YES

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

Proof:
 DP Processor:
  DPs:
   active#(f(f(a()))) -> g#(f(a()))
   active#(f(f(a()))) -> f#(g(f(a())))
   active#(f(f(a()))) -> c#(f(g(f(a()))))
   active#(f(X)) -> active#(X)
   active#(f(X)) -> f#(active(X))
   active#(g(X)) -> active#(X)
   active#(g(X)) -> g#(active(X))
   f#(mark(X)) -> f#(X)
   g#(mark(X)) -> g#(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))
   f#(ok(X)) -> f#(X)
   c#(ok(X)) -> c#(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(f(f(a()))) -> mark(c(f(g(f(a())))))
   active(f(X)) -> f(active(X))
   active(g(X)) -> g(active(X))
   f(mark(X)) -> mark(f(X))
   g(mark(X)) -> mark(g(X))
   proper(f(X)) -> f(proper(X))
   proper(a()) -> ok(a())
   proper(c(X)) -> c(proper(X))
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   c(ok(X)) -> ok(c(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(f(f(a()))) -> g#(f(a()))
    active#(f(f(a()))) -> f#(g(f(a())))
    active#(f(f(a()))) -> c#(f(g(f(a()))))
    active#(f(X)) -> active#(X)
    active#(f(X)) -> f#(active(X))
    active#(g(X)) -> active#(X)
    active#(g(X)) -> g#(active(X))
    f#(mark(X)) -> f#(X)
    g#(mark(X)) -> g#(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))
    f#(ok(X)) -> f#(X)
    c#(ok(X)) -> c#(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(f(f(a()))) -> mark(c(f(g(f(a())))))
    active(f(X)) -> f(active(X))
    active(g(X)) -> g(active(X))
    f(mark(X)) -> mark(f(X))
    g(mark(X)) -> mark(g(X))
    proper(f(X)) -> f(proper(X))
    proper(a()) -> ok(a())
    proper(c(X)) -> c(proper(X))
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    c(ok(X)) -> ok(c(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#(g(X)) -> g#(active(X))
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a()))))
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a()))
    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#(c(X)) -> c#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(c(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#(c(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(c(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(c(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X))
    proper#(c(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X)
    proper#(c(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(c(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(c(X)) -> c#(proper(X)) -> c#(ok(X)) -> c#(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#(c(X)) -> c#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(c(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)
    proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(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#(c(X)) -> c#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(c(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#(f(X)) -> f#(proper(X)) -> f#(mark(X)) -> f#(X)
    c#(ok(X)) -> c#(X) -> c#(ok(X)) -> c#(X)
    f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    f#(ok(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(ok(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(ok(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X)
    active#(g(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    active#(g(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(g(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    active#(g(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    active#(g(X)) -> active#(X) ->
    active#(f(f(a()))) -> c#(f(g(f(a()))))
    active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    active#(g(X)) -> active#(X) ->
    active#(f(f(a()))) -> g#(f(a()))
    active#(f(f(a()))) -> c#(f(g(f(a())))) -> c#(ok(X)) -> c#(X)
    active#(f(f(a()))) -> f#(g(f(a()))) -> f#(ok(X)) -> f#(X)
    active#(f(f(a()))) -> f#(g(f(a()))) -> f#(mark(X)) -> f#(X)
    active#(f(f(a()))) -> g#(f(a())) -> g#(ok(X)) -> g#(X)
    active#(f(f(a()))) -> g#(f(a())) -> g#(mark(X)) -> g#(X)
    active#(f(X)) -> f#(active(X)) -> f#(ok(X)) -> f#(X)
    active#(f(X)) -> f#(active(X)) -> f#(mark(X)) -> f#(X)
    active#(f(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    active#(f(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(f(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    active#(f(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    active#(f(X)) -> active#(X) ->
    active#(f(f(a()))) -> c#(f(g(f(a()))))
    active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a()))
   SCC Processor:
    #sccs: 6
    #rules: 12
    #arcs: 76/484
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(f(f(a()))) -> mark(c(f(g(f(a())))))
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(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 + 0,
      
      [proper](x0) = 1x0 + 0,
      
      [mark](x0) = 2x0 + 4,
      
      [c](x0) = 2,
      
      [g](x0) = x0 + 0,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 0,
      
      [a] = 4
     orientation:
      top#(ok(X)) = X + 0 >= X + 0 = top#(active(X))
      
      top#(mark(X)) = 2X + 4 >= 1X + 0 = top#(proper(X))
      
      active(f(f(a()))) = 4 >= 4 = mark(c(f(g(f(a())))))
      
      active(f(X)) = X + 0 >= X + 0 = f(active(X))
      
      active(g(X)) = X + 0 >= X + 0 = g(active(X))
      
      f(mark(X)) = 2X + 4 >= 2X + 4 = mark(f(X))
      
      g(mark(X)) = 2X + 4 >= 2X + 4 = mark(g(X))
      
      proper(f(X)) = 1X + 1 >= 1X + 0 = f(proper(X))
      
      proper(a()) = 5 >= 4 = ok(a())
      
      proper(c(X)) = 3 >= 2 = c(proper(X))
      
      proper(g(X)) = 1X + 1 >= 1X + 0 = g(proper(X))
      
      f(ok(X)) = X + 0 >= X + 0 = ok(f(X))
      
      c(ok(X)) = 2 >= 2 = ok(c(X))
      
      g(ok(X)) = X + 0 >= X + 0 = ok(g(X))
      
      top(mark(X)) = 0 >= 0 = top(proper(X))
      
      top(ok(X)) = 0 >= 0 = top(active(X))
     problem:
      DPs:
       top#(ok(X)) -> top#(active(X))
      TRS:
       active(f(f(a()))) -> mark(c(f(g(f(a())))))
       active(f(X)) -> f(active(X))
       active(g(X)) -> g(active(X))
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     KBO Processor:
      argument filtering:
       pi(a) = []
       pi(f) = 0
       pi(active) = []
       pi(g) = 0
       pi(c) = 0
       pi(mark) = 0
       pi(proper) = []
       pi(ok) = []
       pi(top) = []
       pi(top#) = 0
      weight function:
       w0 = 1
       w(top#) = w(top) = w(ok) = w(proper) = w(mark) = w(c) = w(g) = w(
       active) = w(f) = w(a) = 1
      precedence:
       top# ~ top ~ proper ~ mark > ok > active > c ~ g ~ f ~ a
      problem:
       DPs:
        
       TRS:
        active(f(f(a()))) -> mark(c(f(g(f(a())))))
        active(f(X)) -> f(active(X))
        active(g(X)) -> g(active(X))
        f(mark(X)) -> mark(f(X))
        g(mark(X)) -> mark(g(X))
        proper(f(X)) -> f(proper(X))
        proper(a()) -> ok(a())
        proper(c(X)) -> c(proper(X))
        proper(g(X)) -> g(proper(X))
        f(ok(X)) -> ok(f(X))
        c(ok(X)) -> ok(c(X))
        g(ok(X)) -> ok(g(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     active#(f(X)) -> active#(X)
     active#(g(X)) -> active#(X)
    TRS:
     active(f(f(a()))) -> mark(c(f(g(f(a())))))
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(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(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(c(f(g(f(a())))))
       active(f(X)) -> f(active(X))
       active(g(X)) -> g(active(X))
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(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#(c(X)) -> proper#(X)
     proper#(g(X)) -> proper#(X)
    TRS:
     active(f(f(a()))) -> mark(c(f(g(f(a())))))
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(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(f(f(a()))) -> mark(c(f(g(f(a())))))
       active(f(X)) -> f(active(X))
       active(g(X)) -> g(active(X))
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     g#(mark(X)) -> g#(X)
     g#(ok(X)) -> g#(X)
    TRS:
     active(f(f(a()))) -> mark(c(f(g(f(a())))))
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(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(f(f(a()))) -> mark(c(f(g(f(a())))))
       active(f(X)) -> f(active(X))
       active(g(X)) -> g(active(X))
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     c#(ok(X)) -> c#(X)
    TRS:
     active(f(f(a()))) -> mark(c(f(g(f(a())))))
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(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(c#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(c(f(g(f(a())))))
       active(f(X)) -> f(active(X))
       active(g(X)) -> g(active(X))
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     f#(mark(X)) -> f#(X)
     f#(ok(X)) -> f#(X)
    TRS:
     active(f(f(a()))) -> mark(c(f(g(f(a())))))
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(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(f(f(a()))) -> mark(c(f(g(f(a())))))
       active(f(X)) -> f(active(X))
       active(g(X)) -> g(active(X))
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed