MAYBE

Problem:
 from(X) -> cons(X,n__from(n__s(X)))
 head(cons(X,XS)) -> X
 2nd(cons(X,XS)) -> head(activate(XS))
 take(0(),XS) -> nil()
 take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 take(X1,X2) -> n__take(X1,X2)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2nd#(cons(X,XS)) -> activate#(XS)
   2nd#(cons(X,XS)) -> head#(activate(XS))
   take#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
   activate#(n__take(X1,X2)) -> activate#(X2)
   activate#(n__take(X1,X2)) -> activate#(X1)
   activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
  TRS:
   from(X) -> cons(X,n__from(n__s(X)))
   head(cons(X,XS)) -> X
   2nd(cons(X,XS)) -> head(activate(XS))
   take(0(),XS) -> nil()
   take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   take(X1,X2) -> n__take(X1,X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
   activate(X) -> X
  TDG Processor:
   DPs:
    2nd#(cons(X,XS)) -> activate#(XS)
    2nd#(cons(X,XS)) -> head#(activate(XS))
    take#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__take(X1,X2)) -> activate#(X2)
    activate#(n__take(X1,X2)) -> activate#(X1)
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
   TRS:
    from(X) -> cons(X,n__from(n__s(X)))
    head(cons(X,XS)) -> X
    2nd(cons(X,XS)) -> head(activate(XS))
    take(0(),XS) -> nil()
    take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
    sel(0(),cons(X,XS)) -> X
    sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    take(X1,X2) -> n__take(X1,X2)
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
    activate(X) -> X
   graph:
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) ->
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) ->
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__s(X)) -> s#(activate(X))
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__s(X)) -> activate#(X)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(activate(X))
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__from(X)) -> activate#(X)
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__s(X)) -> s#(activate(X))
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__s(X)) -> activate#(X)
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(activate(X))
    take#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) ->
    take#(s(N),cons(X,XS)) -> activate#(XS)
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__take(X1,X2)) -> activate#(X2) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__take(X1,X2)) -> activate#(X1) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__from(X)) -> activate#(X)
    2nd#(cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
    2nd#(cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> activate#(X1)
    2nd#(cons(X,XS)) -> activate#(XS) ->
    activate#(n__take(X1,X2)) -> activate#(X2)
    2nd#(cons(X,XS)) -> activate#(XS) ->
    activate#(n__s(X)) -> s#(activate(X))
    2nd#(cons(X,XS)) -> activate#(XS) ->
    activate#(n__s(X)) -> activate#(X)
    2nd#(cons(X,XS)) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(activate(X))
    2nd#(cons(X,XS)) -> activate#(XS) -> activate#(n__from(X)) -> activate#(X)
   SCC Processor:
    #sccs: 2
    #rules: 7
    #arcs: 52/144
    DPs:
     sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    TRS:
     from(X) -> cons(X,n__from(n__s(X)))
     head(cons(X,XS)) -> X
     2nd(cons(X,XS)) -> head(activate(XS))
     take(0(),XS) -> nil()
     take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     take(X1,X2) -> n__take(X1,X2)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
     activate(X) -> X
    Open
    
    DPs:
     activate#(n__from(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X)
     activate#(n__take(X1,X2)) -> activate#(X2)
     activate#(n__take(X1,X2)) -> activate#(X1)
     activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2))
     take#(s(N),cons(X,XS)) -> activate#(XS)
    TRS:
     from(X) -> cons(X,n__from(n__s(X)))
     head(cons(X,XS)) -> X
     2nd(cons(X,XS)) -> head(activate(XS))
     take(0(),XS) -> nil()
     take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     take(X1,X2) -> n__take(X1,X2)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
     activate(X) -> X
    Open