YES

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

Proof:
 DP Processor:
  DPs:
   active#(c()) -> g#(c())
   active#(c()) -> f#(g(c()))
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   f#(ok(X)) -> f#(X)
   g#(ok(X)) -> g#(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(c()) -> mark(f(g(c())))
   active(f(g(X))) -> mark(g(X))
   proper(c()) -> ok(c())
   proper(f(X)) -> f(proper(X))
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(c()) -> g#(c())
    active#(c()) -> f#(g(c()))
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(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(c()) -> mark(f(g(c())))
    active(f(g(X))) -> mark(g(X))
    proper(c()) -> ok(c())
    proper(f(X)) -> f(proper(X))
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    g(ok(X)) -> ok(g(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) -> active#(c()) -> f#(g(c()))
    top#(ok(X)) -> active#(X) -> active#(c()) -> g#(c())
    top#(mark(X)) -> top#(proper(X)) ->
    top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
    f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    active#(c()) -> f#(g(c())) -> f#(ok(X)) -> f#(X)
    active#(c()) -> g#(c()) -> g#(ok(X)) -> g#(X)
   SCC Processor:
    #sccs: 4
    #rules: 6
    #arcs: 28/144
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
     proper(c()) -> ok(c())
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    LPO Processor:
     argument filtering:
      pi(c) = []
      pi(active) = 0
      pi(g) = []
      pi(f) = []
      pi(mark) = [0]
      pi(proper) = 0
      pi(ok) = 0
      pi(top) = 0
      pi(top#) = 0
     precedence:
      c > f > top# ~ top ~ ok ~ proper ~ mark ~ g ~ active
     problem:
      DPs:
       top#(ok(X)) -> top#(active(X))
      TRS:
       active(c()) -> mark(f(g(c())))
       active(f(g(X))) -> mark(g(X))
       proper(c()) -> ok(c())
       proper(f(X)) -> f(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [top#](x0) = x0 + 0,
       
       [top](x0) = 0,
       
       [ok](x0) = x0 + 1,
       
       [proper](x0) = x0,
       
       [mark](x0) = 0,
       
       [f](x0) = x0 + 2,
       
       [g](x0) = x0 + 1,
       
       [active](x0) = 0,
       
       [c] = 3
      orientation:
       top#(ok(X)) = X + 1 >= 0 = top#(active(X))
       
       active(c()) = 0 >= 0 = mark(f(g(c())))
       
       active(f(g(X))) = 0 >= 0 = mark(g(X))
       
       proper(c()) = 3 >= 3 = ok(c())
       
       proper(f(X)) = X + 2 >= X + 2 = f(proper(X))
       
       proper(g(X)) = X + 1 >= X + 1 = g(proper(X))
       
       f(ok(X)) = X + 2 >= X + 2 = ok(f(X))
       
       g(ok(X)) = X + 1 >= X + 1 = ok(g(X))
       
       top(mark(X)) = 0 >= 0 = top(proper(X))
       
       top(ok(X)) = 0 >= 0 = top(active(X))
      problem:
       DPs:
        
       TRS:
        active(c()) -> mark(f(g(c())))
        active(f(g(X))) -> mark(g(X))
        proper(c()) -> ok(c())
        proper(f(X)) -> f(proper(X))
        proper(g(X)) -> g(proper(X))
        f(ok(X)) -> ok(f(X))
        g(ok(X)) -> ok(g(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     proper#(f(X)) -> proper#(X)
     proper#(g(X)) -> proper#(X)
    TRS:
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
     proper(c()) -> ok(c())
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(c()) -> mark(f(g(c())))
       active(f(g(X))) -> mark(g(X))
       proper(c()) -> ok(c())
       proper(f(X)) -> f(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     g#(ok(X)) -> g#(X)
    TRS:
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
     proper(c()) -> ok(c())
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       active(c()) -> mark(f(g(c())))
       active(f(g(X))) -> mark(g(X))
       proper(c()) -> ok(c())
       proper(f(X)) -> f(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     f#(ok(X)) -> f#(X)
    TRS:
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
     proper(c()) -> ok(c())
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 0
     problem:
      DPs:
       
      TRS:
       active(c()) -> mark(f(g(c())))
       active(f(g(X))) -> mark(g(X))
       proper(c()) -> ok(c())
       proper(f(X)) -> f(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed