#2612 ⟨a, b | ababba=bbab⟩

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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. abac ⇒ cb [5]
2. b2c ⇒ cab2a [6]
3. b2ac ⇒ cbab [4]
4. b2ab ⇒ c [2]
5. abab2a ⇒ c [3]
# ab:ababba=bbab a/cb bbab=c magic:0
abac=cb
bbc=cabba
bbac=cbab
bbab=c
ababba=c

Other submonoids of same group

4 unique, 9 total

Σ#PresentationDescriptionRelated
8382⟨a, b | aababba=b⟩Infinite cancellative non-commutative monoid
8592⟨a, b | babb=abaa⟩Infinite cancellative non-commutative monoid
101408⟨a, b | aabaababba=1⟩Infinite non-Abelian group5 iso
101678⟨a, b | aabaababa=b⟩Infinite cancellative non-commutative monoid