YES

Problem:
 a__f(a(),X,X) -> a__f(X,a__b(),b())
 a__b() -> a()
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
 mark(b()) -> a__b()
 mark(a()) -> a()
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 a__b() -> b()

Proof:
 DP Processor:
  DPs:
   a__f#(a(),X,X) -> a__b#()
   a__f#(a(),X,X) -> a__f#(X,a__b(),b())
   mark#(f(X1,X2,X3)) -> mark#(X2)
   mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
   mark#(b()) -> a__b#()
  TRS:
   a__f(a(),X,X) -> a__f(X,a__b(),b())
   a__b() -> a()
   mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
   mark(b()) -> a__b()
   mark(a()) -> a()
   a__f(X1,X2,X3) -> f(X1,X2,X3)
   a__b() -> b()
  TDG Processor:
   DPs:
    a__f#(a(),X,X) -> a__b#()
    a__f#(a(),X,X) -> a__f#(X,a__b(),b())
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
    mark#(b()) -> a__b#()
   TRS:
    a__f(a(),X,X) -> a__f(X,a__b(),b())
    a__b() -> a()
    mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
    mark(b()) -> a__b()
    mark(a()) -> a()
    a__f(X1,X2,X3) -> f(X1,X2,X3)
    a__b() -> b()
   graph:
    mark#(f(X1,X2,X3)) -> mark#(X2) -> mark#(b()) -> a__b#()
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3) ->
    a__f#(a(),X,X) -> a__f#(X,a__b(),b())
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3) ->
    a__f#(a(),X,X) -> a__b#()
    a__f#(a(),X,X) -> a__f#(X,a__b(),b()) ->
    a__f#(a(),X,X) -> a__f#(X,a__b(),b())
    a__f#(a(),X,X) -> a__f#(X,a__b(),b()) -> a__f#(a(),X,X) -> a__b#()
   CDG Processor:
    DPs:
     a__f#(a(),X,X) -> a__b#()
     a__f#(a(),X,X) -> a__f#(X,a__b(),b())
     mark#(f(X1,X2,X3)) -> mark#(X2)
     mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
     mark#(b()) -> a__b#()
    TRS:
     a__f(a(),X,X) -> a__f(X,a__b(),b())
     a__b() -> a()
     mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
     mark(b()) -> a__b()
     mark(a()) -> a()
     a__f(X1,X2,X3) -> f(X1,X2,X3)
     a__b() -> b()
    graph:
     mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3) ->
     a__f#(a(),X,X) -> a__b#()
     mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3) ->
     a__f#(a(),X,X) -> a__f#(X,a__b(),b())
     a__f#(a(),X,X) -> a__f#(X,a__b(),b()) ->
     a__f#(a(),X,X) -> a__b#()
     a__f#(a(),X,X) -> a__f#(X,a__b(),b()) -> a__f#(a(),X,X) -> a__f#(X,a__b(),b())
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 4/25
     DPs:
      a__f#(a(),X,X) -> a__f#(X,a__b(),b())
     TRS:
      a__f(a(),X,X) -> a__f(X,a__b(),b())
      a__b() -> a()
      mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
      mark(b()) -> a__b()
      mark(a()) -> a()
      a__f(X1,X2,X3) -> f(X1,X2,X3)
      a__b() -> b()
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [a__f#](x0, x1, x2) = 3x0 + 4x2 + 0,
       
       [mark](x0) = 5x0,
       
       [f](x0, x1, x2) = x0 + 1x2,
       
       [b] = 0,
       
       [a__b] = 4,
       
       [a__f](x0, x1, x2) = 3x0 + 4x2,
       
       [a] = 2
      orientation:
       a__f#(a(),X,X) = 4X + 5 >= 3X + 4 = a__f#(X,a__b(),b())
       
       a__f(a(),X,X) = 4X + 5 >= 3X + 4 = a__f(X,a__b(),b())
       
       a__b() = 4 >= 2 = a()
       
       mark(f(X1,X2,X3)) = 5X1 + 6X3 >= 3X1 + 4X3 = a__f(X1,mark(X2),X3)
       
       mark(b()) = 5 >= 4 = a__b()
       
       mark(a()) = 7 >= 2 = a()
       
       a__f(X1,X2,X3) = 3X1 + 4X3 >= X1 + 1X3 = f(X1,X2,X3)
       
       a__b() = 4 >= 0 = b()
      problem:
       DPs:
        
       TRS:
        a__f(a(),X,X) -> a__f(X,a__b(),b())
        a__b() -> a()
        mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
        mark(b()) -> a__b()
        mark(a()) -> a()
        a__f(X1,X2,X3) -> f(X1,X2,X3)
        a__b() -> b()
      Qed