MAYBE

Problem:
 fib(N) -> sel(N,fib1(s(0()),s(0())))
 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
 add(0(),X) -> X
 add(s(X),Y) -> s(add(X,Y))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,XS)

Proof:
 DP Processor:
  DPs:
   fib#(N) -> fib1#(s(0()),s(0()))
   fib#(N) -> sel#(N,fib1(s(0()),s(0())))
   fib1#(X,Y) -> add#(X,Y)
   fib1#(X,Y) -> fib1#(Y,add(X,Y))
   add#(s(X),Y) -> add#(X,Y)
   sel#(s(N),cons(X,XS)) -> sel#(N,XS)
  TRS:
   fib(N) -> sel(N,fib1(s(0()),s(0())))
   fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
   add(0(),X) -> X
   add(s(X),Y) -> s(add(X,Y))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,XS)
  Usable Rule Processor:
   DPs:
    fib#(N) -> fib1#(s(0()),s(0()))
    fib#(N) -> sel#(N,fib1(s(0()),s(0())))
    fib1#(X,Y) -> add#(X,Y)
    fib1#(X,Y) -> fib1#(Y,add(X,Y))
    add#(s(X),Y) -> add#(X,Y)
    sel#(s(N),cons(X,XS)) -> sel#(N,XS)
   TRS:
    f11(x,y) -> x
    f11(x,y) -> y
    fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
    add(0(),X) -> X
    add(s(X),Y) -> s(add(X,Y))
   TDG Processor:
    DPs:
     fib#(N) -> fib1#(s(0()),s(0()))
     fib#(N) -> sel#(N,fib1(s(0()),s(0())))
     fib1#(X,Y) -> add#(X,Y)
     fib1#(X,Y) -> fib1#(Y,add(X,Y))
     add#(s(X),Y) -> add#(X,Y)
     sel#(s(N),cons(X,XS)) -> sel#(N,XS)
    TRS:
     f11(x,y) -> x
     f11(x,y) -> y
     fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
    graph:
     add#(s(X),Y) -> add#(X,Y) -> add#(s(X),Y) -> add#(X,Y)
     sel#(s(N),cons(X,XS)) -> sel#(N,XS) ->
     sel#(s(N),cons(X,XS)) -> sel#(N,XS)
     fib1#(X,Y) -> add#(X,Y) -> add#(s(X),Y) -> add#(X,Y)
     fib1#(X,Y) -> fib1#(Y,add(X,Y)) ->
     fib1#(X,Y) -> fib1#(Y,add(X,Y))
     fib1#(X,Y) -> fib1#(Y,add(X,Y)) ->
     fib1#(X,Y) -> add#(X,Y)
     fib#(N) -> sel#(N,fib1(s(0()),s(0()))) ->
     sel#(s(N),cons(X,XS)) -> sel#(N,XS)
     fib#(N) -> fib1#(s(0()),s(0())) ->
     fib1#(X,Y) -> fib1#(Y,add(X,Y))
     fib#(N) -> fib1#(s(0()),s(0())) -> fib1#(X,Y) -> add#(X,Y)
    Restore Modifier:
     DPs:
      fib#(N) -> fib1#(s(0()),s(0()))
      fib#(N) -> sel#(N,fib1(s(0()),s(0())))
      fib1#(X,Y) -> add#(X,Y)
      fib1#(X,Y) -> fib1#(Y,add(X,Y))
      add#(s(X),Y) -> add#(X,Y)
      sel#(s(N),cons(X,XS)) -> sel#(N,XS)
     TRS:
      fib(N) -> sel(N,fib1(s(0()),s(0())))
      fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
      add(0(),X) -> X
      add(s(X),Y) -> s(add(X,Y))
      sel(0(),cons(X,XS)) -> X
      sel(s(N),cons(X,XS)) -> sel(N,XS)
     SCC Processor:
      #sccs: 3
      #rules: 3
      #arcs: 8/36
      DPs:
       fib1#(X,Y) -> fib1#(Y,add(X,Y))
      TRS:
       fib(N) -> sel(N,fib1(s(0()),s(0())))
       fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,XS)
      Open
      
      DPs:
       sel#(s(N),cons(X,XS)) -> sel#(N,XS)
      TRS:
       fib(N) -> sel(N,fib1(s(0()),s(0())))
       fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,XS)
      Open
      
      DPs:
       add#(s(X),Y) -> add#(X,Y)
      TRS:
       fib(N) -> sel(N,fib1(s(0()),s(0())))
       fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,XS)
      Open