#2028 ⟨a, b | abaaabab=ba⟩

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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. aca2c2 ⇒ ca [6]
2. aca2cb ⇒ c [4]
3. ba ⇒ c [2]
4. bc ⇒ c2a2cb [5]
# ab:abaaabab=ba reversed:ac/b ba=c magic:0
acaacc=ca
acaacb=c
ba=c
bc=ccaacb

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
102325⟨a, b | ababaab=baa⟩Infinite cancellative non-commutative monoid
102573⟨a, b | abaaab=baba⟩Infinite cancellative non-commutative monoid