MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(a(),h(x)) -> g#(x)
   f#(a(),h(x)) -> f#(g(x),h(x))
   h#(g(x)) -> h#(a())
   g#(h(x)) -> g#(x)
  TRS:
   f(a(),h(x)) -> f(g(x),h(x))
   h(g(x)) -> h(a())
   g(h(x)) -> g(x)
   h(h(x)) -> x
  Usable Rule Processor:
   DPs:
    f#(a(),h(x)) -> g#(x)
    f#(a(),h(x)) -> f#(g(x),h(x))
    h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x)
   TRS:
    f7(x,y) -> x
    f7(x,y) -> y
    h(g(x)) -> h(a())
    h(h(x)) -> x
    g(h(x)) -> g(x)
   EDG Processor:
    DPs:
     f#(a(),h(x)) -> g#(x)
     f#(a(),h(x)) -> f#(g(x),h(x))
     h#(g(x)) -> h#(a())
     g#(h(x)) -> g#(x)
    TRS:
     f7(x,y) -> x
     f7(x,y) -> y
     h(g(x)) -> h(a())
     h(h(x)) -> x
     g(h(x)) -> g(x)
    graph:
     g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
     f#(a(),h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
     f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> g#(x)
     f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> f#(g(x),h(x))
    Restore Modifier:
     DPs:
      f#(a(),h(x)) -> g#(x)
      f#(a(),h(x)) -> f#(g(x),h(x))
      h#(g(x)) -> h#(a())
      g#(h(x)) -> g#(x)
     TRS:
      f(a(),h(x)) -> f(g(x),h(x))
      h(g(x)) -> h(a())
      g(h(x)) -> g(x)
      h(h(x)) -> x
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/16
      DPs:
       f#(a(),h(x)) -> f#(g(x),h(x))
      TRS:
       f(a(),h(x)) -> f(g(x),h(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(),h(x)) -> f(g(x),h(x))
       h(g(x)) -> h(a())
       g(h(x)) -> g(x)
       h(h(x)) -> x
      Open