#5554 ⟨a, b | aaabaa=babab⟩

Up:Monoids with two generators and one relation
Prev:#5553 ⟨a, b | aaabaa=babaa⟩
Next:#5555 ⟨a, b | aaabaa=babba⟩

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. a3ba2 ⇒ b(ab)2 [1]
2. a3b2(ab)2 ⇒ (ba)4a [2]
3. a2(ab)4 ⇒ (ba)3aba2 [3]
# ab:aaabaa=babab ba
aaabaa=babab
aaabbabab=babababaa
aaabababab=bababaabaa

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
91040⟨a, b | aaabaa=bbb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9784⟨a, b | aaabbbaa=b⟩Infinite cancellative non-commutative monoid
113462⟨a, b | aaabababaa=b⟩Infinite cancellative non-commutative monoid