b ⇒ c [3]
# ab:abaaab=baba ac/b baba=c magic:0
cba=bac
caba=abaaac
caab=bc
caaab=abaac
baba=c
abaaab=c

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
8459⟨a, b | aabbab=ba⟩Infinite cancellative non-commutative monoid
8543⟨a, b | abaab=bba⟩Infinite cancellative non-commutative monoid
101960⟨a, b | aababaab=ba⟩Infinite cancellative non-commutative monoid
102028⟨a, b | abaaabab=ba⟩Infinite cancellative non-commutative monoid
102325⟨a, b | ababaab=baa⟩Infinite cancellative non-commutative monoid