#20094 ⟨a, b | aab=b, abab=bba⟩

Up:Monoids with two generators and two relations
Prev:#20087 ⟨a, b | aab=b, abaa=bbb⟩
Next:#20095 ⟨a, b | aab=b, abab=bbb⟩

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 ⇒ b [1]
2. b2a ⇒ (ab)2 [2]
3. b(ab)2 ⇒ ab3 [4]
# ab:aab=b,abab=bba reversed:a/b
aab=b
bba=abab
babab=abbb

Isomorphic instances

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

1 total

Σ#PresentationMapping
1120101⟨a, b | aab=b, abba=bab⟩φ(a) = a, φ(b) = b