YES

Problem:
 app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))

Proof:
 DP Processor:
  DPs:
   app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x)
   app#(app(F(),app(app(F(),f),x)),x) -> app#(G(),app(app(F(),f),x))
   app#(app(F(),app(app(F(),f),x)),x) -> app#(F(),app(G(),app(app(F(),f),x)))
   app#(app(F(),app(app(F(),f),x)),x) -> app#(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
  TRS:
   app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
  EDG Processor:
   DPs:
    app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x)
    app#(app(F(),app(app(F(),f),x)),x) -> app#(G(),app(app(F(),f),x))
    app#(app(F(),app(app(F(),f),x)),x) -> app#(F(),app(G(),app(app(F(),f),x)))
    app#(app(F(),app(app(F(),f),x)),x) -> app#(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
   TRS:
    app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
   graph:
    app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x) ->
    app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x)
    app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x) ->
    app#(app(F(),app(app(F(),f),x)),x) -> app#(G(),app(app(F(),f),x))
    app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x) ->
    app#(app(F(),app(app(F(),f),x)),x) -> app#(F(),app(G(),app(app(F(),f),x)))
    app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x) ->
    app#(app(F(),app(app(F(),f),x)),x) -> app#(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     app#(app(F(),app(app(F(),f),x)),x) -> app#(f,x)
    TRS:
     app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 0
     problem:
      DPs:
       
      TRS:
       app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
     Qed