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:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [top](x0) = 1x0,
   
   [ok](x0) = 9x0,
   
   [proper](x0) = x0,
   
   [mark](x0) = x0,
   
   [g](x0) = x0,
   
   [h](x0) = 8x0,
   
   [active](x0) = 8x0,
   
   [f](x0) = 8x0
  orientation:
   active(f(X)) = 16X >= 16X = mark(g(h(f(X))))
   
   active(f(X)) = 16X >= 16X = f(active(X))
   
   active(h(X)) = 16X >= 16X = h(active(X))
   
   f(mark(X)) = 8X >= 8X = mark(f(X))
   
   h(mark(X)) = 8X >= 8X = mark(h(X))
   
   proper(f(X)) = 8X >= 8X = f(proper(X))
   
   proper(g(X)) = X >= X = g(proper(X))
   
   proper(h(X)) = 8X >= 8X = h(proper(X))
   
   f(ok(X)) = 17X >= 17X = ok(f(X))
   
   g(ok(X)) = 9X >= 9X = ok(g(X))
   
   h(ok(X)) = 17X >= 17X = ok(h(X))
   
   top(mark(X)) = 1X >= 1X = top(proper(X))
   
   top(ok(X)) = 10X >= 9X = top(active(X))
  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))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [top](x0) = 15x0,
    
    [ok](x0) = 12x0,
    
    [proper](x0) = 1x0,
    
    [mark](x0) = 10x0,
    
    [g](x0) = 2x0,
    
    [h](x0) = x0,
    
    [active](x0) = 12x0,
    
    [f](x0) = x0
   orientation:
    active(f(X)) = 12X >= 12X = mark(g(h(f(X))))
    
    active(f(X)) = 12X >= 12X = f(active(X))
    
    active(h(X)) = 12X >= 12X = h(active(X))
    
    f(mark(X)) = 10X >= 10X = mark(f(X))
    
    h(mark(X)) = 10X >= 10X = mark(h(X))
    
    proper(f(X)) = 1X >= 1X = f(proper(X))
    
    proper(g(X)) = 3X >= 3X = g(proper(X))
    
    proper(h(X)) = 1X >= 1X = h(proper(X))
    
    f(ok(X)) = 12X >= 12X = ok(f(X))
    
    g(ok(X)) = 14X >= 14X = ok(g(X))
    
    h(ok(X)) = 12X >= 12X = ok(h(X))
    
    top(mark(X)) = 25X >= 16X = top(proper(X))
   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))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [ok](x0) = 9x0,
     
     [proper](x0) = 12x0,
     
     [mark](x0) = 11x0,
     
     [g](x0) = x0,
     
     [h](x0) = x0,
     
     [active](x0) = 14x0,
     
     [f](x0) = 1x0
    orientation:
     active(f(X)) = 15X >= 12X = mark(g(h(f(X))))
     
     active(f(X)) = 15X >= 15X = f(active(X))
     
     active(h(X)) = 14X >= 14X = h(active(X))
     
     f(mark(X)) = 12X >= 12X = mark(f(X))
     
     h(mark(X)) = 11X >= 11X = mark(h(X))
     
     proper(f(X)) = 13X >= 13X = f(proper(X))
     
     proper(g(X)) = 12X >= 12X = g(proper(X))
     
     proper(h(X)) = 12X >= 12X = h(proper(X))
     
     f(ok(X)) = 10X >= 10X = ok(f(X))
     
     g(ok(X)) = 9X >= 9X = ok(g(X))
     
     h(ok(X)) = 9X >= 9X = ok(h(X))
    problem:
     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))
    KBO Processor:
     weight function:
      w0 = 1
      w(ok) = w(proper) = w(mark) = w(g) = w(h) = w(active) = w(f) = 1
     precedence:
      active > proper > g ~ h ~ f > ok ~ mark
     problem:
      
     Qed