#14493 ⟨a, b | aaab=b, ababa=a⟩

Up:Monoids with two generators and two relations
Prev:#14490 ⟨a, b | aaab=b, abaaa=b⟩
Next:#14494 ⟨a, b | aaab=b, ababa=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. a4 ⇒ a [7]
2. a3b ⇒ b [1]
3. (ba)2 ⇒ a3 [3]
4. bab2 ⇒ a2b [5]
# ab:aaab=b,ababa=a ab
aaaa=a
aaab=b
baba=aaa
babb=aab

Isomorphic instances

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

1 total

Σ#PresentationMapping
1114513⟨a, b | aaab=b, babaa=a⟩φ(a) = a, φ(b) = b