#21090 ⟨a, b | bb=aa, aaab=aaa⟩

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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. b2 ⇒ a2 [1]
2. ba2 ⇒ a2b [3]
3. a3b ⇒ a3 [2]
4. a2ba ⇒ a3 [5]
5. a5 ⇒ a3 [4]
# ab:bb=aa,aaab=aaa ab
bb=aa
baa=aab
aaab=aaa
aaba=aaa
aaaaa=aaa

Isomorphic instances

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

11 total

Σ#PresentationMapping
1121091⟨a, b | bb=aa, aaab=aab⟩φ(a) = b, φ(b) = a
1121093⟨a, b | bb=aa, aaab=abb⟩φ(a) = a, φ(b) = b
1121094⟨a, b | bb=aa, aaab=baa⟩φ(a) = b, φ(b) = a
1121096⟨a, b | bb=aa, aaab=bba⟩φ(a) = a, φ(b) = b
1121097⟨a, b | bb=aa, aaab=bbb⟩φ(a) = b, φ(b) = a
1121098⟨a, b | bb=aa, aaba=aaa⟩φ(a) = a, φ(b) = b
1121099⟨a, b | bb=aa, aaba=aab⟩φ(a) = b, φ(b) = a
1121101⟨a, b | bb=aa, aaba=abb⟩φ(a) = a, φ(b) = b
1121102⟨a, b | bb=aa, aaba=baa⟩φ(a) = b, φ(b) = a
1121104⟨a, b | bb=aa, aaba=bba⟩φ(a) = a, φ(b) = b
1121105⟨a, b | bb=aa, aaba=bbb⟩φ(a) = b, φ(b) = a