YES

Problem:
 f(X,X) -> f(a(),n__b())
 b() -> a()
 b() -> n__b()
 activate(n__b()) -> b()
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(X,X) -> f#(a(),n__b())
   activate#(n__b()) -> b#()
  TRS:
   f(X,X) -> f(a(),n__b())
   b() -> a()
   b() -> n__b()
   activate(n__b()) -> b()
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(X,X) -> f#(a(),n__b())
    activate#(n__b()) -> b#()
   TRS:
    f(X,X) -> f(a(),n__b())
    b() -> a()
    b() -> n__b()
    activate(n__b()) -> b()
    activate(X) -> X
   graph:
    f#(X,X) -> f#(a(),n__b()) -> f#(X,X) -> f#(a(),n__b())
   EDG Processor:
    DPs:
     f#(X,X) -> f#(a(),n__b())
     activate#(n__b()) -> b#()
    TRS:
     f(X,X) -> f(a(),n__b())
     b() -> a()
     b() -> n__b()
     activate(n__b()) -> b()
     activate(X) -> X
    graph:
     
    Qed