#5321 ⟨a, b | aaa=ab, abb=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. a6 ⇒ a4 [3]
2. ba ⇒ a5 [2]
3. ab ⇒ a3 [1]
# ab:aaa=ab,abb=ba a/b
aaaaaa=aaaa
ba=aaaaa
ab=aaa

Isomorphic instances

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

3 total

Σ#PresentationMapping
1115987⟨a, b | aaa=ab, aaab=ba⟩φ(a) = a, φ(b) = b
1115991⟨a, b | aaa=ab, aaba=ba⟩φ(a) = a, φ(b) = b
1115999⟨a, b | aaa=ab, abaa=ba⟩φ(a) = a, φ(b) = b