#756 ⟨a, b | aaaabbaa=b⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a4b3 ⇒ ba2b2a2 [2]
2. a4b2ab ⇒ ba3b2a2 [3]
3. a4b2a2 ⇒ b [1]
# ab:aaaabbaa=b ba
aaaabbb=baabbaa
aaaabbab=baaabbaa
aaaabbaa=b

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
9885⟨a, b | aaaabaa=bb⟩Infinite cancellative non-commutative monoid
102126⟨a, b | aaaabaa=bab⟩Infinite cancellative non-commutative monoid
114956⟨a, b | aaaabaa=baab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
101588⟨a, b | aaaababaa=b⟩Infinite cancellative non-commutative monoid
113375⟨a, b | aaaabaabaa=b⟩Infinite cancellative non-commutative monoid