#2295 ⟨a, b | abaaaab=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. c2acb ⇒ abc [12]
2. ba2 ⇒ (ac)2b [7]
3. ca2 ⇒ (ac)2 [6]
4. c(ac)2b ⇒ abac [10]
5. a(ac)2b ⇒ c [9]
6. a(cacb)2 ⇒ bc [11]
7. ((ac)2b)2 ⇒ bac [8]
# ab:abaaaab=baa bc/a abaa=c morph:4/1
ccacb=abc
baa=acacb
caa=acac
cacacb=abac
aacacb=c
acacbcacb=bc
acacbacacb=bac

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
91107⟨a, b | abaaab=baa⟩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
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