#12285 ⟨a, b | aaab=ba, baab=b⟩

Up:Monoids with two generators and two relations
Prev:#12283 ⟨a, b | aaab=ba, baaa=b⟩
Next:#12288 ⟨a, b | aaab=ba, babb=a⟩

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. a6b ⇒ b [5]
2. ba ⇒ a3b [1]
3. b2 ⇒ b [6]
# ab:aaab=ba,baab=b reversed:a/b
aaaaaab=b
ba=aaab
bb=b

Isomorphic instances

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

2 total

Σ#PresentationMapping
1112287⟨a, b | aaab=ba, baba=b⟩φ(a) = a, φ(b) = b
1112291⟨a, b | aaab=ba, bbaa=b⟩φ(a) = a, φ(b) = b