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#()
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 7/25
    DPs:
     mark#(f(X1,X2,X3)) -> mark#(X2)
    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()
    Subterm Criterion Processor:
     simple projection:
      pi(mark#) = 0
     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
    
    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) = x0 + 4x2 + 2,
      
      [mark](x0) = x0 + 5,
      
      [f](x0, x1, x2) = 5,
      
      [b] = 0,
      
      [a__b] = 5,
      
      [a__f](x0, x1, x2) = 5,
      
      [a] = 5
     orientation:
      a__f#(a(),X,X) = 4X + 5 >= X + 4 = a__f#(X,a__b(),b())
      
      a__f(a(),X,X) = 5 >= 5 = a__f(X,a__b(),b())
      
      a__b() = 5 >= 5 = a()
      
      mark(f(X1,X2,X3)) = 5 >= 5 = a__f(X1,mark(X2),X3)
      
      mark(b()) = 5 >= 5 = a__b()
      
      mark(a()) = 5 >= 5 = a()
      
      a__f(X1,X2,X3) = 5 >= 5 = f(X1,X2,X3)
      
      a__b() = 5 >= 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