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))))
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [not#](x0) = x0 + 1,
    
    [and](x0, x1) = x0 + x1 + 1,
    
    [or](x0, x1) = x0 + x1 + 1,
    
    [not](x0) = x0
   orientation:
    not#(or(x,y)) = x + y + 2 >= y + 1 = not#(y)
    
    not#(or(x,y)) = x + y + 2 >= y + 1 = not#(not(y))
    
    not#(or(x,y)) = x + y + 2 >= y + 1 = not#(not(not(y)))
    
    not#(or(x,y)) = x + y + 2 >= x + 1 = not#(x)
    
    not#(or(x,y)) = x + y + 2 >= x + 1 = not#(not(x))
    
    not#(or(x,y)) = x + y + 2 >= x + 1 = not#(not(not(x)))
    
    not#(and(x,y)) = x + y + 2 >= y + 1 = not#(y)
    
    not#(and(x,y)) = x + y + 2 >= y + 1 = not#(not(y))
    
    not#(and(x,y)) = x + y + 2 >= y + 1 = not#(not(not(y)))
    
    not#(and(x,y)) = x + y + 2 >= x + 1 = not#(x)
    
    not#(and(x,y)) = x + y + 2 >= x + 1 = not#(not(x))
    
    not#(and(x,y)) = x + y + 2 >= x + 1 = not#(not(not(x)))
    
    not(not(x)) = x >= x = x
    
    not(or(x,y)) = x + y + 1 >= x + y + 1 = and(not(not(not(x))),not(not(not(y))))
    
    not(and(x,y)) = x + y + 1 >= x + y + 1 = or(not(not(not(x))),not(not(not(y))))
   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