#591 ⟨a, b | aab=a, bba=b⟩

Up:Monoids with two generators and two relations
Prev:#590 ⟨a, b | aab=a, bba=a⟩
Next:#593 ⟨a, b | aab=b, aba=b⟩

Properties

Complete 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
  1. a2b ⇒ a
  2. aba ⇒ a
  3. bab ⇒ b
  4. b2a ⇒ b 
# ab:aab=a,bba=b ab
aab=a
aba=a
bab=b
bba=b

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

4 total

Σ#PresentationMapping
106363⟨a, b | aab=a, babba=b⟩φ(a) = a, φ(b) = b
106369⟨a, b | aab=a, bbaab=b⟩φ(a) = a, φ(b) = b
106371⟨a, b | aab=a, bbaba=b⟩φ(a) = a, φ(b) = b
106375⟨a, b | aab=a, bbbaa=b⟩φ(a) = a, φ(b) = b