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))))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [not#](x0) = x0,
    
    [and](x0, x1) = 5x0 + x1 + 0,
    
    [or](x0, x1) = 5x0 + x1 + 0,
    
    [not](x0) = x0
   orientation:
    not#(or(x,y)) = 5x + y + 0 >= y = not#(y)
    
    not#(or(x,y)) = 5x + y + 0 >= y = not#(not(y))
    
    not#(or(x,y)) = 5x + y + 0 >= y = not#(not(not(y)))
    
    not#(or(x,y)) = 5x + y + 0 >= x = not#(x)
    
    not#(or(x,y)) = 5x + y + 0 >= x = not#(not(x))
    
    not#(or(x,y)) = 5x + y + 0 >= x = not#(not(not(x)))
    
    not#(and(x,y)) = 5x + y + 0 >= y = not#(y)
    
    not#(and(x,y)) = 5x + y + 0 >= y = not#(not(y))
    
    not#(and(x,y)) = 5x + y + 0 >= y = not#(not(not(y)))
    
    not#(and(x,y)) = 5x + y + 0 >= x = not#(x)
    
    not#(and(x,y)) = 5x + y + 0 >= x = not#(not(x))
    
    not#(and(x,y)) = 5x + y + 0 >= x = not#(not(not(x)))
    
    not(not(x)) = x >= x = x
    
    not(or(x,y)) = 5x + y + 0 >= 5x + y + 0 = and(not(not(not(x))),not(not(not(y))))
    
    not(and(x,y)) = 5x + y + 0 >= 5x + y + 0 = or(not(not(not(x))),not(not(not(y))))
   problem:
    DPs:
     not#(or(x,y)) -> not#(y)
     not#(or(x,y)) -> not#(not(y))
     not#(or(x,y)) -> not#(not(not(y)))
     not#(and(x,y)) -> not#(y)
     not#(and(x,y)) -> not#(not(y))
     not#(and(x,y)) -> not#(not(not(y)))
    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))))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [not#](x0) = x0,
     
     [and](x0, x1) = 5x1 + -6,
     
     [or](x0, x1) = 5x1 + -6,
     
     [not](x0) = x0
    orientation:
     not#(or(x,y)) = 5y + -6 >= y = not#(y)
     
     not#(or(x,y)) = 5y + -6 >= y = not#(not(y))
     
     not#(or(x,y)) = 5y + -6 >= y = not#(not(not(y)))
     
     not#(and(x,y)) = 5y + -6 >= y = not#(y)
     
     not#(and(x,y)) = 5y + -6 >= y = not#(not(y))
     
     not#(and(x,y)) = 5y + -6 >= y = not#(not(not(y)))
     
     not(not(x)) = x >= x = x
     
     not(or(x,y)) = 5y + -6 >= 5y + -6 = and(not(not(not(x))),not(not(not(y))))
     
     not(and(x,y)) = 5y + -6 >= 5y + -6 = 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