#2506 ⟨a, b | aababa=babb⟩

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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. a2(ba)2 ⇒ bab2 [1]
2. a2b(ab2)2 ⇒ bab(ba)3 [2]
# ab:aababa=babb ba
aababa=babb
aababbabb=babbababa

Other submonoids of same group

4 unique, 10 total

Σ#PresentationDescriptionRelated
9824⟨a, b | aabbbaba=b⟩Infinite cancellative non-commutative monoid
9955⟨a, b | aabbaba=bb⟩Infinite cancellative non-commutative monoid
112922⟨a, b | aaabaabbaba=1⟩Infinite non-Abelian group3 iso, 3 anti-iso
113790⟨a, b | ababbbabba=b⟩Infinite cancellative non-commutative monoid