#15526 ⟨a, b | aaa=bb, ababb=b⟩

Up:Monoids with two generators and two relations
Prev:#15523 ⟨a, b | aaa=bb, ababa=a⟩
Next:#15531 ⟨a, b | aaa=bb, abbbb=a⟩

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. a18 ⇒ a3
  2. ba15 ⇒ b
  3. ab ⇒ ba11
  4. b2 ⇒ a3 
# ab:aaa=bb,ababb=b a/b
aaaaaaaaaaaaaaaaaa=aaa
baaaaaaaaaaaaaaa=b
ab=baaaaaaaaaaa
bb=aaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 1 total

Σ#PresentationDescriptionRelated
1118737⟨a, b | aaa=a, abbbba=b⟩Finite non-commutative monoid with 33 elements

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1115530⟨a, b | aaa=bb, abbba=b⟩φ(a) = a, φ(b) = b