#5277 ⟨a, b | aba=bb, aaab=b⟩

Up:Monoids with two generators and two relations
Prev:#5274 ⟨a, b | aba=bb, aaaa=a⟩
Next:#5285 ⟨a, b | aba=bb, abba=b⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Anti-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. b8 ⇒ b2 [9]
2. bab6 ⇒ ba [8]
3. b3a ⇒ ab3 [3]
4. a2b2 ⇒ ba [5]
5. aba ⇒ b2 [1]
6. ab2a ⇒ b2ab2 [6]
7. ba2 ⇒ b2ab4 [7]
8. a3b ⇒ b [2]
# ab:aba=bb,aaab=b b/a
bbbbbbbb=bb
babbbbbb=ba
bbba=abbb
aabb=ba
aba=bb
abba=bbabb
baa=bbabbbb
aaab=b

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1112474⟨a, b | aabb=ba, abbb=a⟩φ(a) = b, φ(b) = a