#1107 ⟨a, b | abaaab=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. c2ab ⇒ bac [5]
2. acab ⇒ c [4]
3. ba2 ⇒ c [2]
4. ca2 ⇒ (ac)2 [6]
# ab:abaaab=baa bc/a baa=c magic:0
ccab=bac
acab=c
baa=c
caa=acac

Other submonoids of same group

17 unique, 17 total

Σ#PresentationDescriptionRelated
6107⟨a, b | aabb=ba⟩Infinite cancellative non-commutative monoid
6121⟨a, b | baa=abb⟩Infinite cancellative non-commutative monoid
7217⟨a, b | aabab=ba⟩Infinite cancellative non-commutative monoid
7262⟨a, b | abab=baa⟩Infinite cancellative non-commutative monoid
8445⟨a, b | aabaab=ba⟩Infinite cancellative non-commutative monoid
8541⟨a, b | abaab=baa⟩Infinite cancellative non-commutative monoid
9927⟨a, b | aabaaab=ba⟩Infinite cancellative non-commutative monoid
9976⟨a, b | abaabab=ba⟩Infinite cancellative non-commutative monoid
91249⟨a, b | abaab=baba⟩Infinite cancellative non-commutative monoid
101937⟨a, b | aabaaaab=ba⟩Infinite cancellative non-commutative monoid
102295⟨a, b | abaaaab=baa⟩Infinite cancellative non-commutative monoid
114063⟨a, b | aabaaaaab=ba⟩Infinite cancellative non-commutative monoid
114242⟨a, b | abaaabaab=ba⟩Infinite cancellative non-commutative monoid
114289⟨a, b | ababaabab=ba⟩Infinite cancellative non-commutative monoid
114757⟨a, b | abaaaaab=baa⟩Infinite cancellative non-commutative monoid
115349⟨a, b | ababaab=baba⟩Infinite cancellative non-commutative monoid
115827⟨a, b | abaaab=baaba⟩Infinite cancellative non-commutative monoid