#9144 ⟨a, b | aa=a, abab=aba⟩

Up:Monoids with two generators and two relations
Prev:#9124 ⟨a, b | aa=a, aaab=bba⟩
Next:#9145 ⟨a, b | aa=a, abab=abb⟩

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. (ab)2 ⇒ aba [2]
# ab:aa=a,abab=aba ab
aa=a
abab=aba

Isomorphic instances

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

4 total

Σ#PresentationMapping
1125154⟨a, b | aa=a, aabab=aba⟩φ(a) = a, φ(b) = b
1125178⟨a, b | aa=a, abaab=aba⟩φ(a) = a, φ(b) = b
1125671⟨a, b | aa=a, abab=aaba⟩φ(a) = a, φ(b) = b
1125673⟨a, b | aa=a, abab=abaa⟩φ(a) = a, φ(b) = b