#5354 ⟨a, b | aab=aa, aba=ab⟩

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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. a3 ⇒ a2 [3]
2. a2b ⇒ a2 [1]
3. aba ⇒ ab [2]
4. ab2 ⇒ ab [4]
# ab:aab=aa,aba=ab ab
aaa=aa
aab=aa
aba=ab
abb=ab

Isomorphic instances

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

3 total

Σ#PresentationMapping
1116106⟨a, b | aab=aa, abba=ab⟩φ(a) = a, φ(b) = b
1116377⟨a, b | aba=ab, aaab=aa⟩φ(a) = a, φ(b) = b
1116381⟨a, b | aba=ab, aaba=aa⟩φ(a) = a, φ(b) = b