#21016 ⟨a, b | ab=aa, bbaa=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 ⇒ a2 [1]
2. b2a2 ⇒ a3 [2]
3. a5 ⇒ a4 [3]
# ab:ab=aa,bbaa=aaa ab
ab=aa
bbaa=aaa
aaaaa=aaaa

Isomorphic instances

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

7 total

Σ#PresentationMapping
1121017⟨a, b | ab=aa, bbaa=aab⟩φ(a) = a, φ(b) = b
1121018⟨a, b | ab=aa, bbaa=aba⟩φ(a) = a, φ(b) = b
1121019⟨a, b | ab=aa, bbaa=abb⟩φ(a) = a, φ(b) = b
1121024⟨a, b | ab=aa, bbab=aaa⟩φ(a) = a, φ(b) = b
1121025⟨a, b | ab=aa, bbab=aab⟩φ(a) = a, φ(b) = b
1121026⟨a, b | ab=aa, bbab=aba⟩φ(a) = a, φ(b) = b
1121027⟨a, b | ab=aa, bbab=abb⟩φ(a) = a, φ(b) = b