#12461 ⟨a, b | aabb=ab, baaa=a⟩

Up:Monoids with two generators and two relations
Prev:#12457 ⟨a, b | aabb=ab, abba=a⟩
Next:#12462 ⟨a, b | aabb=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. a2 ⇒ a
  2. ba ⇒ a
  3. ab2 ⇒ ab 
# ab:aabb=ab,baaa=a ab
aa=a
ba=a
abb=ab

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
1112463⟨a, b | aabb=ab, baba=a⟩φ(a) = a, φ(b) = b
1119688⟨a, b | aba=a, baabb=ab⟩φ(a) = a, φ(b) = b
1120203⟨a, b | aba=a, aabb=bab⟩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.

9 total

Σ#PresentationMapping
1119474⟨a, b | aab=a, bbaaa=ba⟩φ(a) = a, φ(b) = b
1119478⟨a, b | aab=a, bbaab=ba⟩φ(a) = a, φ(b) = b
1119482⟨a, b | aab=a, bbaba=ba⟩φ(a) = a, φ(b) = b
1119998⟨a, b | aab=a, baab=bba⟩φ(a) = a, φ(b) = b
1120006⟨a, b | aab=a, baba=bba⟩φ(a) = a, φ(b) = b
1120014⟨a, b | aab=a, babb=bba⟩φ(a) = a, φ(b) = b
1120020⟨a, b | aab=a, bbaa=baa⟩φ(a) = a, φ(b) = b
1120021⟨a, b | aab=a, bbaa=bab⟩φ(a) = a, φ(b) = b
1120029⟨a, b | aab=a, bbab=bab⟩φ(a) = a, φ(b) = b