#1604 ⟨a, b | aaa=bb, abb=a⟩

Up:Monoids with two generators and two relations
Prev:#1603 ⟨a, b | aaa=bb, aba=b⟩
Next:#1605 ⟨a, b | aaa=bb, abb=b⟩

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 ⇒ b2 [1]
2. ab2 ⇒ a [2]
3. b2a ⇒ a [3]
4. b4 ⇒ b2 [4]
# ab:aaa=bb,abb=a ab
aaa=bb
abb=a
bba=a
bbbb=bb

Isomorphic instances

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

1 total

Σ#PresentationMapping
105074⟨a, b | aaa=bb, aaaa=a⟩φ(a) = a, φ(b) = b