YES

Problem:
 and(x,false()) -> false()
 and(x,not(false())) -> x
 not(not(x)) -> x
 implies(false(),y) -> not(false())
 implies(x,false()) -> not(x)
 implies(not(x),not(y)) -> implies(y,and(x,y))

Proof:
 DP Processor:
  DPs:
   implies#(false(),y) -> not#(false())
   implies#(x,false()) -> not#(x)
   implies#(not(x),not(y)) -> and#(x,y)
   implies#(not(x),not(y)) -> implies#(y,and(x,y))
  TRS:
   and(x,false()) -> false()
   and(x,not(false())) -> x
   not(not(x)) -> x
   implies(false(),y) -> not(false())
   implies(x,false()) -> not(x)
   implies(not(x),not(y)) -> implies(y,and(x,y))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [implies#](x0, x1) = 3x0 + 3x1 + 0,
    
    [not#](x0) = 0,
    
    [and#](x0, x1) = x1,
    
    [implies](x0, x1) = 5x0 + 4x1 + 0,
    
    [not](x0) = 2x0 + 1,
    
    [and](x0, x1) = 1x0 + 1x1 + 0,
    
    [false] = 0
   orientation:
    implies#(false(),y) = 3y + 3 >= 0 = not#(false())
    
    implies#(x,false()) = 3x + 3 >= 0 = not#(x)
    
    implies#(not(x),not(y)) = 5x + 5y + 4 >= y = and#(x,y)
    
    implies#(not(x),not(y)) = 5x + 5y + 4 >= 4x + 4y + 3 = implies#(y,and(x,y))
    
    and(x,false()) = 1x + 1 >= 0 = false()
    
    and(x,not(false())) = 1x + 3 >= x = x
    
    not(not(x)) = 4x + 3 >= x = x
    
    implies(false(),y) = 4y + 5 >= 2 = not(false())
    
    implies(x,false()) = 5x + 4 >= 2x + 1 = not(x)
    
    implies(not(x),not(y)) = 7x + 6y + 6 >= 5x + 5y + 4 = implies(y,and(x,y))
   problem:
    DPs:
     
    TRS:
     and(x,false()) -> false()
     and(x,not(false())) -> x
     not(not(x)) -> x
     implies(false(),y) -> not(false())
     implies(x,false()) -> not(x)
     implies(not(x),not(y)) -> implies(y,and(x,y))
   Qed