#1984 ⟨a, b | aaa=a, aaba=a⟩

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  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 ⇒ a [1]
2. aba ⇒ a2 [3]
# ab:aaa=a,aaba=a ab
aaa=a
aba=aa

Isomorphic instances

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

12 total

Σ#PresentationMapping
105226⟨a, b | aba=aa, aaba=a⟩φ(a) = a, φ(b) = b
1112150⟨a, b | aaaa=aa, aaba=a⟩φ(a) = a, φ(b) = b
1112242⟨a, b | aaab=ab, aaba=a⟩φ(a) = a, φ(b) = b
1112246⟨a, b | aaab=ab, abaa=a⟩φ(a) = a, φ(b) = b
1114557⟨a, b | aaba=a, ababa=a⟩φ(a) = a, φ(b) = b
1115819⟨a, b | aba=aa, ababa=a⟩φ(a) = a, φ(b) = b
1118692⟨a, b | aaa=a, aaaaba=a⟩φ(a) = a, φ(b) = b
1118696⟨a, b | aaa=a, aaabaa=a⟩φ(a) = a, φ(b) = b
1119239⟨a, b | aaa=a, aaaba=aa⟩φ(a) = a, φ(b) = b
1119247⟨a, b | aaa=a, aabaa=aa⟩φ(a) = a, φ(b) = b
1119778⟨a, b | aaa=a, aaaa=aba⟩φ(a) = a, φ(b) = b
1119790⟨a, b | aaa=a, aaba=aaa⟩φ(a) = a, φ(b) = b