YES

Problem:
 active(f(X)) -> mark(g(h(f(X))))
 active(f(X)) -> f(active(X))
 active(h(X)) -> h(active(X))
 f(mark(X)) -> mark(f(X))
 h(mark(X)) -> mark(h(X))
 proper(f(X)) -> f(proper(X))
 proper(g(X)) -> g(proper(X))
 proper(h(X)) -> h(proper(X))
 f(ok(X)) -> ok(f(X))
 g(ok(X)) -> ok(g(X))
 h(ok(X)) -> ok(h(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(f(X)) -> h#(f(X))
   active#(f(X)) -> g#(h(f(X)))
   active#(f(X)) -> active#(X)
   active#(f(X)) -> f#(active(X))
   active#(h(X)) -> active#(X)
   active#(h(X)) -> h#(active(X))
   f#(mark(X)) -> f#(X)
   h#(mark(X)) -> h#(X)
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   proper#(h(X)) -> proper#(X)
   proper#(h(X)) -> h#(proper(X))
   f#(ok(X)) -> f#(X)
   g#(ok(X)) -> g#(X)
   h#(ok(X)) -> h#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(f(X)) -> mark(g(h(f(X))))
   active(f(X)) -> f(active(X))
   active(h(X)) -> h(active(X))
   f(mark(X)) -> mark(f(X))
   h(mark(X)) -> mark(h(X))
   proper(f(X)) -> f(proper(X))
   proper(g(X)) -> g(proper(X))
   proper(h(X)) -> h(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   h(ok(X)) -> ok(h(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top#](x0) = 1/2x0 + 2,
    
    [proper#](x0) = 1/2x0,
    
    [f#](x0) = 1/2x0,
    
    [g#](x0) = 1/2x0 + 1/2,
    
    [h#](x0) = 1/2x0,
    
    [active#](x0) = 1/2x0 + 3,
    
    [top](x0) = x0 + 1/2,
    
    [ok](x0) = x0 + 4,
    
    [proper](x0) = x0,
    
    [mark](x0) = x0 + 1,
    
    [g](x0) = x0 + 2,
    
    [h](x0) = x0 + 1/2,
    
    [active](x0) = x0 + 7/2,
    
    [f](x0) = x0 + 7/2
   orientation:
    active#(f(X)) = 1/2X + 19/4 >= 1/2X + 7/4 = h#(f(X))
    
    active#(f(X)) = 1/2X + 19/4 >= 1/2X + 5/2 = g#(h(f(X)))
    
    active#(f(X)) = 1/2X + 19/4 >= 1/2X + 3 = active#(X)
    
    active#(f(X)) = 1/2X + 19/4 >= 1/2X + 7/4 = f#(active(X))
    
    active#(h(X)) = 1/2X + 13/4 >= 1/2X + 3 = active#(X)
    
    active#(h(X)) = 1/2X + 13/4 >= 1/2X + 7/4 = h#(active(X))
    
    f#(mark(X)) = 1/2X + 1/2 >= 1/2X = f#(X)
    
    h#(mark(X)) = 1/2X + 1/2 >= 1/2X = h#(X)
    
    proper#(f(X)) = 1/2X + 7/4 >= 1/2X = proper#(X)
    
    proper#(f(X)) = 1/2X + 7/4 >= 1/2X = f#(proper(X))
    
    proper#(g(X)) = 1/2X + 1 >= 1/2X = proper#(X)
    
    proper#(g(X)) = 1/2X + 1 >= 1/2X + 1/2 = g#(proper(X))
    
    proper#(h(X)) = 1/2X + 1/4 >= 1/2X = proper#(X)
    
    proper#(h(X)) = 1/2X + 1/4 >= 1/2X = h#(proper(X))
    
    f#(ok(X)) = 1/2X + 2 >= 1/2X = f#(X)
    
    g#(ok(X)) = 1/2X + 5/2 >= 1/2X + 1/2 = g#(X)
    
    h#(ok(X)) = 1/2X + 2 >= 1/2X = h#(X)
    
    top#(mark(X)) = 1/2X + 5/2 >= 1/2X = proper#(X)
    
    top#(mark(X)) = 1/2X + 5/2 >= 1/2X + 2 = top#(proper(X))
    
    top#(ok(X)) = 1/2X + 4 >= 1/2X + 3 = active#(X)
    
    top#(ok(X)) = 1/2X + 4 >= 1/2X + 15/4 = top#(active(X))
    
    active(f(X)) = X + 7 >= X + 7 = mark(g(h(f(X))))
    
    active(f(X)) = X + 7 >= X + 7 = f(active(X))
    
    active(h(X)) = X + 4 >= X + 4 = h(active(X))
    
    f(mark(X)) = X + 9/2 >= X + 9/2 = mark(f(X))
    
    h(mark(X)) = X + 3/2 >= X + 3/2 = mark(h(X))
    
    proper(f(X)) = X + 7/2 >= X + 7/2 = f(proper(X))
    
    proper(g(X)) = X + 2 >= X + 2 = g(proper(X))
    
    proper(h(X)) = X + 1/2 >= X + 1/2 = h(proper(X))
    
    f(ok(X)) = X + 15/2 >= X + 15/2 = ok(f(X))
    
    g(ok(X)) = X + 6 >= X + 6 = ok(g(X))
    
    h(ok(X)) = X + 9/2 >= X + 9/2 = ok(h(X))
    
    top(mark(X)) = X + 3/2 >= X + 1/2 = top(proper(X))
    
    top(ok(X)) = X + 9/2 >= X + 4 = top(active(X))
   problem:
    DPs:
     
    TRS:
     active(f(X)) -> mark(g(h(f(X))))
     active(f(X)) -> f(active(X))
     active(h(X)) -> h(active(X))
     f(mark(X)) -> mark(f(X))
     h(mark(X)) -> mark(h(X))
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     proper(h(X)) -> h(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     h(ok(X)) -> ok(h(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
   Qed