#519 ⟨a, b | aabaa=bab⟩

Up:Monoid enumeration
Prev:#518 ⟨a, b | aabaa=abb⟩
Next:#520 ⟨a, b | aabaa=bbb⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. a2ba2 ⇒ bab [1]
2. bab2a2 ⇒ a2b2ab [2]
3. (ba)3a ⇒ a(ab)3 [3]
# ab:aabaa=bab ab - -
aabaa=bab
babbaa=aabbab
bababaa=aababab

Other submonoids of same group

11 unique, 23 total

Σ#PresentationPropertiesφ
7182⟨a, b | aabbaa=b⟩Can Inf1
7214⟨a, b | aabaa=bb⟩Can Inf
8378⟨a, b | aababaa=b⟩Can Inf
9672⟨a, b | aababbaba=1⟩Grp Inf10
9796⟨a, b | aabaabaa=b⟩Can Inf
9854⟨a, b | ababbaba=b⟩Can Inf1
91204⟨a, b | aabaa=baab⟩Can Inf
101670⟨a, b | aabaaabaa=b⟩Can Inf
102743⟨a, b | baaab=aabaa⟩Can Inf
114843⟨a, b | ababbaba=bab⟩Can Inf
115943⟨a, b | abbbba=bbabb⟩Can Inf