#11133 ⟨a, b | aaaaa=b, bbbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#11127 ⟨a, b | aaaaa=b, abbbb=1⟩
Next:#11163 ⟨a, b | aaaab=a, bbbbb=1⟩

Properties

Element profile

Complete 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
  1. a25 ⇒ 1
  2. b ⇒ a5 
# ab:aaaaa=b,bbbbb=1 a/b
aaaaaaaaaaaaaaaaaaaaaaaaa=1
b=aaaaa

Staircase diagram

Right Cayley graph

Others with same cardinality

7 unique, 10 total

Σ#PresentationDescriptionRelated
104749⟨a, b | abba=b, baab=a⟩Finite non-commutative monoid with 25 elements
106381⟨a, b | aab=a, bbbbb=b⟩Finite non-commutative monoid with 25 elements1 iso
106536⟨a, b | aaa=a, aaba=bb⟩Finite non-commutative monoid with 25 elements
1114342⟨a, b | aaaa=a, aabba=b⟩Finite non-commutative monoid with 25 elements
1114869⟨a, b | abba=b, bbabb=a⟩Finite non-commutative monoid with 25 elements2 iso
1119634⟨a, b | aba=a, aaaaa=bb⟩Finite non-commutative monoid with 25 elements
1119706⟨a, b | aba=b, aaaaa=bb⟩Finite non-commutative monoid with 25 elements

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ#PresentationMapping
1113298⟨a, b | aaaaa=1, abbbbb=1⟩φ(a) = aaaaaaaaaaaaaaaaaaaa, φ(b) = a
1113305⟨a, b | aaaaa=1, babbbb=1⟩φ(a) = aaaaaaaaaaaaaaaaaaaa, φ(b) = a
1113307⟨a, b | aaaaa=1, bbabbb=1⟩φ(a) = aaaaaaaaaaaaaaaaaaaa, φ(b) = a