#3072 ⟨a, b | ab=a, aaaa=aa⟩

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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. ab ⇒ a [1]
2. a4 ⇒ a2 [2]
# ab:ab=a,aaaa=aa ab
ab=a
aaaa=aa

Isomorphic instances

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

27 total

Σ#PresentationMapping
108988⟨a, b | ab=a, aaaab=aa⟩φ(a) = a, φ(b) = b
108992⟨a, b | ab=a, aaaba=aa⟩φ(a) = a, φ(b) = b
109000⟨a, b | ab=a, aabaa=aa⟩φ(a) = a, φ(b) = b
109016⟨a, b | ab=a, abaaa=aa⟩φ(a) = a, φ(b) = b
109257⟨a, b | ab=a, aaaa=aab⟩φ(a) = a, φ(b) = b
109258⟨a, b | ab=a, aaaa=aba⟩φ(a) = a, φ(b) = b
1124872⟨a, b | ab=a, aaaabb=aa⟩φ(a) = a, φ(b) = b
1124880⟨a, b | ab=a, aaabab=aa⟩φ(a) = a, φ(b) = b
1124884⟨a, b | ab=a, aaabba=aa⟩φ(a) = a, φ(b) = b
1124896⟨a, b | ab=a, aabaab=aa⟩φ(a) = a, φ(b) = b
1124900⟨a, b | ab=a, aababa=aa⟩φ(a) = a, φ(b) = b
1124908⟨a, b | ab=a, aabbaa=aa⟩φ(a) = a, φ(b) = b
1124928⟨a, b | ab=a, abaaab=aa⟩φ(a) = a, φ(b) = b
1124932⟨a, b | ab=a, abaaba=aa⟩φ(a) = a, φ(b) = b
1124940⟨a, b | ab=a, ababaa=aa⟩φ(a) = a, φ(b) = b
1124956⟨a, b | ab=a, abbaaa=aa⟩φ(a) = a, φ(b) = b
1125413⟨a, b | ab=a, aaaab=aab⟩φ(a) = a, φ(b) = b
1125414⟨a, b | ab=a, aaaab=aba⟩φ(a) = a, φ(b) = b
1125421⟨a, b | ab=a, aaaba=aab⟩φ(a) = a, φ(b) = b
1125422⟨a, b | ab=a, aaaba=aba⟩φ(a) = a, φ(b) = b
1125437⟨a, b | ab=a, aabaa=aab⟩φ(a) = a, φ(b) = b
1125438⟨a, b | ab=a, aabaa=aba⟩φ(a) = a, φ(b) = b
1125469⟨a, b | ab=a, abaaa=aab⟩φ(a) = a, φ(b) = b
1125470⟨a, b | ab=a, abaaa=aba⟩φ(a) = a, φ(b) = b
1125795⟨a, b | ab=a, aabb=aaaa⟩φ(a) = a, φ(b) = b
1125802⟨a, b | ab=a, abab=aaaa⟩φ(a) = a, φ(b) = b
1125807⟨a, b | ab=a, abba=aaaa⟩φ(a) = a, φ(b) = b