#549 ⟨a, b | ababa=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. aca ⇒ c [4]
2. c2a ⇒ ac2 [5]
3. cb ⇒ abac [7]
4. cab ⇒ bac [6]
5. bab ⇒ c [2]
# ab:ababa=bab ac/b bab=c magic:0
aca=c
cca=acc
cb=abac
cab=bac
bab=c

Other submonoids of same group

8 unique, 28 total

Σ#PresentationDescriptionRelated
660⟨a, b | aaabba=1⟩Infinite non-Abelian group19 iso
693⟨a, b | abbba=b⟩Infinite cancellative non-commutative monoid
696⟨a, b | aaaa=bb⟩Infinite cancellative non-commutative monoid
6113⟨a, b | abba=bb⟩Infinite cancellative non-commutative monoid
6122⟨a, b | bab=aaa⟩Infinite cancellative non-commutative monoid
8404⟨a, b | abababa=b⟩Infinite cancellative non-commutative monoid1 iso
102355⟨a, b | abbabba=bab⟩Infinite cancellative non-commutative monoid
102586⟨a, b | abaaba=baab⟩Infinite cancellative non-commutative monoid