YES

Problem:
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(s(x),y) -> s(+(x,y))
 double(x) -> +(x,x)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [double](x0) = 6x0,
   
   [+](x0, x1) = 4x0 + x1,
   
   [0] = 0,
   
   [s](x0) = x0 + 4
  orientation:
   double(0()) = 0 >= 0 = 0()
   
   double(s(x)) = 6x + 24 >= 6x + 8 = s(s(double(x)))
   
   +(x,0()) = 4x >= x = x
   
   +(x,s(y)) = 4x + y + 4 >= 4x + y + 4 = s(+(x,y))
   
   +(s(x),y) = 4x + y + 16 >= 4x + y + 4 = s(+(x,y))
   
   double(x) = 6x >= 5x = +(x,x)
  problem:
   double(0()) -> 0()
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   double(x) -> +(x,x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [double](x0) = 4x0,
    
    [+](x0, x1) = 2x0 + 2x1,
    
    [0] = 0,
    
    [s](x0) = x0 + 6
   orientation:
    double(0()) = 0 >= 0 = 0()
    
    +(x,0()) = 2x >= x = x
    
    +(x,s(y)) = 2x + 2y + 12 >= 2x + 2y + 6 = s(+(x,y))
    
    double(x) = 4x >= 4x = +(x,x)
   problem:
    double(0()) -> 0()
    +(x,0()) -> x
    double(x) -> +(x,x)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                    [2 2]     [1]
     [double](x0) = [1 1]x0 + [2],
     
                   [1 2]     [1 0]  
     [+](x0, x1) = [0 1]x0 + [0 0]x1,
     
           [0]
     [0] = [1]
    orientation:
                   [3]    [0]      
     double(0()) = [3] >= [1] = 0()
     
                [1 2]          
     +(x,0()) = [0 1]x >= x = x
     
                 [2 2]    [1]    [2 2]          
     double(x) = [1 1]x + [2] >= [0 1]x = +(x,x)
    problem:
     +(x,0()) -> x
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                         [1 0 0]     [1]
      [+](x0, x1) = x0 + [0 1 0]x1 + [0]
                         [0 0 0]     [0],
      
            [0]
      [0] = [1]
            [0]
     orientation:
                     [1]         
      +(x,0()) = x + [1] >= x = x
                     [0]         
     problem:
      
     Qed