#16165 ⟨a, b | aab=ab, abab=aa⟩

Up:Monoids with two generators and two relations
Prev:#16164 ⟨a, b | aab=ab, abaa=bb⟩
Next:#16166 ⟨a, b | aab=ab, abab=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. a3 ⇒ a2 [3]
2. a2b ⇒ ab [1]
3. aba ⇒ ab [6]
4. ab2 ⇒ a2 [5]
# ab:aab=ab,abab=aa ab
aaa=aa
aab=ab
aba=ab
abb=aa

Isomorphic instances

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

2 total

Σ#PresentationMapping
1116393⟨a, b | aba=ab, abab=aa⟩φ(a) = a, φ(b) = b
1116397⟨a, b | aba=ab, abba=aa⟩φ(a) = a, φ(b) = b