#892 ⟨a, b | aa=a, abbb=a⟩

Up:Monoids with two generators and two relations
Prev:#891 ⟨a, b | aa=a, abba=b⟩
Next:#893 ⟨a, b | aa=a, abbb=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. a2 ⇒ a
  2. ab3 ⇒ a 
# ab:aa=a,abbb=a ab
aa=a
abbb=a

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.

12 total

Σ#PresentationMapping
92870⟨a, b | aa=a, aabbb=a⟩φ(a) = a, φ(b) = b
93022⟨a, b | aa=a, abbb=aa⟩φ(a) = a, φ(b) = b
105140⟨a, b | aab=ab, abbb=a⟩φ(a) = a, φ(b) = b
108582⟨a, b | aa=a, aaabbb=a⟩φ(a) = a, φ(b) = b
108866⟨a, b | aa=a, aabbb=aa⟩φ(a) = a, φ(b) = b
109156⟨a, b | aa=a, abbb=aaa⟩φ(a) = a, φ(b) = b
1115415⟨a, b | aaa=aa, aabbb=a⟩φ(a) = a, φ(b) = b
1115623⟨a, b | aab=ab, aabbb=a⟩φ(a) = a, φ(b) = b
1124058⟨a, b | aa=a, aaaabbb=a⟩φ(a) = a, φ(b) = b
1124615⟨a, b | aa=a, aaabbb=aa⟩φ(a) = a, φ(b) = b
1125168⟨a, b | aa=a, aabbb=aaa⟩φ(a) = a, φ(b) = b
1125679⟨a, b | aa=a, abbb=aaaa⟩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.

3 total

Σ#PresentationMapping
1114480⟨a, b | aaab=b, aaabb=b⟩φ(a) = b, φ(b) = a
1114508⟨a, b | aaab=b, baaab=b⟩φ(a) = b, φ(b) = a
1115665⟨a, b | aab=ab, bbbaa=a⟩φ(a) = a, φ(b) = b