MAYBE
Time: 0.001564
TRS:
 {            f(X1, X2) -> n__f(X1, X2),
              f(g X, Y) -> f(X, n__f(g X, activate Y)),
             activate X -> X,
  activate n__f(X1, X2) -> f(X1, X2)}
 DP:
  DP:
   {            f#(g X, Y) -> f#(X, n__f(g X, activate Y)),
                f#(g X, Y) -> activate# Y,
    activate# n__f(X1, X2) -> f#(X1, X2)}
  TRS:
  {            f(X1, X2) -> n__f(X1, X2),
               f(g X, Y) -> f(X, n__f(g X, activate Y)),
              activate X -> X,
   activate n__f(X1, X2) -> f(X1, X2)}
  UR:
   {            f(X1, X2) -> n__f(X1, X2),
                f(g X, Y) -> f(X, n__f(g X, activate Y)),
               activate X -> X,
    activate n__f(X1, X2) -> f(X1, X2),
                  a(x, y) -> x,
                  a(x, y) -> y}
   EDG:
    {(f#(g X, Y) -> activate# Y, activate# n__f(X1, X2) -> f#(X1, X2))
     (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) -> 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)}
    EDG:
     {(f#(g X, Y) -> activate# Y, activate# n__f(X1, X2) -> f#(X1, X2))
      (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) -> 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)}
     EDG:
      {(f#(g X, Y) -> activate# Y, activate# n__f(X1, X2) -> f#(X1, X2))
       (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) -> 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)}
      EDG:
       {(f#(g X, Y) -> activate# Y, activate# n__f(X1, X2) -> f#(X1, X2))
        (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) -> 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)}
       STATUS:
        arrows: 0.444444
        SCCS (1):
         Scc:
          {            f#(g X, Y) -> f#(X, n__f(g X, activate Y)),
                       f#(g X, Y) -> activate# Y,
           activate# n__f(X1, X2) -> f#(X1, X2)}
         
         SCC (3):
          Strict:
           {            f#(g X, Y) -> f#(X, n__f(g X, activate Y)),
                        f#(g X, Y) -> activate# Y,
            activate# n__f(X1, X2) -> f#(X1, X2)}
          Weak:
          {            f(X1, X2) -> n__f(X1, X2),
                       f(g X, Y) -> f(X, n__f(g X, activate Y)),
                      activate X -> X,
           activate n__f(X1, X2) -> f(X1, X2)}
          Open