YES
O(n^3)
TRS:
 {
       active(f(x)) -> mark(x),
       active(f(x)) -> f(active(x)),
         f(mark(x)) -> mark(f(x)),
           f(ok(x)) -> ok(f(x)),
        f(found(x)) -> found(f(x)),
       top(mark(x)) -> top(check(x)),
   top(active(c())) -> top(mark(c())),
      top(found(x)) -> top(active(x)),
           check(x) -> start(match(f(X()), x)),
        check(f(x)) -> f(check(x)),
       start(ok(x)) -> found(x),
  match(f(x), f(y)) -> f(match(x, y)),
      match(X(), x) -> proper(x),
       proper(f(x)) -> f(proper(x)),
        proper(c()) -> ok(c())
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
         active(f(x)) -> mark(x),
         active(f(x)) -> f(active(x)),
           f(mark(x)) -> mark(f(x)),
             f(ok(x)) -> ok(f(x)),
          f(found(x)) -> found(f(x)),
         top(mark(x)) -> top(check(x)),
     top(active(c())) -> top(mark(c())),
        top(found(x)) -> top(active(x)),
             check(x) -> start(match(f(X()), x)),
          check(f(x)) -> f(check(x)),
         start(ok(x)) -> found(x),
    match(f(x), f(y)) -> f(match(x, y)),
        match(X(), x) -> proper(x),
         proper(f(x)) -> f(proper(x)),
          proper(c()) -> ok(c())
   }
  Matrix Interpretation:
   Interpretation class: triangular
           [X2]    [1 1 3][X2]   [0]
   [found]([X1]) = [0 1 0][X1] + [1]
           [X0]    [0 0 0][X0]   [0]
   
        [X2]    [1 1 0][X2]   [1]
   [ok]([X1]) = [0 1 0][X1] + [1]
        [X0]    [0 0 1][X0]   [0]
   
            [X2]    [1 2 0][X2]   [1]
   [proper]([X1]) = [0 1 0][X1] + [1]
            [X0]    [0 0 0][X0]   [3]
   
         [1]
   [X] = [0]
         [3]
   
           [X5]  [X2]    [1 0 0][X5]   [1 2 0][X2]   [1]
   [match]([X4], [X1]) = [0 0 0][X4] + [0 1 0][X1] + [1]
           [X3]  [X0]    [0 0 1][X3]   [0 0 0][X0]   [0]
   
           [X2]    [1 0 3][X2]   [0]
   [start]([X1]) = [0 1 2][X1] + [0]
           [X0]    [0 0 0][X0]   [0]
   
           [X2]    [1 2 0][X2]   [3]
   [check]([X1]) = [0 1 0][X1] + [1]
           [X0]    [0 0 0][X0]   [0]
   
         [0]
   [c] = [1]
         [3]
   
         [X2]    [1 3 3][X2]   [0]
   [top]([X1]) = [0 0 0][X1] + [0]
         [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 3 0][X2]   [0]
   [f]([X1]) = [0 1 0][X1] + [2]
       [X0]    [0 0 0][X0]   [0]
   
            [X2]    [1 1 0][X2]   [0]
   [active]([X1]) = [0 1 0][X1] + [0]
            [X0]    [0 0 1][X0]   [0]
   
          [X2]    [1 2 0][X2]   [1]
   [mark]([X1]) = [0 1 0][X1] + [2]
          [X0]    [0 0 0][X0]   [0]
   
   
   Qed