#2574 ⟨a, b | aaa=1, aabb=bb⟩

Up:Monoids with two generators and two relations
Prev:#2455 ⟨a, b | aaa=1, bbbbb=b⟩
Next:#2576 ⟨a, b | aaa=1, abab=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. a3 ⇒ 1 [1]
2. ab2 ⇒ b2 [3]
# ab:aaa=1,aabb=bb ab
aaa=1
abb=bb

Isomorphic instances

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

8 total

Σ#PresentationMapping
108049⟨a, b | aaa=1, aabb=abb⟩φ(a) = a, φ(b) = b
108059⟨a, b | aaa=1, abab=bab⟩φ(a) = a, φ(b) = aab
1122206⟨a, b | aaa=1, aaaabb=bb⟩φ(a) = a, φ(b) = b
1122253⟨a, b | aaa=1, abaaab=bb⟩φ(a) = a, φ(b) = b
1122745⟨a, b | aaa=1, aaabb=abb⟩φ(a) = a, φ(b) = b
1122761⟨a, b | aaa=1, aabab=bab⟩φ(a) = a, φ(b) = aab
1122770⟨a, b | aaa=1, aabba=bba⟩φ(a) = a, φ(b) = b
1122827⟨a, b | aaa=1, baaab=abb⟩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
108065⟨a, b | aaa=1, abba=abb⟩φ(a) = a, φ(b) = b
1122218⟨a, b | aaa=1, aaabba=bb⟩φ(a) = a, φ(b) = b
1122748⟨a, b | aaa=1, aaabb=bba⟩φ(a) = a, φ(b) = b