#2745 ⟨a, b | baaab=ababa⟩

Up:Monoids with two generators and one relation
Prev:#2744 ⟨a, b | baaab=aabba⟩
Next:#2746 ⟨a, b | baaab=abbba⟩

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 ⇒ abc [4]
2. ca2b ⇒ abac [7]
3. caba ⇒ ba2c [6]
4. a(ba)2 ⇒ c [2]
5. ba3b ⇒ c [3]
6. ca3b ⇒ ba3c [5]
# ab:baaab=ababa abc ababa=c magic:0
cba=abc
caab=abac
caba=baac
ababa=c
baaab=c
caaab=baaac

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
8587⟨a, b | baab=abba⟩Infinite cancellative non-commutative monoid