#8876 ⟨a, b | aa=a, ababa=bb⟩

Up:Monoids with two generators and two relations
Prev:#8839 ⟨a, b | ab=a, bbbbbb=b⟩
Next:#8878 ⟨a, b | aa=a, ababb=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. a2 ⇒ a [1]
2. ab2 ⇒ b2 [3]
3. b2a ⇒ b2 [4]
4. a(ba)2 ⇒ b2 [2]
# ab:aa=a,ababa=bb ab
aa=a
abb=bb
bba=bb
ababa=bb

Isomorphic instances

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

2 total

Σ#PresentationMapping
1124626⟨a, b | aa=a, aababa=bb⟩φ(a) = a, φ(b) = b
1124652⟨a, b | aa=a, abaaba=bb⟩φ(a) = a, φ(b) = b