#1205 ⟨a, b | aabaa=babb⟩

Up:Monoids with two generators and one relation
Prev:#1204 ⟨a, b | aabaa=baab⟩
Next:#1206 ⟨a, b | aabaa=bbbb⟩

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. bab2 ⇒ a2ba2 [1]
2. a2ba3b2 ⇒ ba(ba2)2 [2]
# ab:aabaa=babb a/b
babb=aabaa
aabaaabb=babaabaa

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
9807⟨a, b | aababbaa=b⟩Infinite cancellative non-commutative monoid
113564⟨a, b | aabaababaa=b⟩Infinite cancellative non-commutative monoid
115904⟨a, b | ababba=bbabb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
101702⟨a, b | aababbaba=b⟩Infinite cancellative non-commutative monoid