#20924 ⟨a, b | ab=aa, aaaa=baa⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. a5 ⇒ a4 [3]
2. ba2 ⇒ a4 [2]
3. ab ⇒ a2 [1]
# ab:ab=aa,aaaa=baa a/b
aaaaa=aaaa
baa=aaaa
ab=aa

Isomorphic instances

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

15 total

Σ#PresentationMapping
1120925⟨a, b | ab=aa, aaaa=bab⟩φ(a) = a, φ(b) = b
1120932⟨a, b | ab=aa, aaab=baa⟩φ(a) = a, φ(b) = b
1120933⟨a, b | ab=aa, aaab=bab⟩φ(a) = a, φ(b) = b
1120940⟨a, b | ab=aa, aaba=baa⟩φ(a) = a, φ(b) = b
1120941⟨a, b | ab=aa, aaba=bab⟩φ(a) = a, φ(b) = b
1120948⟨a, b | ab=aa, aabb=baa⟩φ(a) = a, φ(b) = b
1120949⟨a, b | ab=aa, aabb=bab⟩φ(a) = a, φ(b) = b
1120956⟨a, b | ab=aa, abaa=baa⟩φ(a) = a, φ(b) = b
1120957⟨a, b | ab=aa, abaa=bab⟩φ(a) = a, φ(b) = b
1120964⟨a, b | ab=aa, abab=baa⟩φ(a) = a, φ(b) = b
1120965⟨a, b | ab=aa, abab=bab⟩φ(a) = a, φ(b) = b
1120972⟨a, b | ab=aa, abba=baa⟩φ(a) = a, φ(b) = b
1120973⟨a, b | ab=aa, abba=bab⟩φ(a) = a, φ(b) = b
1120980⟨a, b | ab=aa, abbb=baa⟩φ(a) = a, φ(b) = b
1120981⟨a, b | ab=aa, abbb=bab⟩φ(a) = a, φ(b) = b