#3074 ⟨a, b | ab=a, aaaa=ba⟩

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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. a5 ⇒ a2 [3]
2. ba ⇒ a4 [2]
3. ab ⇒ a [1]
# ab:ab=a,aaaa=ba a/b
aaaaa=aa
ba=aaaa
ab=a

Isomorphic instances

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

20 total

Σ#PresentationMapping
108990⟨a, b | ab=a, aaaab=ba⟩φ(a) = a, φ(b) = b
108994⟨a, b | ab=a, aaaba=ba⟩φ(a) = a, φ(b) = b
109002⟨a, b | ab=a, aabaa=ba⟩φ(a) = a, φ(b) = b
109018⟨a, b | ab=a, abaaa=ba⟩φ(a) = a, φ(b) = b
109261⟨a, b | ab=a, aaaa=bab⟩φ(a) = a, φ(b) = b
1124874⟨a, b | ab=a, aaaabb=ba⟩φ(a) = a, φ(b) = b
1124882⟨a, b | ab=a, aaabab=ba⟩φ(a) = a, φ(b) = b
1124886⟨a, b | ab=a, aaabba=ba⟩φ(a) = a, φ(b) = b
1124898⟨a, b | ab=a, aabaab=ba⟩φ(a) = a, φ(b) = b
1124902⟨a, b | ab=a, aababa=ba⟩φ(a) = a, φ(b) = b
1124910⟨a, b | ab=a, aabbaa=ba⟩φ(a) = a, φ(b) = b
1124930⟨a, b | ab=a, abaaab=ba⟩φ(a) = a, φ(b) = b
1124934⟨a, b | ab=a, abaaba=ba⟩φ(a) = a, φ(b) = b
1124942⟨a, b | ab=a, ababaa=ba⟩φ(a) = a, φ(b) = b
1124958⟨a, b | ab=a, abbaaa=ba⟩φ(a) = a, φ(b) = b
1125417⟨a, b | ab=a, aaaab=bab⟩φ(a) = a, φ(b) = b
1125425⟨a, b | ab=a, aaaba=bab⟩φ(a) = a, φ(b) = b
1125441⟨a, b | ab=a, aabaa=bab⟩φ(a) = a, φ(b) = b
1125473⟨a, b | ab=a, abaaa=bab⟩φ(a) = a, φ(b) = b
1125847⟨a, b | ab=a, babb=aaaa⟩φ(a) = a, φ(b) = b