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:
 DP Processor:
  DPs:
   active#(f(f(X))) -> g#(f(X))
   active#(f(f(X))) -> f#(g(f(X)))
   active#(f(f(X))) -> c#(f(g(f(X))))
   active#(c(X)) -> d#(X)
   active#(h(X)) -> d#(X)
   active#(h(X)) -> c#(d(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#(c(X)) -> proper#(X)
   proper#(c(X)) -> c#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   proper#(d(X)) -> proper#(X)
   proper#(d(X)) -> d#(proper(X))
   proper#(h(X)) -> proper#(X)
   proper#(h(X)) -> h#(proper(X))
   f#(ok(X)) -> f#(X)
   c#(ok(X)) -> c#(X)
   g#(ok(X)) -> g#(X)
   d#(ok(X)) -> d#(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(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))
  CDG Processor:
   DPs:
    active#(f(f(X))) -> g#(f(X))
    active#(f(f(X))) -> f#(g(f(X)))
    active#(f(f(X))) -> c#(f(g(f(X))))
    active#(c(X)) -> d#(X)
    active#(h(X)) -> d#(X)
    active#(h(X)) -> c#(d(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#(c(X)) -> proper#(X)
    proper#(c(X)) -> c#(proper(X))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    proper#(d(X)) -> proper#(X)
    proper#(d(X)) -> d#(proper(X))
    proper#(h(X)) -> proper#(X)
    proper#(h(X)) -> h#(proper(X))
    f#(ok(X)) -> f#(X)
    c#(ok(X)) -> c#(X)
    g#(ok(X)) -> g#(X)
    d#(ok(X)) -> d#(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(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))
   graph:
    
   Qed