MAYBE

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

Proof:
 DP Processor:
  DPs:
   first#(s(X),cons(Y,Z)) -> first#(X,Z)
   from#(X) -> from#(s(X))
  TRS:
   first(0(),X) -> nil()
   first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
   from(X) -> cons(X,from(s(X)))
  CDG Processor:
   DPs:
    first#(s(X),cons(Y,Z)) -> first#(X,Z)
    from#(X) -> from#(s(X))
   TRS:
    first(0(),X) -> nil()
    first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
    from(X) -> cons(X,from(s(X)))
   graph:
    from#(X) -> from#(s(X)) -> from#(X) -> from#(s(X))
    first#(s(X),cons(Y,Z)) -> first#(X,Z) -> first#(s(X),cons(Y,Z)) -> first#(X,Z)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 2/4
    DPs:
     first#(s(X),cons(Y,Z)) -> first#(X,Z)
    TRS:
     first(0(),X) -> nil()
     first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
     from(X) -> cons(X,from(s(X)))
    Open
    
    DPs:
     from#(X) -> from#(s(X))
    TRS:
     first(0(),X) -> nil()
     first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
     from(X) -> cons(X,from(s(X)))
    Open