YES

Problem:
 active(f(f(X))) -> mark(c(f(g(f(X)))))
 active(c(X)) -> mark(d(X))
 active(h(X)) -> mark(c(d(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(c(X)) -> c(proper(X))
 proper(g(X)) -> g(proper(X))
 proper(d(X)) -> d(proper(X))
 proper(h(X)) -> h(proper(X))
 f(ok(X)) -> ok(f(X))
 c(ok(X)) -> ok(c(X))
 g(ok(X)) -> ok(g(X))
 d(ok(X)) -> ok(d(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) = 8x0,
   
   [ok](x0) = 10x0,
   
   [proper](x0) = x0,
   
   [h](x0) = 10x0,
   
   [d](x0) = 11x0,
   
   [mark](x0) = 4x0,
   
   [c](x0) = 5x0,
   
   [g](x0) = 1x0,
   
   [active](x0) = 10x0,
   
   [f](x0) = 3x0
  orientation:
   active(f(f(X))) = 16X >= 16X = mark(c(f(g(f(X)))))
   
   active(c(X)) = 15X >= 15X = mark(d(X))
   
   active(h(X)) = 20X >= 20X = mark(c(d(X)))
   
   active(f(X)) = 13X >= 13X = f(active(X))
   
   active(h(X)) = 20X >= 20X = h(active(X))
   
   f(mark(X)) = 7X >= 7X = mark(f(X))
   
   h(mark(X)) = 14X >= 14X = mark(h(X))
   
   proper(f(X)) = 3X >= 3X = f(proper(X))
   
   proper(c(X)) = 5X >= 5X = c(proper(X))
   
   proper(g(X)) = 1X >= 1X = g(proper(X))
   
   proper(d(X)) = 11X >= 11X = d(proper(X))
   
   proper(h(X)) = 10X >= 10X = h(proper(X))
   
   f(ok(X)) = 13X >= 13X = ok(f(X))
   
   c(ok(X)) = 15X >= 15X = ok(c(X))
   
   g(ok(X)) = 11X >= 11X = ok(g(X))
   
   d(ok(X)) = 21X >= 21X = ok(d(X))
   
   h(ok(X)) = 20X >= 20X = ok(h(X))
   
   top(mark(X)) = 12X >= 8X = top(proper(X))
   
   top(ok(X)) = 18X >= 18X = top(active(X))
  problem:
   active(f(f(X))) -> mark(c(f(g(f(X)))))
   active(c(X)) -> mark(d(X))
   active(h(X)) -> mark(c(d(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(c(X)) -> c(proper(X))
   proper(g(X)) -> g(proper(X))
   proper(d(X)) -> d(proper(X))
   proper(h(X)) -> h(proper(X))
   f(ok(X)) -> ok(f(X))
   c(ok(X)) -> ok(c(X))
   g(ok(X)) -> ok(g(X))
   d(ok(X)) -> ok(d(X))
   h(ok(X)) -> ok(h(X))
   top(ok(X)) -> top(active(X))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [top](x0) = x0,
    
    [ok](x0) = x0,
    
    [proper](x0) = 3x0,
    
    [h](x0) = 2x0,
    
    [d](x0) = x0,
    
    [mark](x0) = x0,
    
    [c](x0) = x0,
    
    [g](x0) = x0,
    
    [active](x0) = x0,
    
    [f](x0) = 8x0
   orientation:
    active(f(f(X))) = 16X >= 16X = mark(c(f(g(f(X)))))
    
    active(c(X)) = X >= X = mark(d(X))
    
    active(h(X)) = 2X >= X = mark(c(d(X)))
    
    active(f(X)) = 8X >= 8X = f(active(X))
    
    active(h(X)) = 2X >= 2X = h(active(X))
    
    f(mark(X)) = 8X >= 8X = mark(f(X))
    
    h(mark(X)) = 2X >= 2X = mark(h(X))
    
    proper(f(X)) = 11X >= 11X = f(proper(X))
    
    proper(c(X)) = 3X >= 3X = c(proper(X))
    
    proper(g(X)) = 3X >= 3X = g(proper(X))
    
    proper(d(X)) = 3X >= 3X = d(proper(X))
    
    proper(h(X)) = 5X >= 5X = h(proper(X))
    
    f(ok(X)) = 8X >= 8X = ok(f(X))
    
    c(ok(X)) = X >= X = ok(c(X))
    
    g(ok(X)) = X >= X = ok(g(X))
    
    d(ok(X)) = X >= X = ok(d(X))
    
    h(ok(X)) = 2X >= 2X = ok(h(X))
    
    top(ok(X)) = X >= X = top(active(X))
   problem:
    active(f(f(X))) -> mark(c(f(g(f(X)))))
    active(c(X)) -> mark(d(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(c(X)) -> c(proper(X))
    proper(g(X)) -> g(proper(X))
    proper(d(X)) -> d(proper(X))
    proper(h(X)) -> h(proper(X))
    f(ok(X)) -> ok(f(X))
    c(ok(X)) -> ok(c(X))
    g(ok(X)) -> ok(g(X))
    d(ok(X)) -> ok(d(X))
    h(ok(X)) -> ok(h(X))
    top(ok(X)) -> top(active(X))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [top](x0) = 15x0,
     
     [ok](x0) = 8x0,
     
     [proper](x0) = 1x0,
     
     [h](x0) = 5x0,
     
     [d](x0) = 2x0,
     
     [mark](x0) = x0,
     
     [c](x0) = 1x0,
     
     [g](x0) = x0,
     
     [active](x0) = 1x0,
     
     [f](x0) = x0
    orientation:
     active(f(f(X))) = 1X >= 1X = mark(c(f(g(f(X)))))
     
     active(c(X)) = 2X >= 2X = mark(d(X))
     
     active(f(X)) = 1X >= 1X = f(active(X))
     
     active(h(X)) = 6X >= 6X = h(active(X))
     
     f(mark(X)) = X >= X = mark(f(X))
     
     h(mark(X)) = 5X >= 5X = mark(h(X))
     
     proper(f(X)) = 1X >= 1X = f(proper(X))
     
     proper(c(X)) = 2X >= 2X = c(proper(X))
     
     proper(g(X)) = 1X >= 1X = g(proper(X))
     
     proper(d(X)) = 3X >= 3X = d(proper(X))
     
     proper(h(X)) = 6X >= 6X = h(proper(X))
     
     f(ok(X)) = 8X >= 8X = ok(f(X))
     
     c(ok(X)) = 9X >= 9X = ok(c(X))
     
     g(ok(X)) = 8X >= 8X = ok(g(X))
     
     d(ok(X)) = 10X >= 10X = ok(d(X))
     
     h(ok(X)) = 13X >= 13X = ok(h(X))
     
     top(ok(X)) = 23X >= 16X = top(active(X))
    problem:
     active(f(f(X))) -> mark(c(f(g(f(X)))))
     active(c(X)) -> mark(d(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(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     proper(d(X)) -> d(proper(X))
     proper(h(X)) -> h(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(X))
     g(ok(X)) -> ok(g(X))
     d(ok(X)) -> ok(d(X))
     h(ok(X)) -> ok(h(X))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [ok](x0) = 1x0,
      
      [proper](x0) = 11x0,
      
      [h](x0) = 1x0,
      
      [d](x0) = 7x0,
      
      [mark](x0) = 1x0,
      
      [c](x0) = x0,
      
      [g](x0) = 13x0,
      
      [active](x0) = 14x0,
      
      [f](x0) = 4x0
     orientation:
      active(f(f(X))) = 22X >= 22X = mark(c(f(g(f(X)))))
      
      active(c(X)) = 14X >= 8X = mark(d(X))
      
      active(f(X)) = 18X >= 18X = f(active(X))
      
      active(h(X)) = 15X >= 15X = h(active(X))
      
      f(mark(X)) = 5X >= 5X = mark(f(X))
      
      h(mark(X)) = 2X >= 2X = mark(h(X))
      
      proper(f(X)) = 15X >= 15X = f(proper(X))
      
      proper(c(X)) = 11X >= 11X = c(proper(X))
      
      proper(g(X)) = 24X >= 24X = g(proper(X))
      
      proper(d(X)) = 18X >= 18X = d(proper(X))
      
      proper(h(X)) = 12X >= 12X = h(proper(X))
      
      f(ok(X)) = 5X >= 5X = ok(f(X))
      
      c(ok(X)) = 1X >= 1X = ok(c(X))
      
      g(ok(X)) = 14X >= 14X = ok(g(X))
      
      d(ok(X)) = 8X >= 8X = ok(d(X))
      
      h(ok(X)) = 2X >= 2X = ok(h(X))
     problem:
      active(f(f(X))) -> mark(c(f(g(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(c(X)) -> c(proper(X))
      proper(g(X)) -> g(proper(X))
      proper(d(X)) -> d(proper(X))
      proper(h(X)) -> h(proper(X))
      f(ok(X)) -> ok(f(X))
      c(ok(X)) -> ok(c(X))
      g(ok(X)) -> ok(g(X))
      d(ok(X)) -> ok(d(X))
      h(ok(X)) -> ok(h(X))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [ok](x0) = x0,
       
       [proper](x0) = x0,
       
       [h](x0) = 1x0,
       
       [d](x0) = 6x0,
       
       [mark](x0) = 1x0,
       
       [c](x0) = x0,
       
       [g](x0) = x0,
       
       [active](x0) = 2x0,
       
       [f](x0) = x0
      orientation:
       active(f(f(X))) = 2X >= 1X = mark(c(f(g(f(X)))))
       
       active(f(X)) = 2X >= 2X = f(active(X))
       
       active(h(X)) = 3X >= 3X = h(active(X))
       
       f(mark(X)) = 1X >= 1X = mark(f(X))
       
       h(mark(X)) = 2X >= 2X = mark(h(X))
       
       proper(f(X)) = X >= X = f(proper(X))
       
       proper(c(X)) = X >= X = c(proper(X))
       
       proper(g(X)) = X >= X = g(proper(X))
       
       proper(d(X)) = 6X >= 6X = d(proper(X))
       
       proper(h(X)) = 1X >= 1X = h(proper(X))
       
       f(ok(X)) = X >= X = ok(f(X))
       
       c(ok(X)) = X >= X = ok(c(X))
       
       g(ok(X)) = X >= X = ok(g(X))
       
       d(ok(X)) = 6X >= 6X = ok(d(X))
       
       h(ok(X)) = 1X >= 1X = 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(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       proper(d(X)) -> d(proper(X))
       proper(h(X)) -> h(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
       d(ok(X)) -> ok(d(X))
       h(ok(X)) -> ok(h(X))
      KBO Processor:
       weight function:
        w0 = 1
        w(ok) = w(proper) = w(h) = w(d) = w(mark) = w(c) = w(g) = w(active) = w(f) = 1
       precedence:
        active > proper > h ~ d ~ c ~ g ~ f > ok ~ mark
       problem:
        
       Qed