#12360 ⟨a, b | aaba=ab, abbb=a⟩

Up:Monoids with two generators and two relations
Prev:#12351 ⟨a, b | aaba=aa, bbbb=b⟩
Next:#12363 ⟨a, b | aaba=ab, baaa=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. a3 ⇒ a
  2. aba ⇒ a2b
  3. ab2a ⇒ a2b2
  4. ab3 ⇒ a 
# ab:aaba=ab,abbb=a ab
aaa=a
aba=aab
abba=aabb
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.

3 total

Σ#PresentationMapping
1118712⟨a, b | aaa=a, aabbab=a⟩φ(a) = a, φ(b) = b
1118724⟨a, b | aaa=a, ababab=a⟩φ(a) = a, φ(b) = b
1119273⟨a, b | aaa=a, abbab=aa⟩φ(a) = a, φ(b) = b