#2192 ⟨a, b | ab=aa, baaa=a⟩

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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. ab ⇒ a2
  2. ba ⇒ a2
  3. a4 ⇒ a 
# ab:ab=aa,baaa=a ab
ab=aa
ba=aa
aaaa=a

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

28 total

Σ#PresentationMapping
92194⟨a, b | ab=aa, baab=a⟩φ(a) = a, φ(b) = b
92196⟨a, b | ab=aa, baba=a⟩φ(a) = a, φ(b) = b
92198⟨a, b | ab=aa, babb=a⟩φ(a) = a, φ(b) = b
104663⟨a, b | aaab=a, baab=a⟩φ(a) = a, φ(b) = b
104665⟨a, b | aaab=a, baba=a⟩φ(a) = a, φ(b) = b
104706⟨a, b | aaba=a, baab=a⟩φ(a) = a, φ(b) = b
104720⟨a, b | aaba=b, abab=b⟩φ(a) = b, φ(b) = a
104722⟨a, b | aaba=b, abba=b⟩φ(a) = b, φ(b) = a
1112896⟨a, b | aab=aaa, baaa=a⟩φ(a) = a, φ(b) = b
1112898⟨a, b | aab=aaa, baab=a⟩φ(a) = a, φ(b) = b
1112900⟨a, b | aab=aaa, baba=a⟩φ(a) = a, φ(b) = b
1112926⟨a, b | aba=aaa, baab=a⟩φ(a) = a, φ(b) = b
1113001⟨a, b | abb=aab, aaba=b⟩φ(a) = b, φ(b) = a
1113007⟨a, b | abb=aab, abba=b⟩φ(a) = b, φ(b) = a
1113021⟨a, b | abb=aba, abaa=b⟩φ(a) = b, φ(b) = a
1113023⟨a, b | abb=aba, abab=b⟩φ(a) = b, φ(b) = a
1113025⟨a, b | abb=aba, abba=b⟩φ(a) = b, φ(b) = a
1113027⟨a, b | abb=aba, abbb=b⟩φ(a) = b, φ(b) = a
1113030⟨a, b | abb=aba, baab=a⟩φ(a) = a, φ(b) = b
1113066⟨a, b | baa=abb, aaab=a⟩φ(a) = a, φ(b) = b
1113069⟨a, b | baa=abb, aaba=b⟩φ(a) = b, φ(b) = a
1113074⟨a, b | baa=abb, abab=a⟩φ(a) = a, φ(b) = b
1113102⟨a, b | bab=aba, aaab=a⟩φ(a) = a, φ(b) = b
1113104⟨a, b | bab=aba, aaba=a⟩φ(a) = a, φ(b) = b
1113105⟨a, b | bab=aba, aaba=b⟩φ(a) = b, φ(b) = a
1113106⟨a, b | bab=aba, aabb=a⟩φ(a) = a, φ(b) = b
1113107⟨a, b | bab=aba, abab=a⟩φ(a) = a, φ(b) = b
1113108⟨a, b | bab=aba, abba=a⟩φ(a) = a, φ(b) = b