MAYBE

Problem:
 f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
 g(b()) -> c()
 b() -> c()
 g(X) -> n__g(X)
 activate(n__g(X)) -> g(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(X,n__g(X),Y) -> activate#(Y)
   f#(X,n__g(X),Y) -> f#(activate(Y),activate(Y),activate(Y))
   activate#(n__g(X)) -> activate#(X)
   activate#(n__g(X)) -> g#(activate(X))
  TRS:
   f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
   g(b()) -> c()
   b() -> c()
   g(X) -> n__g(X)
   activate(n__g(X)) -> g(activate(X))
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(X,n__g(X),Y) -> activate#(Y)
    f#(X,n__g(X),Y) -> f#(activate(Y),activate(Y),activate(Y))
    activate#(n__g(X)) -> activate#(X)
    activate#(n__g(X)) -> g#(activate(X))
   TRS:
    f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
    g(b()) -> c()
    b() -> c()
    g(X) -> n__g(X)
    activate(n__g(X)) -> g(activate(X))
    activate(X) -> X
   graph:
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__g(X)) -> g#(activate(X))
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__g(X)) -> activate#(X)
    f#(X,n__g(X),Y) -> activate#(Y) ->
    activate#(n__g(X)) -> g#(activate(X))
    f#(X,n__g(X),Y) -> activate#(Y) ->
    activate#(n__g(X)) -> activate#(X)
    f#(X,n__g(X),Y) -> f#(activate(Y),activate(Y),activate(Y)) ->
    f#(X,n__g(X),Y) -> f#(activate(Y),activate(Y),activate(Y))
    f#(X,n__g(X),Y) -> f#(activate(Y),activate(Y),activate(Y)) -> f#(X,n__g(X),Y) -> activate#(Y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 6/16
    DPs:
     f#(X,n__g(X),Y) -> f#(activate(Y),activate(Y),activate(Y))
    TRS:
     f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
     g(b()) -> c()
     b() -> c()
     g(X) -> n__g(X)
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    Open
    
    DPs:
     activate#(n__g(X)) -> activate#(X)
    TRS:
     f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
     g(b()) -> c()
     b() -> c()
     g(X) -> n__g(X)
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    KBO Processor:
     argument filtering:
      pi(n__g) = [0]
      pi(f) = []
      pi(activate) = [0]
      pi(b) = []
      pi(g) = [0]
      pi(c) = []
      pi(activate#) = 0
     weight function:
      w0 = 1
      w(activate#) = w(c) = w(g) = w(b) = w(activate) = w(f) = w(n__g) = 1
     precedence:
      activate# ~ b ~ activate ~ f > g > c ~ n__g
     problem:
      DPs:
       
      TRS:
       f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
       g(b()) -> c()
       b() -> c()
       g(X) -> n__g(X)
       activate(n__g(X)) -> g(activate(X))
       activate(X) -> X
     Qed