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:
   [+](x0, x1) = x0 + 3x1,
   
   [s](x0) = x0,
   
   [double](x0) = 4x0,
   
   [0] = 6
  orientation:
   double(0()) = 24 >= 6 = 0()
   
   double(s(x)) = 4x >= 4x = s(s(double(x)))
   
   +(x,0()) = x + 18 >= x = x
   
   +(x,s(y)) = x + 3y >= x + 3y = s(+(x,y))
   
   +(s(x),y) = x + 3y >= x + 3y = s(+(x,y))
   
   double(x) = 4x >= 4x = +(x,x)
  problem:
   double(s(x)) -> s(s(double(x)))
   +(x,s(y)) -> s(+(x,y))
   +(s(x),y) -> s(+(x,y))
   double(x) -> +(x,x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = 4x0 + 3x1 + 4,
    
    [s](x0) = x0,
    
    [double](x0) = 7x0 + 5
   orientation:
    double(s(x)) = 7x + 5 >= 7x + 5 = s(s(double(x)))
    
    +(x,s(y)) = 4x + 3y + 4 >= 4x + 3y + 4 = s(+(x,y))
    
    +(s(x),y) = 4x + 3y + 4 >= 4x + 3y + 4 = s(+(x,y))
    
    double(x) = 7x + 5 >= 7x + 4 = +(x,x)
   problem:
    double(s(x)) -> s(s(double(x)))
    +(x,s(y)) -> s(+(x,y))
    +(s(x),y) -> s(+(x,y))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = 6x0 + x1 + 1,
     
     [s](x0) = x0 + 1,
     
     [double](x0) = 2x0
    orientation:
     double(s(x)) = 2x + 2 >= 2x + 2 = s(s(double(x)))
     
     +(x,s(y)) = 6x + y + 2 >= 6x + y + 2 = s(+(x,y))
     
     +(s(x),y) = 6x + y + 7 >= 6x + y + 2 = s(+(x,y))
    problem:
     double(s(x)) -> s(s(double(x)))
     +(x,s(y)) -> s(+(x,y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 1 0]     [1 1 1]     [0]
      [+](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                    [0 0 0]     [0 1 0]     [1],
      
                [1 0 0]     [0]
      [s](x0) = [0 0 1]x0 + [0]
                [0 1 0]     [1],
      
                     [1 0 0]  
      [double](x0) = [0 1 1]x0
                     [0 1 1]  
     orientation:
                     [1 0 0]    [0]    [1 0 0]    [0]                  
      double(s(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = s(s(double(x)))
                     [0 1 1]    [1]    [0 1 1]    [1]                  
      
                  [1 1 0]    [1 1 1]    [1]    [1 1 0]    [1 1 1]    [0]            
      +(x,s(y)) = [0 0 0]x + [0 1 0]y + [1] >= [0 0 0]x + [0 1 0]y + [1] = s(+(x,y))
                  [0 0 0]    [0 0 1]    [1]    [0 0 0]    [0 0 1]    [1]            
     problem:
      double(s(x)) -> s(s(double(x)))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 0 0]     [0]
       [s](x0) = [0 0 1]x0 + [0]
                 [0 1 0]     [1],
       
                      [1 1 1]  
       [double](x0) = [0 1 1]x0
                      [0 1 1]  
      orientation:
                      [1 1 1]    [1]    [1 1 1]    [0]                  
       double(s(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = s(s(double(x)))
                      [0 1 1]    [1]    [0 1 1]    [1]                  
      problem:
       
      Qed