MAYBE

Problem:
 f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
 f(X1,X2) -> n__f(X1,X2)
 activate(n__f(X1,X2)) -> f(X1,X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(g(X),Y) -> activate#(Y)
   f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y)))
   activate#(n__f(X1,X2)) -> f#(X1,X2)
  TRS:
   f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
   f(X1,X2) -> n__f(X1,X2)
   activate(n__f(X1,X2)) -> f(X1,X2)
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(g(X),Y) -> activate#(Y)
    f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y)))
    activate#(n__f(X1,X2)) -> f#(X1,X2)
   TRS:
    f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
    f(X1,X2) -> n__f(X1,X2)
    activate(n__f(X1,X2)) -> f(X1,X2)
    activate(X) -> X
   graph:
    activate#(n__f(X1,X2)) -> f#(X1,X2) ->
    f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y)))
    activate#(n__f(X1,X2)) -> f#(X1,X2) -> f#(g(X),Y) -> activate#(Y)
    f#(g(X),Y) -> activate#(Y) ->
    activate#(n__f(X1,X2)) -> f#(X1,X2)
    f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y))) ->
    f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y)))
    f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y))) -> f#(g(X),Y) -> activate#(Y)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 5/9
    DPs:
     activate#(n__f(X1,X2)) -> f#(X1,X2)
     f#(g(X),Y) -> activate#(Y)
     f#(g(X),Y) -> f#(X,n__f(g(X),activate(Y)))
    TRS:
     f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
     f(X1,X2) -> n__f(X1,X2)
     activate(n__f(X1,X2)) -> f(X1,X2)
     activate(X) -> X
    Open