#3030 ⟨a, b | aa=a, babb=ab⟩

Up:Monoids with two generators and two relations
Prev:#3025 ⟨a, b | aa=a, abbb=bb⟩
Next:#3031 ⟨a, b | aa=a, babb=ba⟩

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. bab ⇒ ab2 [4]
3. ab3 ⇒ ab [5]
# ab:aa=a,babb=ab ab
aa=a
bab=abb
abbb=ab

Isomorphic instances

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

5 total

Σ#PresentationMapping
108896⟨a, b | aa=a, baabb=ab⟩φ(a) = a, φ(b) = b
109171⟨a, b | aa=a, babb=aab⟩φ(a) = a, φ(b) = b
1124692⟨a, b | aa=a, baaabb=ab⟩φ(a) = a, φ(b) = b
1125227⟨a, b | aa=a, baabb=aab⟩φ(a) = a, φ(b) = b
1125701⟨a, b | aa=a, babb=aaab⟩φ(a) = a, φ(b) = b