MAYBE

Problem:
 f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
 g(s(x)) -> s(g(x))
 g(0()) -> 0()

Proof:
 DP Processor:
  DPs:
   f#(g(x),s(0()),y) -> g#(s(0()))
   f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
   g#(s(x)) -> g#(x)
  TRS:
   f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
   g(s(x)) -> s(g(x))
   g(0()) -> 0()
  Usable Rule Processor:
   DPs:
    f#(g(x),s(0()),y) -> g#(s(0()))
    f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
    g#(s(x)) -> g#(x)
   TRS:
    g(s(x)) -> s(g(x))
    g(0()) -> 0()
   EDG Processor:
    DPs:
     f#(g(x),s(0()),y) -> g#(s(0()))
     f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
     g#(s(x)) -> g#(x)
    TRS:
     g(s(x)) -> s(g(x))
     g(0()) -> 0()
    graph:
     g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x)
     f#(g(x),s(0()),y) -> g#(s(0())) -> g#(s(x)) -> g#(x)
     f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x)) ->
     f#(g(x),s(0()),y) -> g#(s(0()))
     f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x)) -> f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
    Restore Modifier:
     DPs:
      f#(g(x),s(0()),y) -> g#(s(0()))
      f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
      g#(s(x)) -> g#(x)
     TRS:
      f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
      g(s(x)) -> s(g(x))
      g(0()) -> 0()
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
      TRS:
       f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
       g(s(x)) -> s(g(x))
       g(0()) -> 0()
      Open
      
      DPs:
       g#(s(x)) -> g#(x)
      TRS:
       f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
       g(s(x)) -> s(g(x))
       g(0()) -> 0()
      Open