#3178 ⟨a, b | ab=a, baa=aaa⟩

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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. ba2 ⇒ a3 [2]
3. a4 ⇒ a3 [3]
# ab:ab=a,baa=aaa ab
ab=a
baa=aaa
aaaa=aaa

Isomorphic instances

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

20 total

Σ#PresentationMapping
109268⟨a, b | ab=a, aaab=baa⟩φ(a) = a, φ(b) = b
109276⟨a, b | ab=a, aaba=baa⟩φ(a) = a, φ(b) = b
109292⟨a, b | ab=a, abaa=baa⟩φ(a) = a, φ(b) = b
109328⟨a, b | ab=a, baab=aaa⟩φ(a) = a, φ(b) = b
109336⟨a, b | ab=a, baba=aaa⟩φ(a) = a, φ(b) = b
1125432⟨a, b | ab=a, aaabb=baa⟩φ(a) = a, φ(b) = b
1125448⟨a, b | ab=a, aabab=baa⟩φ(a) = a, φ(b) = b
1125456⟨a, b | ab=a, aabba=baa⟩φ(a) = a, φ(b) = b
1125480⟨a, b | ab=a, abaab=baa⟩φ(a) = a, φ(b) = b
1125488⟨a, b | ab=a, ababa=baa⟩φ(a) = a, φ(b) = b
1125504⟨a, b | ab=a, abbaa=baa⟩φ(a) = a, φ(b) = b
1125556⟨a, b | ab=a, baabb=aaa⟩φ(a) = a, φ(b) = b
1125572⟨a, b | ab=a, babab=aaa⟩φ(a) = a, φ(b) = b
1125580⟨a, b | ab=a, babba=aaa⟩φ(a) = a, φ(b) = b
1125829⟨a, b | ab=a, baab=aaab⟩φ(a) = a, φ(b) = b
1125830⟨a, b | ab=a, baab=aaba⟩φ(a) = a, φ(b) = b
1125832⟨a, b | ab=a, baab=abaa⟩φ(a) = a, φ(b) = b
1125838⟨a, b | ab=a, baba=aaab⟩φ(a) = a, φ(b) = b
1125839⟨a, b | ab=a, baba=aaba⟩φ(a) = a, φ(b) = b
1125841⟨a, b | ab=a, baba=abaa⟩φ(a) = a, φ(b) = b