#5365 ⟨a, b | aab=aa, bab=aa⟩

Up:Monoids with two generators and two relations
Prev:#5364 ⟨a, b | aab=aa, baa=bb⟩
Next:#5366 ⟨a, b | aab=aa, bab=ab⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-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. bab2 ⇒ bab [4]
2. a2 ⇒ bab [2]
3. (ba)2 ⇒ (ab)2 [5]
# ab:aab=aa,bab=aa b/a
babb=bab
aa=bab
baba=abab

Isomorphic instances

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

1 total

Σ#PresentationMapping
1116495⟨a, b | aab=aa, bab=aab⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

2 total

Σ#PresentationMapping
1116447⟨a, b | aba=bb, aaba=bb⟩φ(a) = b, φ(b) = a
1116546⟨a, b | aba=bb, abb=aba⟩φ(a) = b, φ(b) = a