#5663 ⟨a, b | aabaab=baaba⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. a2c ⇒ ca [4]
2. bc ⇒ cab [5]
3. ba2ba ⇒ c [2]
4. (a2b)2 ⇒ c [3]
# ab:aabaab=baaba a/cb baaba=c magic:0
aac=ca
bc=cab
baaba=c
aabaab=c

Other submonoids of same group

7 unique, 7 total

Σ#PresentationDescriptionRelated
7258⟨a, b | aabb=baa⟩Infinite cancellative non-commutative monoid
8525⟨a, b | aabab=baa⟩Infinite cancellative non-commutative monoid
91065⟨a, b | aabaab=baa⟩Infinite cancellative non-commutative monoid
91217⟨a, b | aabab=baba⟩Infinite cancellative non-commutative monoid
102211⟨a, b | aabaaab=baa⟩Infinite cancellative non-commutative monoid
114593⟨a, b | aabaaaab=baa⟩Infinite cancellative non-commutative monoid
115317⟨a, b | abaabab=baba⟩Infinite cancellative non-commutative monoid