#199 ⟨a, b | aaaaa=bb⟩

Up:Monoid enumeration
Prev:#198 ⟨a, b | aaaaa=ab⟩
Next:#200 ⟨a, b | aaaab=aa⟩

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. b2a ⇒ ab2 [2]
2. a5 ⇒ b2 [1]
# ab:aaaaa=bb ab - -
bba=abb
aaaaa=bb

Other submonoids of same group

7 unique, 18 total

Σ#PresentationPropertiesφ
7131⟨a, b | aaaabba=1⟩Grp Inf11
7196⟨a, b | abbbba=b⟩Can Inf
7232⟨a, b | abbba=bb⟩Can Inf
7237⟨a, b | aaaa=bab⟩Can Inf
7268⟨a, b | abba=bbb⟩Can Inf
102333⟨a, b | abababa=bab⟩Can Inf
102767⟨a, b | babab=ababa⟩Can Inf