#1758 ⟨a, b | abaaababa=b⟩

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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. aba3b2 ⇒ ba2(ba)2 [2]
2. aba3bab2 ⇒ b2a3(ba)2 [3]
3. aba3(ba)2 ⇒ b [1]
# ab:abaaababa=b ba
abaaabb=baababa
abaaababb=bbaaababa
abaaababa=b

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
8400⟨a, b | abaabba=b⟩Infinite cancellative non-commutative monoid
8534⟨a, b | aabba=bab⟩Infinite cancellative non-commutative monoid
101419⟨a, b | aababaabba=1⟩Infinite non-Abelian group5 iso
102340⟨a, b | ababbba=bab⟩Infinite cancellative non-commutative monoid
102504⟨a, b | aababa=baab⟩Infinite cancellative non-commutative monoid