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
  TDG 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
   graph:
    f#(X,X) -> h#(a()) -> h#(X) -> g#(X,X)
    g#(a(),X) -> f#(b(),activate(X)) -> f#(X,X) -> h#(a())
    g#(a(),X) -> f#(b(),activate(X)) -> f#(X,X) -> a#()
    h#(X) -> g#(X,X) -> g#(a(),X) -> f#(b(),activate(X))
    h#(X) -> g#(X,X) -> g#(a(),X) -> activate#(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