#3104 ⟨a, b | ab=a, baaa=aa⟩

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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. ab ⇒ a [1]
2. a3 ⇒ a2 [4]
3. ba2 ⇒ a2 [5]
# ab:ab=a,baaa=aa ab
ab=a
aaa=aa
baa=aa

Isomorphic instances

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

20 total

Σ#PresentationMapping
109052⟨a, b | ab=a, baaab=aa⟩φ(a) = a, φ(b) = b
109056⟨a, b | ab=a, baaba=aa⟩φ(a) = a, φ(b) = b
109064⟨a, b | ab=a, babaa=aa⟩φ(a) = a, φ(b) = b
109321⟨a, b | ab=a, baaa=aab⟩φ(a) = a, φ(b) = b
109322⟨a, b | ab=a, baaa=aba⟩φ(a) = a, φ(b) = b
1125000⟨a, b | ab=a, baaabb=aa⟩φ(a) = a, φ(b) = b
1125008⟨a, b | ab=a, baabab=aa⟩φ(a) = a, φ(b) = b
1125012⟨a, b | ab=a, baabba=aa⟩φ(a) = a, φ(b) = b
1125024⟨a, b | ab=a, babaab=aa⟩φ(a) = a, φ(b) = b
1125028⟨a, b | ab=a, bababa=aa⟩φ(a) = a, φ(b) = b
1125036⟨a, b | ab=a, babbaa=aa⟩φ(a) = a, φ(b) = b
1125541⟨a, b | ab=a, baaab=aab⟩φ(a) = a, φ(b) = b
1125542⟨a, b | ab=a, baaab=aba⟩φ(a) = a, φ(b) = b
1125549⟨a, b | ab=a, baaba=aab⟩φ(a) = a, φ(b) = b
1125550⟨a, b | ab=a, baaba=aba⟩φ(a) = a, φ(b) = b
1125565⟨a, b | ab=a, babaa=aab⟩φ(a) = a, φ(b) = b
1125566⟨a, b | ab=a, babaa=aba⟩φ(a) = a, φ(b) = b
1125823⟨a, b | ab=a, baaa=aabb⟩φ(a) = a, φ(b) = b
1125825⟨a, b | ab=a, baaa=abab⟩φ(a) = a, φ(b) = b
1125826⟨a, b | ab=a, baaa=abba⟩φ(a) = a, φ(b) = b