#478 ⟨a, b, c | ba=ac, bcb=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. bc ⇒ cb [3]
2. ac ⇒ ba [1]
3. cb2 ⇒ 1 [4]
4. ab2 ⇒ cba [6]
# abc:ba=ac,bcb=1 cba - -
bc=cb
ac=ba
cbb=1
abb=cba

Isomorphic instances

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

2 total

Σ#PresentationMapping
84399⟨a, b, c | aba=1, abcb=c⟩φ(a) = b, φ(b) = c, φ(c) = a
84434⟨a, b, c | aba=1, bacb=c⟩φ(a) = b, φ(b) = c, φ(c) = a