YES

Problem:
 f(f(X)) -> f(a(b(f(X))))
 f(a(g(X))) -> b(X)
 b(X) -> a(X)

Proof:
 DP Processor:
  DPs:
   f#(f(X)) -> b#(f(X))
   f#(f(X)) -> f#(a(b(f(X))))
   f#(a(g(X))) -> b#(X)
  TRS:
   f(f(X)) -> f(a(b(f(X))))
   f(a(g(X))) -> b(X)
   b(X) -> a(X)
  TDG Processor:
   DPs:
    f#(f(X)) -> b#(f(X))
    f#(f(X)) -> f#(a(b(f(X))))
    f#(a(g(X))) -> b#(X)
   TRS:
    f(f(X)) -> f(a(b(f(X))))
    f(a(g(X))) -> b(X)
    b(X) -> a(X)
   graph:
    f#(f(X)) -> f#(a(b(f(X)))) -> f#(a(g(X))) -> b#(X)
    f#(f(X)) -> f#(a(b(f(X)))) -> f#(f(X)) -> f#(a(b(f(X))))
    f#(f(X)) -> f#(a(b(f(X)))) -> f#(f(X)) -> b#(f(X))
   EDG Processor:
    DPs:
     f#(f(X)) -> b#(f(X))
     f#(f(X)) -> f#(a(b(f(X))))
     f#(a(g(X))) -> b#(X)
    TRS:
     f(f(X)) -> f(a(b(f(X))))
     f(a(g(X))) -> b(X)
     b(X) -> a(X)
    graph:
     f#(f(X)) -> f#(a(b(f(X)))) -> f#(a(g(X))) -> b#(X)
    CDG Processor:
     DPs:
      f#(f(X)) -> b#(f(X))
      f#(f(X)) -> f#(a(b(f(X))))
      f#(a(g(X))) -> b#(X)
     TRS:
      f(f(X)) -> f(a(b(f(X))))
      f(a(g(X))) -> b(X)
      b(X) -> a(X)
     graph:
      
     Qed