#1232 ⟨a, b | aabba=baab⟩

Up:Monoids with two generators and one relation
Prev:#1231 ⟨a, b | aabba=baaa⟩
Next:#1233 ⟨a, b | aabba=baba⟩

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. cba ⇒ bc [6]
2. cab ⇒ a2bc [5]
3. ca2b ⇒ ba2c [4]
4. ba2b ⇒ c [2]
5. a2b2a ⇒ c [3]
# ab:aabba=baab ac/b baab=c magic:0
cba=bc
cab=aabc
caab=baac
baab=c
aabba=c

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
115332⟨a, b | abaabba=baab⟩Infinite cancellative non-commutative monoid
115694⟨a, b | aababa=baaab⟩Infinite cancellative non-commutative monoid