MAYBE

Problem:
 dbl(0()) -> 0()
 dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
 dbls(nil()) -> nil()
 dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
 sel(0(),cons(X,Y)) -> activate(X)
 sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
 indx(nil(),X) -> nil()
 indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
 from(X) -> cons(activate(X),n__from(n__s(activate(X))))
 s(X) -> n__s(X)
 dbl(X) -> n__dbl(X)
 dbls(X) -> n__dbls(X)
 sel(X1,X2) -> n__sel(X1,X2)
 indx(X1,X2) -> n__indx(X1,X2)
 from(X) -> n__from(X)
 activate(n__s(X)) -> s(X)
 activate(n__dbl(X)) -> dbl(X)
 activate(n__dbls(X)) -> dbls(X)
 activate(n__sel(X1,X2)) -> sel(X1,X2)
 activate(n__indx(X1,X2)) -> indx(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   dbl#(s(X)) -> activate#(X)
   dbl#(s(X)) -> s#(n__s(n__dbl(activate(X))))
   dbls#(cons(X,Y)) -> activate#(Y)
   dbls#(cons(X,Y)) -> activate#(X)
   sel#(0(),cons(X,Y)) -> activate#(X)
   sel#(s(X),cons(Y,Z)) -> activate#(Z)
   sel#(s(X),cons(Y,Z)) -> activate#(X)
   sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z))
   indx#(cons(X,Y),Z) -> activate#(Y)
   indx#(cons(X,Y),Z) -> activate#(Z)
   indx#(cons(X,Y),Z) -> activate#(X)
   from#(X) -> activate#(X)
   activate#(n__s(X)) -> s#(X)
   activate#(n__dbl(X)) -> dbl#(X)
   activate#(n__dbls(X)) -> dbls#(X)
   activate#(n__sel(X1,X2)) -> sel#(X1,X2)
   activate#(n__indx(X1,X2)) -> indx#(X1,X2)
   activate#(n__from(X)) -> from#(X)
  TRS:
   dbl(0()) -> 0()
   dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
   dbls(nil()) -> nil()
   dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
   sel(0(),cons(X,Y)) -> activate(X)
   sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
   indx(nil(),X) -> nil()
   indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
   from(X) -> cons(activate(X),n__from(n__s(activate(X))))
   s(X) -> n__s(X)
   dbl(X) -> n__dbl(X)
   dbls(X) -> n__dbls(X)
   sel(X1,X2) -> n__sel(X1,X2)
   indx(X1,X2) -> n__indx(X1,X2)
   from(X) -> n__from(X)
   activate(n__s(X)) -> s(X)
   activate(n__dbl(X)) -> dbl(X)
   activate(n__dbls(X)) -> dbls(X)
   activate(n__sel(X1,X2)) -> sel(X1,X2)
   activate(n__indx(X1,X2)) -> indx(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  CDG Processor:
   DPs:
    dbl#(s(X)) -> activate#(X)
    dbl#(s(X)) -> s#(n__s(n__dbl(activate(X))))
    dbls#(cons(X,Y)) -> activate#(Y)
    dbls#(cons(X,Y)) -> activate#(X)
    sel#(0(),cons(X,Y)) -> activate#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z)
    sel#(s(X),cons(Y,Z)) -> activate#(X)
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z))
    indx#(cons(X,Y),Z) -> activate#(Y)
    indx#(cons(X,Y),Z) -> activate#(Z)
    indx#(cons(X,Y),Z) -> activate#(X)
    from#(X) -> activate#(X)
    activate#(n__s(X)) -> s#(X)
    activate#(n__dbl(X)) -> dbl#(X)
    activate#(n__dbls(X)) -> dbls#(X)
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    activate#(n__from(X)) -> from#(X)
   TRS:
    dbl(0()) -> 0()
    dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
    dbls(nil()) -> nil()
    dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
    sel(0(),cons(X,Y)) -> activate(X)
    sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
    indx(nil(),X) -> nil()
    indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
    from(X) -> cons(activate(X),n__from(n__s(activate(X))))
    s(X) -> n__s(X)
    dbl(X) -> n__dbl(X)
    dbls(X) -> n__dbls(X)
    sel(X1,X2) -> n__sel(X1,X2)
    indx(X1,X2) -> n__indx(X1,X2)
    from(X) -> n__from(X)
    activate(n__s(X)) -> s(X)
    activate(n__dbl(X)) -> dbl(X)
    activate(n__dbls(X)) -> dbls(X)
    activate(n__sel(X1,X2)) -> sel(X1,X2)
    activate(n__indx(X1,X2)) -> indx(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(X) -> X
   graph:
    from#(X) -> activate#(X) -> activate#(n__s(X)) -> s#(X)
    from#(X) -> activate#(X) -> activate#(n__dbl(X)) -> dbl#(X)
    from#(X) -> activate#(X) -> activate#(n__dbls(X)) -> dbls#(X)
    from#(X) -> activate#(X) -> activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    from#(X) -> activate#(X) -> activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    from#(X) -> activate#(X) -> activate#(n__from(X)) -> from#(X)
    indx#(cons(X,Y),Z) -> activate#(Z) ->
    activate#(n__s(X)) -> s#(X)
    indx#(cons(X,Y),Z) -> activate#(Z) ->
    activate#(n__dbl(X)) -> dbl#(X)
    indx#(cons(X,Y),Z) -> activate#(Z) ->
    activate#(n__dbls(X)) -> dbls#(X)
    indx#(cons(X,Y),Z) -> activate#(Z) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    indx#(cons(X,Y),Z) -> activate#(Z) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    indx#(cons(X,Y),Z) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(X)
    indx#(cons(X,Y),Z) -> activate#(Y) ->
    activate#(n__s(X)) -> s#(X)
    indx#(cons(X,Y),Z) -> activate#(Y) ->
    activate#(n__dbl(X)) -> dbl#(X)
    indx#(cons(X,Y),Z) -> activate#(Y) ->
    activate#(n__dbls(X)) -> dbls#(X)
    indx#(cons(X,Y),Z) -> activate#(Y) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    indx#(cons(X,Y),Z) -> activate#(Y) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    indx#(cons(X,Y),Z) -> activate#(Y) ->
    activate#(n__from(X)) -> from#(X)
    indx#(cons(X,Y),Z) -> activate#(X) ->
    activate#(n__s(X)) -> s#(X)
    indx#(cons(X,Y),Z) -> activate#(X) ->
    activate#(n__dbl(X)) -> dbl#(X)
    indx#(cons(X,Y),Z) -> activate#(X) ->
    activate#(n__dbls(X)) -> dbls#(X)
    indx#(cons(X,Y),Z) -> activate#(X) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    indx#(cons(X,Y),Z) -> activate#(X) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    indx#(cons(X,Y),Z) -> activate#(X) ->
    activate#(n__from(X)) -> from#(X)
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z)) ->
    sel#(0(),cons(X,Y)) -> activate#(X)
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z)) ->
    sel#(s(X),cons(Y,Z)) -> activate#(Z)
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z)) ->
    sel#(s(X),cons(Y,Z)) -> activate#(X)
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z)) ->
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z))
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__s(X)) -> s#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__dbl(X)) -> dbl#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__dbls(X)) -> dbls#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__dbl(X)) -> dbl#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__dbls(X)) -> dbls#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    sel#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    sel#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(X)
    sel#(0(),cons(X,Y)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(X)
    sel#(0(),cons(X,Y)) -> activate#(X) ->
    activate#(n__dbl(X)) -> dbl#(X)
    sel#(0(),cons(X,Y)) -> activate#(X) ->
    activate#(n__dbls(X)) -> dbls#(X)
    sel#(0(),cons(X,Y)) -> activate#(X) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    sel#(0(),cons(X,Y)) -> activate#(X) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    sel#(0(),cons(X,Y)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(X)
    dbls#(cons(X,Y)) -> activate#(Y) -> activate#(n__s(X)) -> s#(X)
    dbls#(cons(X,Y)) -> activate#(Y) ->
    activate#(n__dbl(X)) -> dbl#(X)
    dbls#(cons(X,Y)) -> activate#(Y) ->
    activate#(n__dbls(X)) -> dbls#(X)
    dbls#(cons(X,Y)) -> activate#(Y) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    dbls#(cons(X,Y)) -> activate#(Y) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    dbls#(cons(X,Y)) -> activate#(Y) ->
    activate#(n__from(X)) -> from#(X)
    dbls#(cons(X,Y)) -> activate#(X) -> activate#(n__s(X)) -> s#(X)
    dbls#(cons(X,Y)) -> activate#(X) ->
    activate#(n__dbl(X)) -> dbl#(X)
    dbls#(cons(X,Y)) -> activate#(X) ->
    activate#(n__dbls(X)) -> dbls#(X)
    dbls#(cons(X,Y)) -> activate#(X) ->
    activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    dbls#(cons(X,Y)) -> activate#(X) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    dbls#(cons(X,Y)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(X)
    activate#(n__from(X)) -> from#(X) ->
    from#(X) -> activate#(X)
    activate#(n__indx(X1,X2)) -> indx#(X1,X2) ->
    indx#(cons(X,Y),Z) -> activate#(Y)
    activate#(n__indx(X1,X2)) -> indx#(X1,X2) ->
    indx#(cons(X,Y),Z) -> activate#(Z)
    activate#(n__indx(X1,X2)) -> indx#(X1,X2) ->
    indx#(cons(X,Y),Z) -> activate#(X)
    activate#(n__sel(X1,X2)) -> sel#(X1,X2) ->
    sel#(0(),cons(X,Y)) -> activate#(X)
    activate#(n__sel(X1,X2)) -> sel#(X1,X2) ->
    sel#(s(X),cons(Y,Z)) -> activate#(Z)
    activate#(n__sel(X1,X2)) -> sel#(X1,X2) ->
    sel#(s(X),cons(Y,Z)) -> activate#(X)
    activate#(n__sel(X1,X2)) -> sel#(X1,X2) ->
    sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z))
    activate#(n__dbls(X)) -> dbls#(X) ->
    dbls#(cons(X,Y)) -> activate#(Y)
    activate#(n__dbls(X)) -> dbls#(X) ->
    dbls#(cons(X,Y)) -> activate#(X)
    activate#(n__dbl(X)) -> dbl#(X) -> dbl#(s(X)) -> activate#(X)
    activate#(n__dbl(X)) -> dbl#(X) ->
    dbl#(s(X)) -> s#(n__s(n__dbl(activate(X))))
    dbl#(s(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(X)
    dbl#(s(X)) -> activate#(X) -> activate#(n__dbl(X)) -> dbl#(X)
    dbl#(s(X)) -> activate#(X) -> activate#(n__dbls(X)) -> dbls#(X)
    dbl#(s(X)) -> activate#(X) -> activate#(n__sel(X1,X2)) -> sel#(X1,X2)
    dbl#(s(X)) -> activate#(X) ->
    activate#(n__indx(X1,X2)) -> indx#(X1,X2)
    dbl#(s(X)) -> activate#(X) -> activate#(n__from(X)) -> from#(X)
   Restore Modifier:
    DPs:
     dbl#(s(X)) -> activate#(X)
     dbl#(s(X)) -> s#(n__s(n__dbl(activate(X))))
     dbls#(cons(X,Y)) -> activate#(Y)
     dbls#(cons(X,Y)) -> activate#(X)
     sel#(0(),cons(X,Y)) -> activate#(X)
     sel#(s(X),cons(Y,Z)) -> activate#(Z)
     sel#(s(X),cons(Y,Z)) -> activate#(X)
     sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z))
     indx#(cons(X,Y),Z) -> activate#(Y)
     indx#(cons(X,Y),Z) -> activate#(Z)
     indx#(cons(X,Y),Z) -> activate#(X)
     from#(X) -> activate#(X)
     activate#(n__s(X)) -> s#(X)
     activate#(n__dbl(X)) -> dbl#(X)
     activate#(n__dbls(X)) -> dbls#(X)
     activate#(n__sel(X1,X2)) -> sel#(X1,X2)
     activate#(n__indx(X1,X2)) -> indx#(X1,X2)
     activate#(n__from(X)) -> from#(X)
    TRS:
     dbl(0()) -> 0()
     dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
     dbls(nil()) -> nil()
     dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
     sel(0(),cons(X,Y)) -> activate(X)
     sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
     indx(nil(),X) -> nil()
     indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
     from(X) -> cons(activate(X),n__from(n__s(activate(X))))
     s(X) -> n__s(X)
     dbl(X) -> n__dbl(X)
     dbls(X) -> n__dbls(X)
     sel(X1,X2) -> n__sel(X1,X2)
     indx(X1,X2) -> n__indx(X1,X2)
     from(X) -> n__from(X)
     activate(n__s(X)) -> s(X)
     activate(n__dbl(X)) -> dbl(X)
     activate(n__dbls(X)) -> dbls(X)
     activate(n__sel(X1,X2)) -> sel(X1,X2)
     activate(n__indx(X1,X2)) -> indx(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(X) -> X
    SCC Processor:
     #sccs: 1
     #rules: 16
     #arcs: 76/324
     DPs:
      from#(X) -> activate#(X)
      activate#(n__from(X)) -> from#(X)
      activate#(n__indx(X1,X2)) -> indx#(X1,X2)
      indx#(cons(X,Y),Z) -> activate#(X)
      activate#(n__sel(X1,X2)) -> sel#(X1,X2)
      sel#(s(X),cons(Y,Z)) -> sel#(activate(X),activate(Z))
      sel#(s(X),cons(Y,Z)) -> activate#(X)
      activate#(n__dbls(X)) -> dbls#(X)
      dbls#(cons(X,Y)) -> activate#(X)
      activate#(n__dbl(X)) -> dbl#(X)
      dbl#(s(X)) -> activate#(X)
      dbls#(cons(X,Y)) -> activate#(Y)
      sel#(s(X),cons(Y,Z)) -> activate#(Z)
      sel#(0(),cons(X,Y)) -> activate#(X)
      indx#(cons(X,Y),Z) -> activate#(Z)
      indx#(cons(X,Y),Z) -> activate#(Y)
     TRS:
      dbl(0()) -> 0()
      dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
      dbls(nil()) -> nil()
      dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
      sel(0(),cons(X,Y)) -> activate(X)
      sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
      indx(nil(),X) -> nil()
      indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
      from(X) -> cons(activate(X),n__from(n__s(activate(X))))
      s(X) -> n__s(X)
      dbl(X) -> n__dbl(X)
      dbls(X) -> n__dbls(X)
      sel(X1,X2) -> n__sel(X1,X2)
      indx(X1,X2) -> n__indx(X1,X2)
      from(X) -> n__from(X)
      activate(n__s(X)) -> s(X)
      activate(n__dbl(X)) -> dbl(X)
      activate(n__dbls(X)) -> dbls(X)
      activate(n__sel(X1,X2)) -> sel(X1,X2)
      activate(n__indx(X1,X2)) -> indx(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(X) -> X
     Open