#3560 ⟨a, b | aabaabaaba=b⟩

Up:Monoid enumeration
Prev:#3559 ⟨a, b | aabaabaaba=a⟩
Next:#3561 ⟨a, b | aabaabaabb=a⟩

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. a2b2 ⇒ (ba)2 [2]
2. (a2b)3a ⇒ b [1]
# ab:aabaabaaba=b ba - -
aabb=baba
aabaabaaba=b

Other submonoids of same group

7 unique, 26 total

Σ#PresentationPropertiesφ
7254⟨a, b | aaba=bbb⟩Can Inf
8290⟨a, b | aaababba=1⟩Grp Inf19
8478⟨a, b | ababba=bb⟩Can Inf
9863⟨a, b | abbabbba=b⟩Can Inf
91263⟨a, b | ababa=babb⟩Can Inf
114796⟨a, b | abaababa=bab⟩Can Inf
115405⟨a, b | abbabba=babb⟩Can Inf

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationProperties
7186⟨a, b | aabbba=b⟩Can Inf
9804⟨a, b | aabababa=b⟩Can Inf