YES

Problem:
 a(f(),0()) -> a(s(),0())
 a(d(),0()) -> 0()
 a(d(),a(s(),x)) -> a(s(),a(s(),a(d(),a(p(),a(s(),x)))))
 a(f(),a(s(),x)) -> a(d(),a(f(),a(p(),a(s(),x))))
 a(p(),a(s(),x)) -> x

Proof:
 Uncurry Processor:
  f1(0()) -> s1(0())
  d1(0()) -> 0()
  d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
  f1(s1(x)) -> d1(f1(p1(s1(x))))
  p1(s1(x)) -> x
  a(f(),x1) -> f1(x1)
  a(s(),x1) -> s1(x1)
  a(d(),x1) -> d1(x1)
  a(p(),x1) -> p1(x1)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]     [0]
    [p1](x0) = [0 0 1]x0 + [0]
               [0 0 1]     [1],
    
               [1 0 0]  
    [d1](x0) = [0 0 0]x0
               [0 0 0]  ,
    
               [1 0 0]  
    [s1](x0) = [0 0 0]x0
               [0 1 1]  ,
    
               [1 0 0]     [1]
    [f1](x0) = [1 0 1]x0 + [0]
               [0 1 0]     [0],
    
          [0]
    [p] = [1]
          [0],
    
          [0]
    [d] = [0]
          [0],
    
          [0]
    [s] = [0]
          [0],
    
                  [1 0 0]     [1 1 1]     [1]
    [a](x0, x1) = [0 0 0]x0 + [1 0 1]x1 + [1]
                  [0 1 0]     [0 1 1]     [0],
    
          [0]
    [0] = [0]
          [0],
    
          [0]
    [f] = [1]
          [0]
   orientation:
              [1]    [0]          
    f1(0()) = [0] >= [0] = s1(0())
              [0]    [0]          
    
              [0]    [0]      
    d1(0()) = [0] >= [0] = 0()
              [0]    [0]      
    
                [1 0 0]     [1 0 0]                         
    d1(s1(x)) = [0 0 0]x >= [0 0 0]x = s1(s1(d1(p1(s1(x)))))
                [0 0 0]     [0 0 0]                         
    
                [1 0 0]    [1]    [1 0 0]    [1]                    
    f1(s1(x)) = [1 1 1]x + [0] >= [0 0 0]x + [0] = d1(f1(p1(s1(x))))
                [0 0 0]    [0]    [0 0 0]    [0]                    
    
                [1 0 0]    [0]         
    p1(s1(x)) = [0 1 1]x + [0] >= x = x
                [0 1 1]    [1]         
    
                [1 1 1]     [1]    [1 0 0]     [1]         
    a(f(),x1) = [1 0 1]x1 + [1] >= [1 0 1]x1 + [0] = f1(x1)
                [0 1 1]     [1]    [0 1 0]     [0]         
    
                [1 1 1]     [1]    [1 0 0]           
    a(s(),x1) = [1 0 1]x1 + [1] >= [0 0 0]x1 = s1(x1)
                [0 1 1]     [0]    [0 1 1]           
    
                [1 1 1]     [1]    [1 0 0]           
    a(d(),x1) = [1 0 1]x1 + [1] >= [0 0 0]x1 = d1(x1)
                [0 1 1]     [0]    [0 0 0]           
    
                [1 1 1]     [1]    [1 0 0]     [0]         
    a(p(),x1) = [1 0 1]x1 + [1] >= [0 0 1]x1 + [0] = p1(x1)
                [0 1 1]     [1]    [0 0 1]     [1]         
   problem:
    d1(0()) -> 0()
    d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
    f1(s1(x)) -> d1(f1(p1(s1(x))))
    p1(s1(x)) -> x
    a(f(),x1) -> f1(x1)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 0 0]     [0]
     [p1](x0) = [0 1 0]x0 + [0]
                [0 1 0]     [1],
     
                [1 1 0]  
     [d1](x0) = [0 1 0]x0
                [0 0 0]  ,
     
                [1 0 0]  
     [s1](x0) = [0 1 1]x0
                [0 0 0]  ,
     
                [1 0 0]     [1]
     [f1](x0) = [0 0 0]x0 + [0]
                [1 1 0]     [0],
     
                   [1 0 1]     [1 1 0]  
     [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [1 1 1]  ,
     
           [0]
     [0] = [1]
           [0],
     
           [0]
     [f] = [0]
           [1]
    orientation:
               [1]    [0]      
     d1(0()) = [1] >= [1] = 0()
               [0]    [0]      
     
                 [1 1 1]     [1 1 1]                         
     d1(s1(x)) = [0 1 1]x >= [0 1 1]x = s1(s1(d1(p1(s1(x)))))
                 [0 0 0]     [0 0 0]                         
     
                 [1 0 0]    [1]    [1 0 0]    [1]                    
     f1(s1(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = d1(f1(p1(s1(x))))
                 [1 1 1]    [0]    [0 0 0]    [0]                    
     
                 [1 0 0]    [0]         
     p1(s1(x)) = [0 1 1]x + [0] >= x = x
                 [0 1 1]    [1]         
     
                 [1 1 0]     [1]    [1 0 0]     [1]         
     a(f(),x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = f1(x1)
                 [1 1 1]     [0]    [1 1 0]     [0]         
    problem:
     d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
     f1(s1(x)) -> d1(f1(p1(s1(x))))
     p1(s1(x)) -> x
     a(f(),x1) -> f1(x1)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                 [1 0 0]  
      [p1](x0) = [1 0 0]x0
                 [1 1 0]  ,
      
                 [1 0 0]  
      [d1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
                 [1 1 0]  
      [s1](x0) = [0 0 1]x0
                 [0 0 0]  ,
      
                 [1 0 0]     [0]
      [f1](x0) = [1 0 0]x0 + [1]
                 [0 0 0]     [0],
      
                    [1 1 0]     [1 1 0]     [0]
      [a](x0, x1) = [0 0 0]x0 + [1 1 1]x1 + [1]
                    [0 0 0]     [1 0 0]     [0],
      
            [0]
      [f] = [1]
            [0]
     orientation:
                  [1 1 0]     [1 1 0]                         
      d1(s1(x)) = [0 0 0]x >= [0 0 0]x = s1(s1(d1(p1(s1(x)))))
                  [0 0 0]     [0 0 0]                         
      
                  [1 1 0]    [0]    [1 1 0]                     
      f1(s1(x)) = [1 1 0]x + [1] >= [0 0 0]x = d1(f1(p1(s1(x))))
                  [0 0 0]    [0]    [0 0 0]                     
      
                  [1 1 0]          
      p1(s1(x)) = [1 1 0]x >= x = x
                  [1 1 1]          
      
                  [1 1 0]     [1]    [1 0 0]     [0]         
      a(f(),x1) = [1 1 1]x1 + [1] >= [1 0 0]x1 + [1] = f1(x1)
                  [1 0 0]     [0]    [0 0 0]     [0]         
     problem:
      d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
      f1(s1(x)) -> d1(f1(p1(s1(x))))
      p1(s1(x)) -> x
     DP Processor:
      DPs:
       d{1,#}(s1(x)) -> p{1,#}(s1(x))
       d{1,#}(s1(x)) -> d{1,#}(p1(s1(x)))
       f{1,#}(s1(x)) -> p{1,#}(s1(x))
       f{1,#}(s1(x)) -> f{1,#}(p1(s1(x)))
       f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x))))
      TRS:
       d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
       f1(s1(x)) -> d1(f1(p1(s1(x))))
       p1(s1(x)) -> x
      TDG Processor:
       DPs:
        d{1,#}(s1(x)) -> p{1,#}(s1(x))
        d{1,#}(s1(x)) -> d{1,#}(p1(s1(x)))
        f{1,#}(s1(x)) -> p{1,#}(s1(x))
        f{1,#}(s1(x)) -> f{1,#}(p1(s1(x)))
        f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x))))
       TRS:
        d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
        f1(s1(x)) -> d1(f1(p1(s1(x))))
        p1(s1(x)) -> x
       graph:
        f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) ->
        f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x))))
        f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) ->
        f{1,#}(s1(x)) -> f{1,#}(p1(s1(x)))
        f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) ->
        f{1,#}(s1(x)) -> p{1,#}(s1(x))
        f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) ->
        d{1,#}(s1(x)) -> d{1,#}(p1(s1(x)))
        f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) ->
        d{1,#}(s1(x)) -> p{1,#}(s1(x))
        d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) ->
        d{1,#}(s1(x)) -> d{1,#}(p1(s1(x)))
        d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) -> d{1,#}(s1(x)) -> p{1,#}(s1(x))
       SCC Processor:
        #sccs: 2
        #rules: 2
        #arcs: 7/25
        DPs:
         f{1,#}(s1(x)) -> f{1,#}(p1(s1(x)))
        TRS:
         d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
         f1(s1(x)) -> d1(f1(p1(s1(x))))
         p1(s1(x)) -> x
        CDG Processor:
         DPs:
          f{1,#}(s1(x)) -> f{1,#}(p1(s1(x)))
         TRS:
          d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
          f1(s1(x)) -> d1(f1(p1(s1(x))))
          p1(s1(x)) -> x
         graph:
          
         Qed
        
        DPs:
         d{1,#}(s1(x)) -> d{1,#}(p1(s1(x)))
        TRS:
         d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
         f1(s1(x)) -> d1(f1(p1(s1(x))))
         p1(s1(x)) -> x
        CDG Processor:
         DPs:
          d{1,#}(s1(x)) -> d{1,#}(p1(s1(x)))
         TRS:
          d1(s1(x)) -> s1(s1(d1(p1(s1(x)))))
          f1(s1(x)) -> d1(f1(p1(s1(x))))
          p1(s1(x)) -> x
         graph:
          
         Qed