#5390 ⟨a, b | aab=ba, aba=aa⟩

Up:Monoids with two generators and two relations
Prev:#5389 ⟨a, b | aab=ab, bba=ba⟩
Next:#5391 ⟨a, b | aab=ba, aba=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. ba ⇒ a2 [6]
2. a3 ⇒ a2 [5]
3. a2b ⇒ a2 [7]
# ab:aab=ba,aba=aa ab
ba=aa
aaa=aa
aab=aa

Isomorphic instances

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

5 total

Σ#PresentationMapping
1116213⟨a, b | aab=ba, aaab=aa⟩φ(a) = a, φ(b) = b
1116217⟨a, b | aab=ba, aaba=aa⟩φ(a) = a, φ(b) = b
1116225⟨a, b | aab=ba, abaa=aa⟩φ(a) = a, φ(b) = b
1116241⟨a, b | aab=ba, baaa=aa⟩φ(a) = a, φ(b) = b
1116354⟨a, b | aba=aa, abab=ba⟩φ(a) = a, φ(b) = b