#451 ⟨a, b | bab=ab, bbb=1⟩

Up:Monoids with two generators and two relations
Prev:#450 ⟨a, b | bab=aa, bbb=1⟩
Next:#455 ⟨a, b | aaaa=1, aabb=1⟩

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. ba ⇒ a
  2. b3 ⇒ 1 
# ab:bab=ab,bbb=1 ab
ba=a
bbb=1

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.

10 total

Σ#PresentationMapping
92419⟨a, b | aaa=1, aaaab=b⟩φ(a) = b, φ(b) = a
92564⟨a, b | aaa=1, aaab=ab⟩φ(a) = b, φ(b) = a
92569⟨a, b | aaa=1, aaba=ba⟩φ(a) = b, φ(b) = a
107483⟨a, b | aaa=1, aaaaab=b⟩φ(a) = b, φ(b) = a
108031⟨a, b | aaa=1, aaab=aab⟩φ(a) = b, φ(b) = a
108040⟨a, b | aaa=1, aaba=aba⟩φ(a) = b, φ(b) = a
1122196⟨a, b | aaa=1, aaaaab=ab⟩φ(a) = b, φ(b) = a
1122201⟨a, b | aaa=1, aaaaba=ba⟩φ(a) = b, φ(b) = a
1122727⟨a, b | aaa=1, aaaab=aab⟩φ(a) = b, φ(b) = a
1122736⟨a, b | aaa=1, aaaba=aba⟩φ(a) = b, φ(b) = a