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The following steps can be applied to test for equivalence between any two valid expressions .

  1. Transform both expression to long normal form (see Transforming expressions to normal forms ).
  2. Render these normal forms according the canonical representation (see Canonical representations .
  3. Perform a simple string comparison between the two long normal forms in canonical representation:
    1. If the strings are identical then the expressions being tested are equivalent;
    2. If the strings are not identical the two expressions being tested are not logically equivalent.


Note that this does not prove that the expressions are not equivalent. This limitation applies for the following reasons: