MAYBE

Problem:
 from(X) -> cons(X,from(s(X)))
 first(0(),Z) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
 sel(0(),cons(X,Z)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)

Proof:
 DP Processor:
  DPs:
   from#(X) -> from#(s(X))
   first#(s(X),cons(Y,Z)) -> first#(X,Z)
   sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
  TRS:
   from(X) -> cons(X,from(s(X)))
   first(0(),Z) -> nil()
   first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
   sel(0(),cons(X,Z)) -> X
   sel(s(X),cons(Y,Z)) -> sel(X,Z)
  Usable Rule Processor:
   DPs:
    from#(X) -> from#(s(X))
    first#(s(X),cons(Y,Z)) -> first#(X,Z)
    sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
   TRS:
    
   CDG Processor:
    DPs:
     from#(X) -> from#(s(X))
     first#(s(X),cons(Y,Z)) -> first#(X,Z)
     sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
    TRS:
     
    graph:
     from#(X) -> from#(s(X)) -> from#(X) -> from#(s(X))
    Restore Modifier:
     DPs:
      from#(X) -> from#(s(X))
      first#(s(X),cons(Y,Z)) -> first#(X,Z)
      sel#(s(X),cons(Y,Z)) -> sel#(X,Z)
     TRS:
      from(X) -> cons(X,from(s(X)))
      first(0(),Z) -> nil()
      first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
      sel(0(),cons(X,Z)) -> X
      sel(s(X),cons(Y,Z)) -> sel(X,Z)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 1/9
      DPs:
       from#(X) -> from#(s(X))
      TRS:
       from(X) -> cons(X,from(s(X)))
       first(0(),Z) -> nil()
       first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
       sel(0(),cons(X,Z)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,Z)
      Open