#8882 ⟨a, b | aa=a, abbab=ab⟩

Up:Monoids with two generators and two relations
Prev:#8879 ⟨a, b | aa=a, ababb=ba⟩
Next:#8883 ⟨a, b | aa=a, abbab=ba⟩

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. ab2ab ⇒ ab [2]
# ab:aa=a,abbab=ab ab
aa=a
abbab=ab

Isomorphic instances

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

3 total

Σ#PresentationMapping
1124635⟨a, b | aa=a, aabbab=ab⟩φ(a) = a, φ(b) = b
1124670⟨a, b | aa=a, abbaab=ab⟩φ(a) = a, φ(b) = b
1125199⟨a, b | aa=a, abbab=aab⟩φ(a) = a, φ(b) = b