#1616 ⟨a, b | aaabaabaa=b⟩

Up:Monoid enumeration
Prev:#1615 ⟨a, b | aaabaabaa=a⟩
Next:#1617 ⟨a, b | aaabaabab=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. a3ba2b2 ⇒ ba(ba2)2 [2]
2. a(a2b)2ab ⇒ (ba2)3 [3]
3. a3(ba2)2 ⇒ b [1]
# ab:aaabaabaa=b ba - -
aaabaabb=babaabaa
aaabaabab=baabaabaa
aaabaabaa=b

Other submonoids of same group

6 unique, 11 total

Σ#PresentationPropertiesφ
8431⟨a, b | aaabaa=bb⟩Can Inf
91038⟨a, b | aaabaa=bab⟩Can Inf
102430⟨a, b | aaabaa=baab⟩Can Inf
113070⟨a, b | aabababbaba=1⟩Grp Inf5
113775⟨a, b | abababbaba=b⟩Can Inf
115550⟨a, b | aaabaa=baaab⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
8366⟨a, b | aaabbaa=b⟩Can Inf
9769⟨a, b | aaababaa=b⟩Can Inf
113434⟨a, b | aaabaaabaa=b⟩Can Inf