#4273 ⟨a, b | abaabbaab=ba⟩

Up:Monoid enumeration
Prev:#4272 ⟨a, b | abaabbaab=ab⟩
Next:#4274 ⟨a, b | abaabbaab=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. c(cbc3bcb)2 ⇒ bc [7]
2. ba ⇒ a(cb)2 [3]
3. ca ⇒ acbc2 [6]
4. a2(cbc3bcb)2 ⇒ c [8]
# ab:abaabbaab=ba bc/a baa=c morph:3/0
ccbcccbcbcbcccbcb=bc
ba=acbcb
ca=acbcc
aacbcccbcbcbcccbcb=c

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
9950⟨a, b | aabbaab=ba⟩Can Inf
114110⟨a, b | aababaaab=ba⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
91132⟨a, b | abbaab=baa⟩Can Inf
114815⟨a, b | ababaaab=baa⟩Can Inf
115922⟨a, b | abbaab=baaba⟩Can Inf