MAYBE

Problem:
 h(X) -> g(X,X)
 g(a(),X) -> f(b(),activate(X))
 f(X,X) -> h(a())
 a() -> b()
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   h#(X) -> g#(X,X)
   g#(a(),X) -> activate#(X)
   g#(a(),X) -> f#(b(),activate(X))
   f#(X,X) -> a#()
   f#(X,X) -> h#(a())
  TRS:
   h(X) -> g(X,X)
   g(a(),X) -> f(b(),activate(X))
   f(X,X) -> h(a())
   a() -> b()
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    h#(X) -> g#(X,X)
    g#(a(),X) -> activate#(X)
    g#(a(),X) -> f#(b(),activate(X))
    f#(X,X) -> a#()
    f#(X,X) -> h#(a())
   TRS:
    f11(x,y) -> x
    f11(x,y) -> y
    activate(X) -> X
    a() -> b()
   CDG Processor:
    DPs:
     h#(X) -> g#(X,X)
     g#(a(),X) -> activate#(X)
     g#(a(),X) -> f#(b(),activate(X))
     f#(X,X) -> a#()
     f#(X,X) -> h#(a())
    TRS:
     f11(x,y) -> x
     f11(x,y) -> y
     activate(X) -> X
     a() -> b()
    graph:
     f#(X,X) -> h#(a()) -> h#(X) -> g#(X,X)
     g#(a(),X) -> f#(b(),activate(X)) -> f#(X,X) -> a#()
     g#(a(),X) -> f#(b(),activate(X)) -> f#(X,X) -> h#(a())
     h#(X) -> g#(X,X) -> g#(a(),X) -> activate#(X)
     h#(X) -> g#(X,X) -> g#(a(),X) -> f#(b(),activate(X))
    Restore Modifier:
     DPs:
      h#(X) -> g#(X,X)
      g#(a(),X) -> activate#(X)
      g#(a(),X) -> f#(b(),activate(X))
      f#(X,X) -> a#()
      f#(X,X) -> h#(a())
     TRS:
      h(X) -> g(X,X)
      g(a(),X) -> f(b(),activate(X))
      f(X,X) -> h(a())
      a() -> b()
      activate(X) -> X
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 5/25
      DPs:
       f#(X,X) -> h#(a())
       h#(X) -> g#(X,X)
       g#(a(),X) -> f#(b(),activate(X))
      TRS:
       h(X) -> g(X,X)
       g(a(),X) -> f(b(),activate(X))
       f(X,X) -> h(a())
       a() -> b()
       activate(X) -> X
      Open