#9158 ⟨a, b | aa=a, abbb=aba⟩

Up:Monoids with two generators and two relations
Prev:#9155 ⟨a, b | aa=a, abba=bbb⟩
Next:#9159 ⟨a, b | aa=a, abbb=abb⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

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. a2 ⇒ a [1]
2. ab3 ⇒ aba [2]
# ab:aa=a,abbb=aba ab
aa=a
abbb=aba

Isomorphic instances

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

3 total

Σ#PresentationMapping
1125170⟨a, b | aa=a, aabbb=aba⟩φ(a) = a, φ(b) = b
1125681⟨a, b | aa=a, abbb=aaba⟩φ(a) = a, φ(b) = b
1125683⟨a, b | aa=a, abbb=abaa⟩φ(a) = a, φ(b) = b