#589 ⟨a, b | baba=abab⟩

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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. ca ⇒ ac [5]
2. cb ⇒ bc [4]
3. (ab)2 ⇒ c [2]
4. (ba)2 ⇒ c [3]
# ab:baba=abab abc abab=c magic:0
ca=ac
cb=bc
abab=c
baba=c

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
6120⟨a, b | baa=aab⟩Infinite cancellative non-commutative monoid
102750⟨a, b | baaba=abaab⟩Infinite cancellative non-commutative monoid