YES

Problem:
 active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
 mark(f(X1,X2)) -> active(f(mark(X1),X2))
 mark(g(X)) -> active(g(mark(X)))
 f(mark(X1),X2) -> f(X1,X2)
 f(X1,mark(X2)) -> f(X1,X2)
 f(active(X1),X2) -> f(X1,X2)
 f(X1,active(X2)) -> f(X1,X2)
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)

Proof:
 DP Processor:
  DPs:
   active#(f(g(X),Y)) -> f#(X,f(g(X),Y))
   active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
   mark#(f(X1,X2)) -> mark#(X1)
   mark#(f(X1,X2)) -> f#(mark(X1),X2)
   mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
   mark#(g(X)) -> mark#(X)
   mark#(g(X)) -> g#(mark(X))
   mark#(g(X)) -> active#(g(mark(X)))
   f#(mark(X1),X2) -> f#(X1,X2)
   f#(X1,mark(X2)) -> f#(X1,X2)
   f#(active(X1),X2) -> f#(X1,X2)
   f#(X1,active(X2)) -> f#(X1,X2)
   g#(mark(X)) -> g#(X)
   g#(active(X)) -> g#(X)
  TRS:
   active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
   mark(f(X1,X2)) -> active(f(mark(X1),X2))
   mark(g(X)) -> active(g(mark(X)))
   f(mark(X1),X2) -> f(X1,X2)
   f(X1,mark(X2)) -> f(X1,X2)
   f(active(X1),X2) -> f(X1,X2)
   f(X1,active(X2)) -> f(X1,X2)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  TDG Processor:
   DPs:
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y))
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
    mark#(f(X1,X2)) -> mark#(X1)
    mark#(f(X1,X2)) -> f#(mark(X1),X2)
    mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
    mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> g#(mark(X))
    mark#(g(X)) -> active#(g(mark(X)))
    f#(mark(X1),X2) -> f#(X1,X2)
    f#(X1,mark(X2)) -> f#(X1,X2)
    f#(active(X1),X2) -> f#(X1,X2)
    f#(X1,active(X2)) -> f#(X1,X2)
    g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X)
   TRS:
    active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
    mark(f(X1,X2)) -> active(f(mark(X1),X2))
    mark(g(X)) -> active(g(mark(X)))
    f(mark(X1),X2) -> f(X1,X2)
    f(X1,mark(X2)) -> f(X1,X2)
    f(active(X1),X2) -> f(X1,X2)
    f(X1,active(X2)) -> f(X1,X2)
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
   graph:
    g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    mark#(f(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> active#(g(mark(X)))
    mark#(f(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> g#(mark(X))
    mark#(f(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> mark#(X)
    mark#(f(X1,X2)) -> mark#(X1) ->
    mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
    mark#(f(X1,X2)) -> mark#(X1) -> mark#(f(X1,X2)) -> f#(mark(X1),X2)
    mark#(f(X1,X2)) -> mark#(X1) -> mark#(f(X1,X2)) -> mark#(X1)
    mark#(f(X1,X2)) -> f#(mark(X1),X2) ->
    f#(X1,active(X2)) -> f#(X1,X2)
    mark#(f(X1,X2)) -> f#(mark(X1),X2) ->
    f#(active(X1),X2) -> f#(X1,X2)
    mark#(f(X1,X2)) -> f#(mark(X1),X2) ->
    f#(X1,mark(X2)) -> f#(X1,X2)
    mark#(f(X1,X2)) -> f#(mark(X1),X2) ->
    f#(mark(X1),X2) -> f#(X1,X2)
    mark#(f(X1,X2)) -> active#(f(mark(X1),X2)) ->
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
    mark#(f(X1,X2)) -> active#(f(mark(X1),X2)) ->
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y))
    mark#(g(X)) -> g#(mark(X)) -> g#(active(X)) -> g#(X)
    mark#(g(X)) -> g#(mark(X)) -> g#(mark(X)) -> g#(X)
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(mark(X)))
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> g#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
    mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> f#(mark(X1),X2)
    mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> mark#(X1)
    mark#(g(X)) -> active#(g(mark(X))) ->
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
    mark#(g(X)) -> active#(g(mark(X))) ->
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y))
    f#(mark(X1),X2) -> f#(X1,X2) -> f#(X1,active(X2)) -> f#(X1,X2)
    f#(mark(X1),X2) -> f#(X1,X2) -> f#(active(X1),X2) -> f#(X1,X2)
    f#(mark(X1),X2) -> f#(X1,X2) -> f#(X1,mark(X2)) -> f#(X1,X2)
    f#(mark(X1),X2) -> f#(X1,X2) -> f#(mark(X1),X2) -> f#(X1,X2)
    f#(active(X1),X2) -> f#(X1,X2) -> f#(X1,active(X2)) -> f#(X1,X2)
    f#(active(X1),X2) -> f#(X1,X2) -> f#(active(X1),X2) -> f#(X1,X2)
    f#(active(X1),X2) -> f#(X1,X2) -> f#(X1,mark(X2)) -> f#(X1,X2)
    f#(active(X1),X2) -> f#(X1,X2) -> f#(mark(X1),X2) -> f#(X1,X2)
    f#(X1,mark(X2)) -> f#(X1,X2) -> f#(X1,active(X2)) -> f#(X1,X2)
    f#(X1,mark(X2)) -> f#(X1,X2) -> f#(active(X1),X2) -> f#(X1,X2)
    f#(X1,mark(X2)) -> f#(X1,X2) -> f#(X1,mark(X2)) -> f#(X1,X2)
    f#(X1,mark(X2)) -> f#(X1,X2) -> f#(mark(X1),X2) -> f#(X1,X2)
    f#(X1,active(X2)) -> f#(X1,X2) -> f#(X1,active(X2)) -> f#(X1,X2)
    f#(X1,active(X2)) -> f#(X1,X2) -> f#(active(X1),X2) -> f#(X1,X2)
    f#(X1,active(X2)) -> f#(X1,X2) -> f#(X1,mark(X2)) -> f#(X1,X2)
    f#(X1,active(X2)) -> f#(X1,X2) ->
    f#(mark(X1),X2) -> f#(X1,X2)
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
    mark#(g(X)) -> active#(g(mark(X)))
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
    mark#(g(X)) -> g#(mark(X))
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
    mark#(g(X)) -> mark#(X)
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
    mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
    mark#(f(X1,X2)) -> f#(mark(X1),X2)
    active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
    mark#(f(X1,X2)) -> mark#(X1)
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y)) ->
    f#(X1,active(X2)) -> f#(X1,X2)
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y)) ->
    f#(active(X1),X2) -> f#(X1,X2)
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y)) ->
    f#(X1,mark(X2)) -> f#(X1,X2)
    active#(f(g(X),Y)) -> f#(X,f(g(X),Y)) -> f#(mark(X1),X2) -> f#(X1,X2)
   SCC Processor:
    #sccs: 3
    #rules: 11
    #arcs: 52/196
    DPs:
     mark#(f(X1,X2)) -> mark#(X1)
     mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
     active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
     mark#(g(X)) -> mark#(X)
     mark#(g(X)) -> active#(g(mark(X)))
    TRS:
     active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
     mark(f(X1,X2)) -> active(f(mark(X1),X2))
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X1),X2) -> f(X1,X2)
     f(X1,mark(X2)) -> f(X1,X2)
     f(active(X1),X2) -> f(X1,X2)
     f(X1,active(X2)) -> f(X1,X2)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    CDG Processor:
     DPs:
      mark#(f(X1,X2)) -> mark#(X1)
      mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
      active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
      mark#(g(X)) -> mark#(X)
      mark#(g(X)) -> active#(g(mark(X)))
     TRS:
      active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
      mark(f(X1,X2)) -> active(f(mark(X1),X2))
      mark(g(X)) -> active(g(mark(X)))
      f(mark(X1),X2) -> f(X1,X2)
      f(X1,mark(X2)) -> f(X1,X2)
      f(active(X1),X2) -> f(X1,X2)
      f(X1,active(X2)) -> f(X1,X2)
      g(mark(X)) -> g(X)
      g(active(X)) -> g(X)
     graph:
      mark#(f(X1,X2)) -> mark#(X1) -> mark#(f(X1,X2)) -> mark#(X1)
      mark#(f(X1,X2)) -> mark#(X1) ->
      mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
      mark#(f(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> mark#(X)
      mark#(f(X1,X2)) -> mark#(X1) ->
      mark#(g(X)) -> active#(g(mark(X)))
      mark#(f(X1,X2)) -> active#(f(mark(X1),X2)) ->
      active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
      mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> mark#(X1)
      mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
      mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
      mark#(g(X)) -> mark#(X) ->
      mark#(g(X)) -> active#(g(mark(X)))
      active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) ->
      mark#(f(X1,X2)) -> mark#(X1)
      active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y))) -> mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
     SCC Processor:
      #sccs: 1
      #rules: 4
      #arcs: 11/25
      DPs:
       mark#(f(X1,X2)) -> mark#(X1)
       mark#(g(X)) -> mark#(X)
       mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
       active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
      TRS:
       active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
       mark(f(X1,X2)) -> active(f(mark(X1),X2))
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X1),X2) -> f(X1,X2)
       f(X1,mark(X2)) -> f(X1,X2)
       f(active(X1),X2) -> f(X1,X2)
       f(X1,active(X2)) -> f(X1,X2)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [mark#](x0) = x0,
        
        [active#](x0) = x0 + 0,
        
        [mark](x0) = x0,
        
        [active](x0) = x0,
        
        [f](x0, x1) = 7x0 + x1 + 0,
        
        [g](x0) = x0 + 0
       orientation:
        mark#(f(X1,X2)) = 7X1 + X2 + 0 >= X1 = mark#(X1)
        
        mark#(g(X)) = X + 0 >= X = mark#(X)
        
        mark#(f(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active#(f(mark(X1),X2))
        
        active#(f(g(X),Y)) = 7X + Y + 7 >= 7X + Y + 7 = mark#(f(X,f(g(X),Y)))
        
        active(f(g(X),Y)) = 7X + Y + 7 >= 7X + Y + 7 = mark(f(X,f(g(X),Y)))
        
        mark(f(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active(f(mark(X1),X2))
        
        mark(g(X)) = X + 0 >= X + 0 = active(g(mark(X)))
        
        f(mark(X1),X2) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = f(X1,X2)
        
        f(X1,mark(X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = f(X1,X2)
        
        f(active(X1),X2) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = f(X1,X2)
        
        f(X1,active(X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = f(X1,X2)
        
        g(mark(X)) = X + 0 >= X + 0 = g(X)
        
        g(active(X)) = X + 0 >= X + 0 = g(X)
       problem:
        DPs:
         mark#(g(X)) -> mark#(X)
         mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
         active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
        TRS:
         active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
         mark(f(X1,X2)) -> active(f(mark(X1),X2))
         mark(g(X)) -> active(g(mark(X)))
         f(mark(X1),X2) -> f(X1,X2)
         f(X1,mark(X2)) -> f(X1,X2)
         f(active(X1),X2) -> f(X1,X2)
         f(X1,active(X2)) -> f(X1,X2)
         g(mark(X)) -> g(X)
         g(active(X)) -> g(X)
       SCC Processor:
        #sccs: 2
        #rules: 3
        #arcs: 9/9
        DPs:
         mark#(g(X)) -> mark#(X)
        TRS:
         active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
         mark(f(X1,X2)) -> active(f(mark(X1),X2))
         mark(g(X)) -> active(g(mark(X)))
         f(mark(X1),X2) -> f(X1,X2)
         f(X1,mark(X2)) -> f(X1,X2)
         f(active(X1),X2) -> f(X1,X2)
         f(X1,active(X2)) -> f(X1,X2)
         g(mark(X)) -> g(X)
         g(active(X)) -> g(X)
        Subterm Criterion Processor:
         simple projection:
          pi(mark#) = 0
         problem:
          DPs:
           
          TRS:
           active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
           mark(f(X1,X2)) -> active(f(mark(X1),X2))
           mark(g(X)) -> active(g(mark(X)))
           f(mark(X1),X2) -> f(X1,X2)
           f(X1,mark(X2)) -> f(X1,X2)
           f(active(X1),X2) -> f(X1,X2)
           f(X1,active(X2)) -> f(X1,X2)
           g(mark(X)) -> g(X)
           g(active(X)) -> g(X)
         Qed
        
        DPs:
         mark#(f(X1,X2)) -> active#(f(mark(X1),X2))
         active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
        TRS:
         active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
         mark(f(X1,X2)) -> active(f(mark(X1),X2))
         mark(g(X)) -> active(g(mark(X)))
         f(mark(X1),X2) -> f(X1,X2)
         f(X1,mark(X2)) -> f(X1,X2)
         f(active(X1),X2) -> f(X1,X2)
         f(X1,active(X2)) -> f(X1,X2)
         g(mark(X)) -> g(X)
         g(active(X)) -> g(X)
        Arctic Interpretation Processor:
         dimension: 1
         interpretation:
          [mark#](x0) = 2x0 + 0,
          
          [active#](x0) = x0 + 1,
          
          [mark](x0) = x0,
          
          [active](x0) = x0,
          
          [f](x0, x1) = x0 + 0,
          
          [g](x0) = 4x0 + 2
         orientation:
          mark#(f(X1,X2)) = 2X1 + 2 >= X1 + 1 = active#(f(mark(X1),X2))
          
          active#(f(g(X),Y)) = 4X + 2 >= 2X + 2 = mark#(f(X,f(g(X),Y)))
          
          active(f(g(X),Y)) = 4X + 2 >= X + 0 = mark(f(X,f(g(X),Y)))
          
          mark(f(X1,X2)) = X1 + 0 >= X1 + 0 = active(f(mark(X1),X2))
          
          mark(g(X)) = 4X + 2 >= 4X + 2 = active(g(mark(X)))
          
          f(mark(X1),X2) = X1 + 0 >= X1 + 0 = f(X1,X2)
          
          f(X1,mark(X2)) = X1 + 0 >= X1 + 0 = f(X1,X2)
          
          f(active(X1),X2) = X1 + 0 >= X1 + 0 = f(X1,X2)
          
          f(X1,active(X2)) = X1 + 0 >= X1 + 0 = f(X1,X2)
          
          g(mark(X)) = 4X + 2 >= 4X + 2 = g(X)
          
          g(active(X)) = 4X + 2 >= 4X + 2 = g(X)
         problem:
          DPs:
           active#(f(g(X),Y)) -> mark#(f(X,f(g(X),Y)))
          TRS:
           active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
           mark(f(X1,X2)) -> active(f(mark(X1),X2))
           mark(g(X)) -> active(g(mark(X)))
           f(mark(X1),X2) -> f(X1,X2)
           f(X1,mark(X2)) -> f(X1,X2)
           f(active(X1),X2) -> f(X1,X2)
           f(X1,active(X2)) -> f(X1,X2)
           g(mark(X)) -> g(X)
           g(active(X)) -> g(X)
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 2/1
          
    
    DPs:
     f#(mark(X1),X2) -> f#(X1,X2)
     f#(X1,mark(X2)) -> f#(X1,X2)
     f#(active(X1),X2) -> f#(X1,X2)
     f#(X1,active(X2)) -> f#(X1,X2)
    TRS:
     active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
     mark(f(X1,X2)) -> active(f(mark(X1),X2))
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X1),X2) -> f(X1,X2)
     f(X1,mark(X2)) -> f(X1,X2)
     f(active(X1),X2) -> f(X1,X2)
     f(X1,active(X2)) -> f(X1,X2)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 1
     problem:
      DPs:
       f#(mark(X1),X2) -> f#(X1,X2)
       f#(active(X1),X2) -> f#(X1,X2)
      TRS:
       active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
       mark(f(X1,X2)) -> active(f(mark(X1),X2))
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X1),X2) -> f(X1,X2)
       f(X1,mark(X2)) -> f(X1,X2)
       f(active(X1),X2) -> f(X1,X2)
       f(X1,active(X2)) -> f(X1,X2)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Subterm Criterion Processor:
      simple projection:
       pi(f#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
        mark(f(X1,X2)) -> active(f(mark(X1),X2))
        mark(g(X)) -> active(g(mark(X)))
        f(mark(X1),X2) -> f(X1,X2)
        f(X1,mark(X2)) -> f(X1,X2)
        f(active(X1),X2) -> f(X1,X2)
        f(X1,active(X2)) -> f(X1,X2)
        g(mark(X)) -> g(X)
        g(active(X)) -> g(X)
      Qed
    
    DPs:
     g#(mark(X)) -> g#(X)
     g#(active(X)) -> g#(X)
    TRS:
     active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
     mark(f(X1,X2)) -> active(f(mark(X1),X2))
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X1),X2) -> f(X1,X2)
     f(X1,mark(X2)) -> f(X1,X2)
     f(active(X1),X2) -> f(X1,X2)
     f(X1,active(X2)) -> f(X1,X2)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
       mark(f(X1,X2)) -> active(f(mark(X1),X2))
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X1),X2) -> f(X1,X2)
       f(X1,mark(X2)) -> f(X1,X2)
       f(active(X1),X2) -> f(X1,X2)
       f(X1,active(X2)) -> f(X1,X2)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Qed