MAYBE

Problem:
 f(X) -> cons(X,f(g(X)))
 g(0()) -> s(0())
 g(s(X)) -> s(s(g(X)))
 sel(0(),cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)

Proof:
 DP Processor:
  DPs:
   f#(X) -> g#(X)
   f#(X) -> f#(g(X))
   g#(s(X)) -> g#(X)
   sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
  TRS:
   f(X) -> cons(X,f(g(X)))
   g(0()) -> s(0())
   g(s(X)) -> s(s(g(X)))
   sel(0(),cons(X,Y)) -> X
   sel(s(X),cons(Y,Z)) -> sel(X,Z)
  Usable Rule Processor:
   DPs:
    f#(X) -> g#(X)
    f#(X) -> f#(g(X))
    g#(s(X)) -> g#(X)
    sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
   TRS:
    g(0()) -> s(0())
    g(s(X)) -> s(s(g(X)))
   TDG Processor:
    DPs:
     f#(X) -> g#(X)
     f#(X) -> f#(g(X))
     g#(s(X)) -> g#(X)
     sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
    TRS:
     g(0()) -> s(0())
     g(s(X)) -> s(s(g(X)))
    graph:
     sel#(s(X),cons(Y,Z)) -> sel#(X,Z) -> sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
     g#(s(X)) -> g#(X) -> g#(s(X)) -> g#(X)
     f#(X) -> g#(X) -> g#(s(X)) -> g#(X)
     f#(X) -> f#(g(X)) -> f#(X) -> f#(g(X))
     f#(X) -> f#(g(X)) -> f#(X) -> g#(X)
    Restore Modifier:
     DPs:
      f#(X) -> g#(X)
      f#(X) -> f#(g(X))
      g#(s(X)) -> g#(X)
      sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
     TRS:
      f(X) -> cons(X,f(g(X)))
      g(0()) -> s(0())
      g(s(X)) -> s(s(g(X)))
      sel(0(),cons(X,Y)) -> X
      sel(s(X),cons(Y,Z)) -> sel(X,Z)
     SCC Processor:
      #sccs: 3
      #rules: 3
      #arcs: 5/16
      DPs:
       f#(X) -> f#(g(X))
      TRS:
       f(X) -> cons(X,f(g(X)))
       g(0()) -> s(0())
       g(s(X)) -> s(s(g(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,Z)
      Open
      
      DPs:
       g#(s(X)) -> g#(X)
      TRS:
       f(X) -> cons(X,f(g(X)))
       g(0()) -> s(0())
       g(s(X)) -> s(s(g(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,Z)
      Open
      
      DPs:
       sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
      TRS:
       f(X) -> cons(X,f(g(X)))
       g(0()) -> s(0())
       g(s(X)) -> s(s(g(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,Z)
      Open