YES

Problem:
 a__f(0()) -> cons(0(),f(s(0())))
 a__f(s(0())) -> a__f(a__p(s(0())))
 a__p(s(0())) -> 0()
 mark(f(X)) -> a__f(mark(X))
 mark(p(X)) -> a__p(mark(X))
 mark(0()) -> 0()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 a__f(X) -> f(X)
 a__p(X) -> p(X)

Proof:
 DP Processor:
  DPs:
   a__f#(s(0())) -> a__p#(s(0()))
   a__f#(s(0())) -> a__f#(a__p(s(0())))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(p(X)) -> mark#(X)
   mark#(p(X)) -> a__p#(mark(X))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__f(0()) -> cons(0(),f(s(0())))
   a__f(s(0())) -> a__f(a__p(s(0())))
   a__p(s(0())) -> 0()
   mark(f(X)) -> a__f(mark(X))
   mark(p(X)) -> a__p(mark(X))
   mark(0()) -> 0()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   a__f(X) -> f(X)
   a__p(X) -> p(X)
  EDG Processor:
   DPs:
    a__f#(s(0())) -> a__p#(s(0()))
    a__f#(s(0())) -> a__f#(a__p(s(0())))
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X))
    mark#(p(X)) -> mark#(X)
    mark#(p(X)) -> a__p#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__f(0()) -> cons(0(),f(s(0())))
    a__f(s(0())) -> a__f(a__p(s(0())))
    a__p(s(0())) -> 0()
    mark(f(X)) -> a__f(mark(X))
    mark(p(X)) -> a__p(mark(X))
    mark(0()) -> 0()
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    a__f(X) -> f(X)
    a__p(X) -> p(X)
   graph:
    mark#(p(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(p(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(p(X)) -> mark#(X) -> mark#(p(X)) -> mark#(X)
    mark#(p(X)) -> mark#(X) -> mark#(p(X)) -> a__p#(mark(X))
    mark#(p(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(p(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(p(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(p(X)) -> a__p#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(p(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(p(X)) -> a__p#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(f(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X)) -> a__f#(s(0())) -> a__p#(s(0()))
    mark#(f(X)) -> a__f#(mark(X)) -> a__f#(s(0())) -> a__f#(a__p(s(0())))
    mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(p(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(p(X)) -> a__p#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__f#(s(0())) -> a__f#(a__p(s(0()))) ->
    a__f#(s(0())) -> a__p#(s(0()))
    a__f#(s(0())) -> a__f#(a__p(s(0()))) -> a__f#(s(0())) -> a__f#(a__p(s(0())))
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 28/64
    DPs:
     mark#(p(X)) -> mark#(X)
     mark#(s(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(f(X)) -> mark#(X)
    TRS:
     a__f(0()) -> cons(0(),f(s(0())))
     a__f(s(0())) -> a__f(a__p(s(0())))
     a__p(s(0())) -> 0()
     mark(f(X)) -> a__f(mark(X))
     mark(p(X)) -> a__p(mark(X))
     mark(0()) -> 0()
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     a__f(X) -> f(X)
     a__p(X) -> p(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [mark#](x0) = x0,
      
      [p](x0) = x0,
      
      [mark](x0) = x0,
      
      [a__p](x0) = x0,
      
      [cons](x0, x1) = x0 + x1,
      
      [f](x0) = x0 + 1,
      
      [s](x0) = x0,
      
      [a__f](x0) = x0 + 1,
      
      [0] = 0
     orientation:
      mark#(p(X)) = X >= X = mark#(X)
      
      mark#(s(X)) = X >= X = mark#(X)
      
      mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1)
      
      mark#(f(X)) = X + 1 >= X = mark#(X)
      
      a__f(0()) = 1 >= 1 = cons(0(),f(s(0())))
      
      a__f(s(0())) = 1 >= 1 = a__f(a__p(s(0())))
      
      a__p(s(0())) = 0 >= 0 = 0()
      
      mark(f(X)) = X + 1 >= X + 1 = a__f(mark(X))
      
      mark(p(X)) = X >= X = a__p(mark(X))
      
      mark(0()) = 0 >= 0 = 0()
      
      mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2)
      
      mark(s(X)) = X >= X = s(mark(X))
      
      a__f(X) = X + 1 >= X + 1 = f(X)
      
      a__p(X) = X >= X = p(X)
     problem:
      DPs:
       mark#(p(X)) -> mark#(X)
       mark#(s(X)) -> mark#(X)
       mark#(cons(X1,X2)) -> mark#(X1)
      TRS:
       a__f(0()) -> cons(0(),f(s(0())))
       a__f(s(0())) -> a__f(a__p(s(0())))
       a__p(s(0())) -> 0()
       mark(f(X)) -> a__f(mark(X))
       mark(p(X)) -> a__p(mark(X))
       mark(0()) -> 0()
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       a__f(X) -> f(X)
       a__p(X) -> p(X)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [mark#](x0) = x0,
       
       [p](x0) = x0,
       
       [mark](x0) = x0,
       
       [a__p](x0) = x0,
       
       [cons](x0, x1) = x0,
       
       [f](x0) = 1,
       
       [s](x0) = x0 + 1,
       
       [a__f](x0) = 1,
       
       [0] = 0
      orientation:
       mark#(p(X)) = X >= X = mark#(X)
       
       mark#(s(X)) = X + 1 >= X = mark#(X)
       
       mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1)
       
       a__f(0()) = 1 >= 0 = cons(0(),f(s(0())))
       
       a__f(s(0())) = 1 >= 1 = a__f(a__p(s(0())))
       
       a__p(s(0())) = 1 >= 0 = 0()
       
       mark(f(X)) = 1 >= 1 = a__f(mark(X))
       
       mark(p(X)) = X >= X = a__p(mark(X))
       
       mark(0()) = 0 >= 0 = 0()
       
       mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2)
       
       mark(s(X)) = X + 1 >= X + 1 = s(mark(X))
       
       a__f(X) = 1 >= 1 = f(X)
       
       a__p(X) = X >= X = p(X)
      problem:
       DPs:
        mark#(p(X)) -> mark#(X)
        mark#(cons(X1,X2)) -> mark#(X1)
       TRS:
        a__f(0()) -> cons(0(),f(s(0())))
        a__f(s(0())) -> a__f(a__p(s(0())))
        a__p(s(0())) -> 0()
        mark(f(X)) -> a__f(mark(X))
        mark(p(X)) -> a__p(mark(X))
        mark(0()) -> 0()
        mark(cons(X1,X2)) -> cons(mark(X1),X2)
        mark(s(X)) -> s(mark(X))
        a__f(X) -> f(X)
        a__p(X) -> p(X)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [mark#](x0) = x0 + 1,
        
        [p](x0) = x0 + 1,
        
        [mark](x0) = x0,
        
        [a__p](x0) = x0 + 1,
        
        [cons](x0, x1) = x0 + 1,
        
        [f](x0) = 1,
        
        [s](x0) = 0,
        
        [a__f](x0) = 1,
        
        [0] = 0
       orientation:
        mark#(p(X)) = X + 2 >= X + 1 = mark#(X)
        
        mark#(cons(X1,X2)) = X1 + 2 >= X1 + 1 = mark#(X1)
        
        a__f(0()) = 1 >= 1 = cons(0(),f(s(0())))
        
        a__f(s(0())) = 1 >= 1 = a__f(a__p(s(0())))
        
        a__p(s(0())) = 1 >= 0 = 0()
        
        mark(f(X)) = 1 >= 1 = a__f(mark(X))
        
        mark(p(X)) = X + 1 >= X + 1 = a__p(mark(X))
        
        mark(0()) = 0 >= 0 = 0()
        
        mark(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(mark(X1),X2)
        
        mark(s(X)) = 0 >= 0 = s(mark(X))
        
        a__f(X) = 1 >= 1 = f(X)
        
        a__p(X) = X + 1 >= X + 1 = p(X)
       problem:
        DPs:
         
        TRS:
         a__f(0()) -> cons(0(),f(s(0())))
         a__f(s(0())) -> a__f(a__p(s(0())))
         a__p(s(0())) -> 0()
         mark(f(X)) -> a__f(mark(X))
         mark(p(X)) -> a__p(mark(X))
         mark(0()) -> 0()
         mark(cons(X1,X2)) -> cons(mark(X1),X2)
         mark(s(X)) -> s(mark(X))
         a__f(X) -> f(X)
         a__p(X) -> p(X)
       Qed
    
    DPs:
     a__f#(s(0())) -> a__f#(a__p(s(0())))
    TRS:
     a__f(0()) -> cons(0(),f(s(0())))
     a__f(s(0())) -> a__f(a__p(s(0())))
     a__p(s(0())) -> 0()
     mark(f(X)) -> a__f(mark(X))
     mark(p(X)) -> a__p(mark(X))
     mark(0()) -> 0()
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     a__f(X) -> f(X)
     a__p(X) -> p(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [a__f#](x0) = x0,
      
      [p](x0) = 0,
      
      [mark](x0) = x0,
      
      [a__p](x0) = 0,
      
      [cons](x0, x1) = 0,
      
      [f](x0) = 0,
      
      [s](x0) = 1,
      
      [a__f](x0) = 0,
      
      [0] = 0
     orientation:
      a__f#(s(0())) = 1 >= 0 = a__f#(a__p(s(0())))
      
      a__f(0()) = 0 >= 0 = cons(0(),f(s(0())))
      
      a__f(s(0())) = 0 >= 0 = a__f(a__p(s(0())))
      
      a__p(s(0())) = 0 >= 0 = 0()
      
      mark(f(X)) = 0 >= 0 = a__f(mark(X))
      
      mark(p(X)) = 0 >= 0 = a__p(mark(X))
      
      mark(0()) = 0 >= 0 = 0()
      
      mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2)
      
      mark(s(X)) = 1 >= 1 = s(mark(X))
      
      a__f(X) = 0 >= 0 = f(X)
      
      a__p(X) = 0 >= 0 = p(X)
     problem:
      DPs:
       
      TRS:
       a__f(0()) -> cons(0(),f(s(0())))
       a__f(s(0())) -> a__f(a__p(s(0())))
       a__p(s(0())) -> 0()
       mark(f(X)) -> a__f(mark(X))
       mark(p(X)) -> a__p(mark(X))
       mark(0()) -> 0()
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       a__f(X) -> f(X)
       a__p(X) -> p(X)
     Qed