#8887 ⟨a, b | aa=a, abbba=bb⟩

Up:Monoids with two generators and two relations
Prev:#8886 ⟨a, b | aa=a, abbba=ab⟩
Next:#8889 ⟨a, b | aa=a, abbbb=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. a2 ⇒ a [1]
2. ab2 ⇒ b2 [3]
3. b2a ⇒ b2 [5]
4. b3 ⇒ b2 [6]
# ab:aa=a,abbba=bb ab
aa=a
abb=bb
bba=bb
bbb=bb

Isomorphic instances

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

2 total

Σ#PresentationMapping
1124641⟨a, b | aa=a, aabbba=bb⟩φ(a) = a, φ(b) = b
1124664⟨a, b | aa=a, ababba=bb⟩φ(a) = a, φ(b) = b