#2090 ⟨a, b | aba=a, aabb=a⟩

Up:Monoids with two generators and two relations
Prev:#2084 ⟨a, b | aba=a, aaaa=a⟩
Next:#2094 ⟨a, b | aba=a, abba=a⟩

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. aba ⇒ a
  2. a2b2 ⇒ a 
# ab:aba=a,aabb=a ab
aba=a
aabb=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.

4 total

Σ#PresentationMapping
1119108⟨a, b | aba=a, aababb=a⟩φ(a) = a, φ(b) = b
1119122⟨a, b | aba=a, abaabb=a⟩φ(a) = a, φ(b) = b
1119689⟨a, b | aba=a, baabb=ba⟩φ(a) = a, φ(b) = b
1120200⟨a, b | aba=a, aabb=aba⟩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
1112344⟨a, b | aaba=aa, bbaa=a⟩φ(a) = a, φ(b) = b