#3187 ⟨a, b | ab=a, bba=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. b2a ⇒ a3 [2]
3. a4 ⇒ a2 [3]
# ab:ab=a,bba=aaa ab
ab=a
bba=aaa
aaaa=aa

Isomorphic instances

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

14 total

Σ#PresentationMapping
109270⟨a, b | ab=a, aaab=bba⟩φ(a) = a, φ(b) = b
109278⟨a, b | ab=a, aaba=bba⟩φ(a) = a, φ(b) = b
109294⟨a, b | ab=a, abaa=bba⟩φ(a) = a, φ(b) = b
109360⟨a, b | ab=a, bbab=aaa⟩φ(a) = a, φ(b) = b
1125434⟨a, b | ab=a, aaabb=bba⟩φ(a) = a, φ(b) = b
1125450⟨a, b | ab=a, aabab=bba⟩φ(a) = a, φ(b) = b
1125458⟨a, b | ab=a, aabba=bba⟩φ(a) = a, φ(b) = b
1125482⟨a, b | ab=a, abaab=bba⟩φ(a) = a, φ(b) = b
1125490⟨a, b | ab=a, ababa=bba⟩φ(a) = a, φ(b) = b
1125506⟨a, b | ab=a, abbaa=bba⟩φ(a) = a, φ(b) = b
1125620⟨a, b | ab=a, bbabb=aaa⟩φ(a) = a, φ(b) = b
1125871⟨a, b | ab=a, bbab=aaab⟩φ(a) = a, φ(b) = b
1125872⟨a, b | ab=a, bbab=aaba⟩φ(a) = a, φ(b) = b
1125874⟨a, b | ab=a, bbab=abaa⟩φ(a) = a, φ(b) = b