#2598 ⟨a, b | ababab=bbaa⟩

Up:Monoids with two generators and one relation
Prev:#2597 ⟨a, b | ababab=baba⟩
Next:#2599 ⟨a, b | ababba=aaaa⟩

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. ab ⇒ c [2]
2. b2ac ⇒ c3b [5]
3. cbac ⇒ ac3b [6]
4. b2a2 ⇒ c3 [3]
5. cba2 ⇒ ac3 [4]
# ab:ababab=bbaa bc/a ab=c morph:2/0
ab=c
bbac=cccb
cbac=acccb
bbaa=ccc
cbaa=accc

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
91191⟨a, b | aaabb=baba⟩Infinite cancellative non-commutative monoid
115583⟨a, b | aaabab=baaba⟩Infinite cancellative non-commutative monoid