#3018 ⟨a, b | aa=a, abab=bb⟩

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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. a2 ⇒ a [1]
2. ab2 ⇒ b2 [3]
3. (ab)2 ⇒ b2 [2]
4. b2ab ⇒ b3 [4]
# ab:aa=a,abab=bb ab
aa=a
abb=bb
abab=bb
bbab=bbb

Isomorphic instances

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

5 total

Σ#PresentationMapping
108861⟨a, b | aa=a, aabab=bb⟩φ(a) = a, φ(b) = b
108873⟨a, b | aa=a, abaab=bb⟩φ(a) = a, φ(b) = b
1124610⟨a, b | aa=a, aaabab=bb⟩φ(a) = a, φ(b) = b
1124622⟨a, b | aa=a, aabaab=bb⟩φ(a) = a, φ(b) = b
1124649⟨a, b | aa=a, abaaab=bb⟩φ(a) = a, φ(b) = b