#1883 ⟨a, b | aaabaaab=ba⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. a(a2c)2 ⇒ ca [6]
2. a3ca2b ⇒ c [4]
3. ba ⇒ c [2]
4. bc ⇒ (ca2)2b [5]
# ab:aaabaaab=ba reversed:ac/b ba=c magic:0
aaacaac=ca
aaacaab=c
ba=c
bc=caacaab

Other submonoids of same group

8 unique, 8 total

Σ#PresentationDescriptionRelated
7210⟨a, b | aaabb=ba⟩Infinite cancellative non-commutative monoid
8434⟨a, b | aaabab=ba⟩Infinite cancellative non-commutative monoid
8583⟨a, b | baaa=abab⟩Infinite cancellative non-commutative monoid
9903⟨a, b | aaabaab=ba⟩Infinite cancellative non-commutative monoid
91120⟨a, b | ababab=baa⟩Infinite cancellative non-commutative monoid
113957⟨a, b | aaabaaaab=ba⟩Infinite cancellative non-commutative monoid
114787⟨a, b | abaabaab=baa⟩Infinite cancellative non-commutative monoid
115874⟨a, b | ababab=baaba⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationDescriptionRelated
7245⟨a, b | aaab=bba⟩Infinite cancellative non-commutative monoid
9942⟨a, b | aababab=ba⟩Infinite cancellative non-commutative monoid
91247⟨a, b | abaab=baaa⟩Infinite cancellative non-commutative monoid
102571⟨a, b | abaaab=baaa⟩Infinite cancellative non-commutative monoid
114086⟨a, b | aabaabaab=ba⟩Infinite cancellative non-commutative monoid
114265⟨a, b | abaababab=ba⟩Infinite cancellative non-commutative monoid
115289⟨a, b | abaaaab=baaa⟩Infinite cancellative non-commutative monoid