#1853 ⟨a, b | aaaabaaa=bb⟩

Up:Monoids with two generators and one relation
Prev:#1852 ⟨a, b | aaaabaaa=ba⟩
Next:#1854 ⟨a, b | aaaabaab=aa⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. b2 ⇒ a4ba3 [1]
2. a(a3b)2 ⇒ ba4ba3 [2]
# ab:aaaabaaa=bb a/b
bb=aaaabaaa
aaaabaaab=baaaabaaa

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
114428⟨a, b | aaaabaaa=bab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
101596⟨a, b | aaaabbaaa=b⟩Infinite cancellative non-commutative monoid
113383⟨a, b | aaaababaaa=b⟩Infinite cancellative non-commutative monoid