YES

Problem:
 d(0()) -> 0()
 d(s(x)) -> s(s(d(x)))
 e(s(x),y) -> e(x,d(y))
 sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                   [1 1 1]     [1 0 0]  
   [sup](x0, x1) = [1 0 0]x0 + [1 0 0]x1
                   [0 0 0]     [0 0 0]  ,
   
                 [1 0 0]     [1 0 0]  
   [e](x0, x1) = [1 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
             [1 0 0]     [0]
   [s](x0) = [0 0 1]x0 + [0]
             [0 1 0]     [1],
   
             [1 0 0]  
   [d](x0) = [0 1 1]x0
             [0 1 1]  ,
   
         [0]
   [0] = [0]
         [0]
  orientation:
            [0]    [0]      
   d(0()) = [0] >= [0] = 0()
            [0]    [0]      
   
             [1 0 0]    [0]    [1 0 0]    [0]             
   d(s(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = s(s(d(x)))
             [0 1 1]    [1]    [0 1 1]    [1]             
   
               [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]             
   e(s(x),y) = [1 0 0]x + [0 0 0]y >= [1 0 0]x + [0 0 0]y = e(x,d(y))
               [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]             
   
                        [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 0 0]                      
   sup(s(x),e(0(),y)) = [1 0 0]x + [1 0 0]y + [0] >= [1 0 0]x + [1 0 0]y = sup(x,e(y,s(0())))
                        [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                      
  problem:
   d(0()) -> 0()
   d(s(x)) -> s(s(d(x)))
   e(s(x),y) -> e(x,d(y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 1 1]     [1 0 0]  
    [e](x0, x1) = [1 1 1]x0 + [0 0 0]x1
                  [0 1 1]     [1 0 0]  ,
    
              [1 0 0]     [0]
    [s](x0) = [0 0 1]x0 + [0]
              [0 1 0]     [1],
    
              [1 0 0]  
    [d](x0) = [0 1 1]x0
              [1 1 1]  ,
    
          [0]
    [0] = [0]
          [1]
   orientation:
             [0]    [0]      
    d(0()) = [1] >= [0] = 0()
             [1]    [1]      
    
              [1 0 0]    [0]    [1 0 0]    [0]             
    d(s(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = s(s(d(x)))
              [1 1 1]    [1]    [1 1 1]    [1]             
    
                [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 0 0]             
    e(s(x),y) = [1 1 1]x + [0 0 0]y + [1] >= [1 1 1]x + [0 0 0]y = e(x,d(y))
                [0 1 1]    [1 0 0]    [1]    [0 1 1]    [1 0 0]             
   problem:
    d(0()) -> 0()
    d(s(x)) -> s(s(d(x)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 
     [s](x0) = x0
                 ,
     
               [1 0 0]     [1]
     [d](x0) = [0 1 0]x0 + [0]
               [0 0 0]     [1],
     
           [0]
     [0] = [0]
           [0]
    orientation:
              [1]    [0]      
     d(0()) = [0] >= [0] = 0()
              [1]    [0]      
     
               [1 0 0]    [1]    [1 0 0]    [1]             
     d(s(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = s(s(d(x)))
               [0 0 0]    [1]    [0 0 0]    [1]             
    problem:
     d(s(x)) -> s(s(d(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]  
      [d](x0) = [0 1 1]x0
                [0 1 1]  
     orientation:
                [1 1 1]    [1]    [1 1 1]    [0]             
      d(s(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = s(s(d(x)))
                [0 1 1]    [1]    [0 1 1]    [1]             
     problem:
      
     Qed