YES

Problem:
 f(s(x)) -> s(f(f(p(s(x)))))
 f(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> p#(s(x))
   f#(s(x)) -> f#(p(s(x)))
   f#(s(x)) -> f#(f(p(s(x))))
  TRS:
   f(s(x)) -> s(f(f(p(s(x)))))
   f(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    f#(s(x)) -> p#(s(x))
    f#(s(x)) -> f#(p(s(x)))
    f#(s(x)) -> f#(f(p(s(x))))
   TRS:
    f(s(x)) -> s(f(f(p(s(x)))))
    f(0()) -> 0()
    p(s(x)) -> x
   graph:
    f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> f#(f(p(s(x))))
    f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> f#(p(s(x)))
    f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> p#(s(x))
    f#(s(x)) -> f#(f(p(s(x)))) -> f#(s(x)) -> f#(f(p(s(x))))
    f#(s(x)) -> f#(f(p(s(x)))) -> f#(s(x)) -> f#(p(s(x)))
    f#(s(x)) -> f#(f(p(s(x)))) -> f#(s(x)) -> p#(s(x))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     f#(s(x)) -> f#(p(s(x)))
     f#(s(x)) -> f#(f(p(s(x))))
    TRS:
     f(s(x)) -> s(f(f(p(s(x)))))
     f(0()) -> 0()
     p(s(x)) -> x
    Matrix Interpretation Processor: dim=3
     
     interpretation:
      [f#](x0) = [1 0 0]x0,
      
            [0]
      [0] = [0]
            [0],
      
                [0 1 0]  
      [p](x0) = [0 0 2]x0
                [0 0 1]  ,
      
                [1 0 0]     [0]
      [f](x0) = [1 0 0]x0 + [2]
                [1 0 1]     [0],
      
                [3 0 0]     [3]
      [s](x0) = [1 0 0]x0 + [0]
                [0 1 1]     [1]
     orientation:
      f#(s(x)) = [3 0 0]x + [3] >= [1 0 0]x = f#(p(s(x)))
      
      f#(s(x)) = [3 0 0]x + [3] >= [1 0 0]x = f#(f(p(s(x))))
      
                [3 0 0]    [3]    [3 0 0]    [3]                   
      f(s(x)) = [3 0 0]x + [5] >= [1 0 0]x + [0] = s(f(f(p(s(x)))))
                [3 1 1]    [4]    [3 1 1]    [4]                   
      
               [0]    [0]      
      f(0()) = [2] >= [0] = 0()
               [0]    [0]      
      
                [1 0 0]    [0]         
      p(s(x)) = [0 2 2]x + [2] >= x = x
                [0 1 1]    [1]         
     problem:
      DPs:
       
      TRS:
       f(s(x)) -> s(f(f(p(s(x)))))
       f(0()) -> 0()
       p(s(x)) -> x
     Qed