YES

Problem:
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 from(X) -> cons(X,n__from(n__s(X)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   first#(s(X),cons(Y,Z)) -> activate#(Z)
   activate#(n__first(X1,X2)) -> activate#(X2)
   activate#(n__first(X1,X2)) -> activate#(X1)
   activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
   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))
  TRS:
   first(0(),X) -> nil()
   first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
   from(X) -> cons(X,n__from(n__s(X)))
   first(X1,X2) -> n__first(X1,X2)
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  TDG Processor:
   DPs:
    first#(s(X),cons(Y,Z)) -> activate#(Z)
    activate#(n__first(X1,X2)) -> activate#(X2)
    activate#(n__first(X1,X2)) -> activate#(X1)
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
    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))
   TRS:
    first(0(),X) -> nil()
    first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
    from(X) -> cons(X,n__from(n__s(X)))
    first(X1,X2) -> n__first(X1,X2)
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
   graph:
    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__from(X)) -> activate#(X) ->
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__first(X1,X2)) -> activate#(X1)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__first(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)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__first(X1,X2)) -> activate#(X1)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__first(X1,X2)) -> activate#(X2)
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__first(X1,X2)) -> activate#(X1)
    activate#(n__first(X1,X2)) -> activate#(X2) ->
    activate#(n__first(X1,X2)) -> activate#(X2)
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__first(X1,X2)) -> activate#(X1)
    activate#(n__first(X1,X2)) -> activate#(X1) ->
    activate#(n__first(X1,X2)) -> activate#(X2)
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) ->
    first#(s(X),cons(Y,Z)) -> activate#(Z)
    first#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__s(X)) -> s#(activate(X))
    first#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__s(X)) -> activate#(X)
    first#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(activate(X))
    first#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__from(X)) -> activate#(X)
    first#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
    first#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__first(X1,X2)) -> activate#(X1)
    first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> activate#(X2)
   SCC Processor:
    #sccs: 1
    #rules: 6
    #arcs: 36/64
    DPs:
     activate#(n__from(X)) -> activate#(X)
     activate#(n__first(X1,X2)) -> activate#(X2)
     activate#(n__first(X1,X2)) -> activate#(X1)
     activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
     first#(s(X),cons(Y,Z)) -> activate#(Z)
     activate#(n__s(X)) -> activate#(X)
    TRS:
     first(0(),X) -> nil()
     first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
     from(X) -> cons(X,n__from(n__s(X)))
     first(X1,X2) -> n__first(X1,X2)
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [activate#](x0) = 4x0 + 0,
      
      [first#](x0, x1) = x0 + 4x1 + 0,
      
      [n__from](x0) = x0,
      
      [n__s](x0) = x0,
      
      [from](x0) = x0,
      
      [n__first](x0, x1) = x0 + 1x1 + 3,
      
      [activate](x0) = x0,
      
      [cons](x0, x1) = x0 + x1,
      
      [s](x0) = x0,
      
      [nil] = 2,
      
      [first](x0, x1) = x0 + 1x1 + 3,
      
      [0] = 0
     orientation:
      activate#(n__from(X)) = 4X + 0 >= 4X + 0 = activate#(X)
      
      activate#(n__first(X1,X2)) = 4X1 + 5X2 + 7 >= 4X2 + 0 = activate#(X2)
      
      activate#(n__first(X1,X2)) = 4X1 + 5X2 + 7 >= 4X1 + 0 = activate#(X1)
      
      activate#(n__first(X1,X2)) = 4X1 + 5X2 + 7 >= X1 + 4X2 + 0 = first#(activate(X1),activate(X2))
      
      first#(s(X),cons(Y,Z)) = X + 4Y + 4Z + 0 >= 4Z + 0 = activate#(Z)
      
      activate#(n__s(X)) = 4X + 0 >= 4X + 0 = activate#(X)
      
      first(0(),X) = 1X + 3 >= 2 = nil()
      
      first(s(X),cons(Y,Z)) = X + 1Y + 1Z + 3 >= X + Y + 1Z + 3 = cons(Y,n__first(X,activate(Z)))
      
      from(X) = X >= X = cons(X,n__from(n__s(X)))
      
      first(X1,X2) = X1 + 1X2 + 3 >= X1 + 1X2 + 3 = n__first(X1,X2)
      
      from(X) = X >= X = n__from(X)
      
      s(X) = X >= X = n__s(X)
      
      activate(n__first(X1,X2)) = X1 + 1X2 + 3 >= X1 + 1X2 + 3 = first(activate(X1),activate(X2))
      
      activate(n__from(X)) = X >= X = from(activate(X))
      
      activate(n__s(X)) = X >= X = s(activate(X))
      
      activate(X) = X >= X = X
     problem:
      DPs:
       activate#(n__from(X)) -> activate#(X)
       activate#(n__first(X1,X2)) -> activate#(X1)
       first#(s(X),cons(Y,Z)) -> activate#(Z)
       activate#(n__s(X)) -> activate#(X)
      TRS:
       first(0(),X) -> nil()
       first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
       from(X) -> cons(X,n__from(n__s(X)))
       first(X1,X2) -> n__first(X1,X2)
       from(X) -> n__from(X)
       s(X) -> n__s(X)
       activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
       activate(n__from(X)) -> from(activate(X))
       activate(n__s(X)) -> s(activate(X))
       activate(X) -> X
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 26/16
      DPs:
       activate#(n__from(X)) -> activate#(X)
       activate#(n__first(X1,X2)) -> activate#(X1)
       activate#(n__s(X)) -> activate#(X)
      TRS:
       first(0(),X) -> nil()
       first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
       from(X) -> cons(X,n__from(n__s(X)))
       first(X1,X2) -> n__first(X1,X2)
       from(X) -> n__from(X)
       s(X) -> n__s(X)
       activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
       activate(n__from(X)) -> from(activate(X))
       activate(n__s(X)) -> s(activate(X))
       activate(X) -> X
      Subterm Criterion Processor:
       simple projection:
        pi(activate#) = 0
       problem:
        DPs:
         
        TRS:
         first(0(),X) -> nil()
         first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
         from(X) -> cons(X,n__from(n__s(X)))
         first(X1,X2) -> n__first(X1,X2)
         from(X) -> n__from(X)
         s(X) -> n__s(X)
         activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
         activate(n__from(X)) -> from(activate(X))
         activate(n__s(X)) -> s(activate(X))
         activate(X) -> X
       Qed