(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
not(not(x)) → x
not(or(x, y)) → and(not(not(not(x))), not(not(not(y))))
not(and(x, y)) → or(not(not(not(x))), not(not(not(y))))
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
NOT(or(x, y)) → NOT(not(not(x)))
NOT(or(x, y)) → NOT(not(x))
NOT(or(x, y)) → NOT(x)
NOT(or(x, y)) → NOT(not(not(y)))
NOT(or(x, y)) → NOT(not(y))
NOT(or(x, y)) → NOT(y)
NOT(and(x, y)) → NOT(not(not(x)))
NOT(and(x, y)) → NOT(not(x))
NOT(and(x, y)) → NOT(x)
NOT(and(x, y)) → NOT(not(not(y)))
NOT(and(x, y)) → NOT(not(y))
NOT(and(x, y)) → NOT(y)
The TRS R consists of the following rules:
not(not(x)) → x
not(or(x, y)) → and(not(not(not(x))), not(not(not(y))))
not(and(x, y)) → or(not(not(not(x))), not(not(not(y))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.