MAYBE
Time: 0.099033
TRS:
 {            f(X1, X2) -> n__f(X1, X2),
              f(g X, Y) -> f(X, n__f(n__g X, activate Y)),
             activate X -> X,
  activate n__f(X1, X2) -> f(activate X1, X2),
        activate n__g X -> g activate X,
                    g X -> n__g X}
 DP:
  DP:
   {            f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)),
                f#(g X, Y) -> activate# Y,
    activate# n__f(X1, X2) -> f#(activate X1, X2),
    activate# n__f(X1, X2) -> activate# X1,
          activate# n__g X -> activate# X,
          activate# n__g X -> g# activate X}
  TRS:
  {            f(X1, X2) -> n__f(X1, X2),
               f(g X, Y) -> f(X, n__f(n__g X, activate Y)),
              activate X -> X,
   activate n__f(X1, X2) -> f(activate X1, X2),
         activate n__g X -> g activate X,
                     g X -> n__g X}
  UR:
   {            f(X1, X2) -> n__f(X1, X2),
                f(g X, Y) -> f(X, n__f(n__g X, activate Y)),
               activate X -> X,
    activate n__f(X1, X2) -> f(activate X1, X2),
          activate n__g X -> g activate X,
                      g X -> n__g X,
                  a(x, y) -> x,
                  a(x, y) -> y}
   EDG:
    {(activate# n__f(X1, X2) -> f#(activate X1, X2), f#(g X, Y) -> activate# Y)
     (activate# n__f(X1, X2) -> f#(activate X1, X2), f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)))
     (f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)), f#(g X, Y) -> activate# Y)
     (f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)), f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)))
     (activate# n__g X -> activate# X, activate# n__f(X1, X2) -> f#(activate X1, X2))
     (activate# n__g X -> activate# X, activate# n__f(X1, X2) -> activate# X1)
     (activate# n__g X -> activate# X, activate# n__g X -> activate# X)
     (activate# n__g X -> activate# X, activate# n__g X -> g# activate X)
     (activate# n__f(X1, X2) -> activate# X1, activate# n__f(X1, X2) -> f#(activate X1, X2))
     (activate# n__f(X1, X2) -> activate# X1, activate# n__f(X1, X2) -> activate# X1)
     (activate# n__f(X1, X2) -> activate# X1, activate# n__g X -> activate# X)
     (activate# n__f(X1, X2) -> activate# X1, activate# n__g X -> g# activate X)
     (f#(g X, Y) -> activate# Y, activate# n__f(X1, X2) -> f#(activate X1, X2))
     (f#(g X, Y) -> activate# Y, activate# n__f(X1, X2) -> activate# X1)
     (f#(g X, Y) -> activate# Y, activate# n__g X -> activate# X)
     (f#(g X, Y) -> activate# Y, activate# n__g X -> g# activate X)}
    STATUS:
     arrows: 0.555556
     SCCS (1):
      Scc:
       {            f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)),
                    f#(g X, Y) -> activate# Y,
        activate# n__f(X1, X2) -> f#(activate X1, X2),
        activate# n__f(X1, X2) -> activate# X1,
              activate# n__g X -> activate# X}
      
      SCC (5):
       Strict:
        {            f#(g X, Y) -> f#(X, n__f(n__g X, activate Y)),
                     f#(g X, Y) -> activate# Y,
         activate# n__f(X1, X2) -> f#(activate X1, X2),
         activate# n__f(X1, X2) -> activate# X1,
               activate# n__g X -> activate# X}
       Weak:
       {            f(X1, X2) -> n__f(X1, X2),
                    f(g X, Y) -> f(X, n__f(n__g X, activate Y)),
                   activate X -> X,
        activate n__f(X1, X2) -> f(activate X1, X2),
              activate n__g X -> g activate X,
                          g X -> n__g X}
       Open