#1065 ⟨a, b | aabaab=baa⟩

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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. c2b ⇒ bc [5]
2. cacb ⇒ bac [6]
3. a2cb ⇒ c [4]
4. ba2 ⇒ c [2]
5. ca2 ⇒ a2c2 [7]
# ab:aabaab=baa bc/a baa=c magic:0
ccb=bc
cacb=bac
aacb=c
baa=c
caa=aacc

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
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
115663⟨a, b | aabaab=baaba⟩Infinite cancellative non-commutative monoid