#8887 ⟨a, b | aa=a, abbba=bb⟩

Up:Monoids with two generators and two relations
Prev:#8886 ⟨a, b | aa=a, abbba=ab⟩
Next:#8889 ⟨a, b | aa=a, abbbb=ab⟩

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. ab2 ⇒ b2
  3. b2a ⇒ b2
  4. b3 ⇒ b2 
# ab:aa=a,abbba=bb ab
aa=a
abb=bb
bba=bb
bbb=bb

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
1124641⟨a, b | aa=a, aabbba=bb⟩φ(a) = a, φ(b) = b
1124664⟨a, b | aa=a, ababba=bb⟩φ(a) = a, φ(b) = b