#4164 ⟨a, b | abb=aba, baa=a⟩

Up:Monoids with two generators and two relations
Prev:#4163 ⟨a, b | abb=aab, bbb=b⟩
Next:#4165 ⟨a, b | abb=aba, baa=b⟩

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. ba ⇒ a2 [6]
2. a3 ⇒ a [5]
3. ab2 ⇒ a [7]
# ab:abb=aba,baa=a ab
ba=aa
aaa=a
abb=a

Isomorphic instances

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

3 total

Σ#PresentationMapping
106407⟨a, b | aab=b, abbaa=b⟩φ(a) = b, φ(b) = a
106476⟨a, b | aba=a, baabb=a⟩φ(a) = a, φ(b) = b
106711⟨a, b | aab=b, bbaa=ab⟩φ(a) = b, φ(b) = a