#5415 ⟨a, b | aba=aa, bab=aa⟩

Up:Monoids with two generators and two relations
Prev:#5414 ⟨a, b | aab=bb, bba=aa⟩
Next:#5416 ⟨a, b | aba=aa, bab=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. a2b ⇒ a3 [3]
2. aba ⇒ a2 [1]
3. ba2 ⇒ a3 [4]
4. bab ⇒ a2 [2]
5. a4 ⇒ a3 [5]
# ab:aba=aa,bab=aa ab
aab=aaa
aba=aa
baa=aaa
bab=aa
aaaa=aaa

Isomorphic instances

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

2 total

Σ#PresentationMapping
1116531⟨a, b | aba=aa, bab=aba⟩φ(a) = a, φ(b) = b
1116550⟨a, b | aba=bb, bab=aba⟩φ(a) = b, φ(b) = a