#5345 ⟨a, b | aaa=bb, abb=aa⟩

Up:Monoids with two generators and two relations
Prev:#5344 ⟨a, b | aaa=bb, aba=bb⟩
Next:#5346 ⟨a, b | aaa=bb, abb=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. b6 ⇒ b2 [8]
2. ab2 ⇒ b4 [6]
3. b2a ⇒ b4 [7]
4. a2 ⇒ b4 [9]
# ab:aaa=bb,abb=aa b/a
bbbbbb=bb
abb=bbbb
bba=bbbb
aa=bbbb

Isomorphic instances

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

3 total

Σ#PresentationMapping
1116045⟨a, b | aaa=bb, aaaa=aa⟩φ(a) = a, φ(b) = b
1116285⟨a, b | aab=bb, aabb=aa⟩φ(a) = b, φ(b) = a
1116309⟨a, b | aab=bb, baab=aa⟩φ(a) = b, φ(b) = a