MAYBE

Problem:
 f(a(),x) -> f(g(x),x)
 h(g(x)) -> h(a())
 g(h(x)) -> g(x)
 h(h(x)) -> x

Proof:
 DP Processor:
  DPs:
   f#(a(),x) -> g#(x)
   f#(a(),x) -> f#(g(x),x)
   h#(g(x)) -> h#(a())
   g#(h(x)) -> g#(x)
  TRS:
   f(a(),x) -> f(g(x),x)
   h(g(x)) -> h(a())
   g(h(x)) -> g(x)
   h(h(x)) -> x
  TDG Processor:
   DPs:
    f#(a(),x) -> g#(x)
    f#(a(),x) -> f#(g(x),x)
    h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x)
   TRS:
    f(a(),x) -> f(g(x),x)
    h(g(x)) -> h(a())
    g(h(x)) -> g(x)
    h(h(x)) -> x
   graph:
    h#(g(x)) -> h#(a()) -> h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
    f#(a(),x) -> g#(x) -> g#(h(x)) -> g#(x)
    f#(a(),x) -> f#(g(x),x) -> f#(a(),x) -> f#(g(x),x)
    f#(a(),x) -> f#(g(x),x) -> f#(a(),x) -> g#(x)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 5/16
    DPs:
     f#(a(),x) -> f#(g(x),x)
    TRS:
     f(a(),x) -> f(g(x),x)
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    Open
    
    DPs:
     g#(h(x)) -> g#(x)
    TRS:
     f(a(),x) -> f(g(x),x)
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    Open
    
    DPs:
     h#(g(x)) -> h#(a())
    TRS:
     f(a(),x) -> f(g(x),x)
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    Open