MAYBE

Problem:
 f(x,x) -> f(i(x),g(g(x)))
 f(x,y) -> x
 g(x) -> i(x)
 f(x,i(x)) -> f(x,x)
 f(i(x),i(g(x))) -> a()

Proof:
 DP Processor:
  DPs:
   f#(x,x) -> g#(x)
   f#(x,x) -> g#(g(x))
   f#(x,x) -> f#(i(x),g(g(x)))
   f#(x,i(x)) -> f#(x,x)
  TRS:
   f(x,x) -> f(i(x),g(g(x)))
   f(x,y) -> x
   g(x) -> i(x)
   f(x,i(x)) -> f(x,x)
   f(i(x),i(g(x))) -> a()
  Usable Rule Processor:
   DPs:
    f#(x,x) -> g#(x)
    f#(x,x) -> g#(g(x))
    f#(x,x) -> f#(i(x),g(g(x)))
    f#(x,i(x)) -> f#(x,x)
   TRS:
    g(x) -> i(x)
   TDG Processor:
    DPs:
     f#(x,x) -> g#(x)
     f#(x,x) -> g#(g(x))
     f#(x,x) -> f#(i(x),g(g(x)))
     f#(x,i(x)) -> f#(x,x)
    TRS:
     g(x) -> i(x)
    graph:
     f#(x,i(x)) -> f#(x,x) -> f#(x,i(x)) -> f#(x,x)
     f#(x,i(x)) -> f#(x,x) -> f#(x,x) -> f#(i(x),g(g(x)))
     f#(x,i(x)) -> f#(x,x) -> f#(x,x) -> g#(g(x))
     f#(x,i(x)) -> f#(x,x) -> f#(x,x) -> g#(x)
     f#(x,x) -> f#(i(x),g(g(x))) -> f#(x,i(x)) -> f#(x,x)
     f#(x,x) -> f#(i(x),g(g(x))) -> f#(x,x) -> f#(i(x),g(g(x)))
     f#(x,x) -> f#(i(x),g(g(x))) -> f#(x,x) -> g#(g(x))
     f#(x,x) -> f#(i(x),g(g(x))) -> f#(x,x) -> g#(x)
    Restore Modifier:
     DPs:
      f#(x,x) -> g#(x)
      f#(x,x) -> g#(g(x))
      f#(x,x) -> f#(i(x),g(g(x)))
      f#(x,i(x)) -> f#(x,x)
     TRS:
      f(x,x) -> f(i(x),g(g(x)))
      f(x,y) -> x
      g(x) -> i(x)
      f(x,i(x)) -> f(x,x)
      f(i(x),i(g(x))) -> a()
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 8/16
      DPs:
       f#(x,i(x)) -> f#(x,x)
       f#(x,x) -> f#(i(x),g(g(x)))
      TRS:
       f(x,x) -> f(i(x),g(g(x)))
       f(x,y) -> x
       g(x) -> i(x)
       f(x,i(x)) -> f(x,x)
       f(i(x),i(g(x))) -> a()
      Open