#1132 ⟨a, b | abbaab=baa⟩

Up:Monoids with two generators and one relation
Prev:#1131 ⟨a, b | abbaab=aba⟩
Next:#1133 ⟨a, b | abbbba=aaa⟩

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. abcb ⇒ c [4]
2. bac ⇒ (cb)2 [5]
3. ba2 ⇒ c [2]
4. abc2 ⇒ ca2 [6]
# ab:abbaab=baa b/ca baa=c magic:0
abcb=c
bac=cbcb
baa=c
abcc=caa

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
9950⟨a, b | aabbaab=ba⟩Infinite cancellative non-commutative monoid
114110⟨a, b | aababaaab=ba⟩Infinite cancellative non-commutative monoid
114273⟨a, b | abaabbaab=ba⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
114815⟨a, b | ababaaab=baa⟩Infinite cancellative non-commutative monoid
115922⟨a, b | abbaab=baaba⟩Infinite cancellative non-commutative monoid