#885 ⟨a, b | aaaabaa=bb⟩

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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. b2 ⇒ a4ba2 [1]
2. a4ba2b ⇒ ba4ba2 [2]
# ab:aaaabaa=bb a/b
bb=aaaabaa
aaaabaab=baaaabaa

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
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

3 unique, 3 total

Σ#PresentationDescriptionRelated
9756⟨a, b | aaaabbaa=b⟩Infinite cancellative non-commutative monoid
101588⟨a, b | aaaababaa=b⟩Infinite cancellative non-commutative monoid
113375⟨a, b | aaaabaabaa=b⟩Infinite cancellative non-commutative monoid