#1988 ⟨a, b | aaa=a, abab=a⟩

Up:Monoids with two generators and two relations
Prev:#1987 ⟨a, b | aaa=a, aabb=b⟩
Next:#1990 ⟨a, b | aaa=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. a3 ⇒ a
  2. aba ⇒ a2b
  3. ab2 ⇒ a2 
# ab:aaa=a,abab=a ab
aaa=a
aba=aab
abb=aa

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
1112154⟨a, b | aaaa=aa, abab=a⟩φ(a) = a, φ(b) = b
1112248⟨a, b | aaab=ab, abab=a⟩φ(a) = a, φ(b) = b
1112352⟨a, b | aaba=ab, aabb=a⟩φ(a) = a, φ(b) = b
1112356⟨a, b | aaba=ab, abab=a⟩φ(a) = a, φ(b) = b
1112358⟨a, b | aaba=ab, abba=a⟩φ(a) = a, φ(b) = b
1114759⟨a, b | abab=a, abbbb=a⟩φ(a) = a, φ(b) = b
1118698⟨a, b | aaa=a, aaabab=a⟩φ(a) = a, φ(b) = b
1118704⟨a, b | aaa=a, aabaab=a⟩φ(a) = a, φ(b) = b
1118718⟨a, b | aaa=a, abaaab=a⟩φ(a) = a, φ(b) = b
1119250⟨a, b | aaa=a, aabab=aa⟩φ(a) = a, φ(b) = b
1119262⟨a, b | aaa=a, abaab=aa⟩φ(a) = a, φ(b) = b
1119806⟨a, b | aaa=a, abab=aaa⟩φ(a) = a, φ(b) = b