YES

Problem:
 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))))

Proof:
 DP Processor:
  DPs:
   not#(or(x,y)) -> not#(y)
   not#(or(x,y)) -> not#(not(y))
   not#(or(x,y)) -> not#(not(not(y)))
   not#(or(x,y)) -> not#(x)
   not#(or(x,y)) -> not#(not(x))
   not#(or(x,y)) -> not#(not(not(x)))
   not#(and(x,y)) -> not#(y)
   not#(and(x,y)) -> not#(not(y))
   not#(and(x,y)) -> not#(not(not(y)))
   not#(and(x,y)) -> not#(x)
   not#(and(x,y)) -> not#(not(x))
   not#(and(x,y)) -> not#(not(not(x)))
  TRS:
   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))))
  KBO Processor:
   argument filtering:
    pi(not) = [0]
    pi(or) = [0,1]
    pi(and) = [0,1]
    pi(not#) = 0
   weight function:
    w0 = 1
    w(not#) = 1
    w(and) = w(or) = w(not) = 0
   precedence:
    not# > not > and ~ or
   problem:
    DPs:
     
    TRS:
     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))))
   Qed