#784 ⟨a, b | aaabbbaa=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. a3b4 ⇒ bab3a2 [2]
2. a3b3ab ⇒ ba2b3a2 [3]
3. a3b3a2 ⇒ b [1]
# ab:aaabbbaa=b ba
aaabbbb=babbbaa
aaabbbab=baabbbaa
aaabbbaa=b

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
91040⟨a, b | aaabaa=bbb⟩Infinite cancellative non-commutative monoid
115554⟨a, b | aaabaa=babab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
113462⟨a, b | aaabababaa=b⟩Infinite cancellative non-commutative monoid