#4086 ⟨a, b | aabaabaab=ba⟩

Up:Monoid enumeration
Prev:#4085 ⟨a, b | aabaabaab=ab⟩
Next:#4087 ⟨a, b | aabaabaab=bb⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. a(ac)3 ⇒ ca [6]
2. a2(ca)2b ⇒ c [4]
3. ba ⇒ c [2]
4. bc ⇒ (ca)3b [5]
# ab:aabaabaab=ba reversed:ac/b ba=c magic:0
aacacac=ca
aacacab=c
ba=c
bc=cacacab

Other submonoids of same group

9 unique, 9 total

Σ#PresentationProperties
7210⟨a, b | aaabb=ba⟩Can Inf
8434⟨a, b | aaabab=ba⟩Can Inf
8583⟨a, b | baaa=abab⟩Can Inf
9903⟨a, b | aaabaab=ba⟩Can Inf
91120⟨a, b | ababab=baa⟩Can Inf
101883⟨a, b | aaabaaab=ba⟩Can Inf
113957⟨a, b | aaabaaaab=ba⟩Can Inf
114787⟨a, b | abaabaab=baa⟩Can Inf
115874⟨a, b | ababab=baaba⟩Can Inf

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationProperties
7245⟨a, b | aaab=bba⟩Can Inf
9942⟨a, b | aababab=ba⟩Can Inf
91247⟨a, b | abaab=baaa⟩Can Inf
102571⟨a, b | abaaab=baaa⟩Can Inf
114265⟨a, b | abaababab=ba⟩Can Inf
115289⟨a, b | abaaaab=baaa⟩Can Inf