#21084 ⟨a, b | bb=aa, aaaa=aaa⟩

Up:Monoids with two generators and two relations
Prev:#21071 ⟨a, b | ba=ab, aabb=aab⟩
Next:#21086 ⟨a, b | bb=aa, aaaa=aba⟩

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 ⇒ b4 [4]
2. ab2 ⇒ b4 [3]
3. b2a ⇒ b4 [2]
4. a2 ⇒ b2 [1]
# ab:bb=aa,aaaa=aaa b/a
bbbbbb=bbbb
abb=bbbb
bba=bbbb
aa=bb

Isomorphic instances

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

10 total

Σ#PresentationMapping
1121085⟨a, b | bb=aa, aaaa=aab⟩φ(a) = b, φ(b) = a
1121087⟨a, b | bb=aa, aaaa=abb⟩φ(a) = a, φ(b) = b
1121089⟨a, b | bb=aa, aaaa=bbb⟩φ(a) = b, φ(b) = a
1121106⟨a, b | bb=aa, aabb=aaa⟩φ(a) = a, φ(b) = b
1121107⟨a, b | bb=aa, aabb=aab⟩φ(a) = b, φ(b) = a
1121109⟨a, b | bb=aa, aabb=baa⟩φ(a) = b, φ(b) = a
1121114⟨a, b | bb=aa, abba=aaa⟩φ(a) = a, φ(b) = b
1121115⟨a, b | bb=aa, abba=aab⟩φ(a) = b, φ(b) = a
1121117⟨a, b | bb=aa, abba=abb⟩φ(a) = a, φ(b) = b
1121119⟨a, b | bb=aa, abba=bbb⟩φ(a) = b, φ(b) = a