#8879 ⟨a, b | aa=a, ababb=ba⟩

Up:Monoids with two generators and two relations
Prev:#8878 ⟨a, b | aa=a, ababb=ab⟩
Next:#8882 ⟨a, b | aa=a, abbab=ab⟩

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. aba ⇒ ba [3]
3. ab2a ⇒ b2a [5]
4. bab2 ⇒ ba [4]
5. b3a ⇒ ba [6]
# ab:aa=a,ababb=ba ab
aa=a
aba=ba
abba=bba
babb=ba
bbba=ba

Isomorphic instances

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

3 total

Σ#PresentationMapping
1124629⟨a, b | aa=a, aababb=ba⟩φ(a) = a, φ(b) = b
1124655⟨a, b | aa=a, abaabb=ba⟩φ(a) = a, φ(b) = b
1125194⟨a, b | aa=a, ababb=baa⟩φ(a) = a, φ(b) = b