#1200 ⟨a, b | aa=1, babb=bb⟩

Up:Monoids with two generators and two relations
Prev:#1193 ⟨a, b | aa=1, abbb=bb⟩
Next:#1203 ⟨a, b | aa=1, bbbb=bb⟩

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. a2 ⇒ 1 [1]
2. bab2 ⇒ b2 [2]
# ab:aa=1,babb=bb ab
aa=1
babb=bb

Isomorphic instances

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

6 total

Σ#PresentationMapping
109970⟨a, b | aa=1, aababb=bb⟩φ(a) = a, φ(b) = b
1010034⟨a, b | aa=1, baaabb=bb⟩φ(a) = a, φ(b) = b
1010277⟨a, b | aa=1, ababb=abb⟩φ(a) = a, φ(b) = b
1010515⟨a, b | aa=1, babb=aabb⟩φ(a) = a, φ(b) = b
1010521⟨a, b | aa=1, babb=baab⟩φ(a) = a, φ(b) = b
1010525⟨a, b | aa=1, bbaa=babb⟩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.

3 total

Σ#PresentationMapping
109977⟨a, b | aa=1, aabbab=bb⟩φ(a) = a, φ(b) = b
1010038⟨a, b | aa=1, baabab=bb⟩φ(a) = a, φ(b) = b
1010285⟨a, b | aa=1, abbab=abb⟩φ(a) = a, φ(b) = b