#4711 ⟨a, b | aaba=a, babb=b⟩

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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. aba2 ⇒ a [8]
2. a2ba ⇒ a [1]
3. b2a ⇒ ba2 [6]
4. ba2b ⇒ b [4]
5. ba3b ⇒ b2 [5]
6. ab2 ⇒ a2b [3]
7. b3 ⇒ ba4b [7]
# ab:aaba=a,babb=b a/b
abaa=a
aaba=a
bba=baa
baab=b
baaab=bb
abb=aab
bbb=baaaab

Isomorphic instances

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

1 total

Σ#PresentationMapping
104748⟨a, b | abba=a, baab=b⟩φ(a) = a, φ(b) = b