#8900 ⟨a, b | aa=a, babab=ab⟩

Up:Monoids with two generators and two relations
Prev:#8891 ⟨a, b | aa=a, abbbb=bb⟩
Next:#8901 ⟨a, b | aa=a, babab=bb⟩

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. a2 ⇒ a
  2. (ab)2 ⇒ bab
  3. b2ab ⇒ ab 
# ab:aa=a,babab=ab ab
aa=a
abab=bab
bbab=ab

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.

2 total

Σ#PresentationMapping
1124696⟨a, b | aa=a, baabab=ab⟩φ(a) = a, φ(b) = b
1125235⟨a, b | aa=a, babab=aab⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1124697⟨a, b | aa=a, baabab=ba⟩φ(a) = a, φ(b) = b