YES
O(n^2)
TRS:
 {
               f(X) -> n__f(X),
             f(0()) -> cons(0(), n__f(s(0()))),
          f(s(0())) -> f(p(s(0()))),
          p(s(0())) -> 0(),
        activate(X) -> X,
  activate(n__f(X)) -> f(X)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                 f(X) -> n__f(X),
               f(0()) -> cons(0(), n__f(s(0()))),
            f(s(0())) -> f(p(s(0()))),
            p(s(0())) -> 0(),
          activate(X) -> X,
    activate(n__f(X)) -> f(X)
   }
  Matrix Interpretation:
   Interpretation class: triangular
              [X1]    [1 1][X1]   [1]
   [activate]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 0][X1]   [0]
   [p]([X0]) = [0 0][X0] + [1]
   
       [X1]    [1 1][X1]   [1]
   [f]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 0][X1]   [1]
   [s]([X0]) = [0 1][X0] + [1]
   
          [X1]    [1 0][X1]   [0]
   [n__f]([X0]) = [0 1][X0] + [1]
   
         [0]
   [0] = [1]
   
          [X3]  [X1]    [1 0][X3]   [1 0][X1]   [0]
   [cons]([X2], [X0]) = [0 0][X2] + [0 0][X0] + [0]
   
   
   Qed