#1937 ⟨a, b | aabaaaab=ba⟩

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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. a2c2 ⇒ ca [6]
2. (a2c)4b ⇒ c [4]
3. ba ⇒ a2cb [3]
4. bc ⇒ c3ac(a2c)2b [9]
# ab:aabaaaab=ba reversed:ac/b baaaa=c morph:5/0
aacc=ca
aacaacaacaacb=c
ba=aacb
bc=cccacaacaacb

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
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