#7138 ⟨a, b | bb=aa, aaaa=aa⟩

Up:Monoids with two generators and two relations
Prev:#7130 ⟨a, b | ba=ab, aabb=ab⟩
Next:#7139 ⟨a, b | bb=aa, aaaa=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. b2 ⇒ a2 [1]
2. ba2 ⇒ a2b [3]
3. a4 ⇒ a2 [2]
# ab:bb=aa,aaaa=aa ab
bb=aa
baa=aab
aaaa=aa

Isomorphic instances

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

4 total

Σ#PresentationMapping
107140⟨a, b | bb=aa, aaaa=bb⟩φ(a) = a, φ(b) = b
107149⟨a, b | bb=aa, aabb=aa⟩φ(a) = a, φ(b) = b
107155⟨a, b | bb=aa, abba=aa⟩φ(a) = a, φ(b) = b
107157⟨a, b | bb=aa, abba=bb⟩φ(a) = a, φ(b) = b