#2303 ⟨a, b | abaaaba=bab⟩

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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. cb ⇒ aba3c [6]
2. cab ⇒ bac [4]
3. ca2ba ⇒ aba2c [5]
4. ca3ba ⇒ bc [7]
5. bab ⇒ c [2]
6. aba3ba ⇒ c [3]
# ab:abaaaba=bab ac/b bab=c magic:0
cb=abaaac
cab=bac
caaba=abaac
caaaba=bc
bab=c
abaaaba=c

Other submonoids of same group

3 unique, 5 total

Σ#PresentationDescriptionRelated
8315⟨a, b | aabbabba=1⟩Infinite non-Abelian group2 iso
8471⟨a, b | abaaba=bb⟩Infinite cancellative non-commutative monoid
101810⟨a, b | abbababba=b⟩Infinite cancellative non-commutative monoid