YES

Problem:
 fst(0(),Z) -> nil()
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 from(X) -> cons(X,n__from(s(X)))
 add(0(),X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 len(nil()) -> 0()
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 from(X) -> n__from(X)
 add(X1,X2) -> n__add(X1,X2)
 len(X) -> n__len(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   fst#(s(X),cons(Y,Z)) -> activate#(Z)
   fst#(s(X),cons(Y,Z)) -> activate#(X)
   add#(s(X),Y) -> activate#(X)
   len#(cons(X,Z)) -> activate#(Z)
   activate#(n__fst(X1,X2)) -> fst#(X1,X2)
   activate#(n__from(X)) -> from#(X)
   activate#(n__add(X1,X2)) -> add#(X1,X2)
   activate#(n__len(X)) -> len#(X)
  TRS:
   fst(0(),Z) -> nil()
   fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
   from(X) -> cons(X,n__from(s(X)))
   add(0(),X) -> X
   add(s(X),Y) -> s(n__add(activate(X),Y))
   len(nil()) -> 0()
   len(cons(X,Z)) -> s(n__len(activate(Z)))
   fst(X1,X2) -> n__fst(X1,X2)
   from(X) -> n__from(X)
   add(X1,X2) -> n__add(X1,X2)
   len(X) -> n__len(X)
   activate(n__fst(X1,X2)) -> fst(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__add(X1,X2)) -> add(X1,X2)
   activate(n__len(X)) -> len(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    fst#(s(X),cons(Y,Z)) -> activate#(Z)
    fst#(s(X),cons(Y,Z)) -> activate#(X)
    add#(s(X),Y) -> activate#(X)
    len#(cons(X,Z)) -> activate#(Z)
    activate#(n__fst(X1,X2)) -> fst#(X1,X2)
    activate#(n__from(X)) -> from#(X)
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    activate#(n__len(X)) -> len#(X)
   TRS:
    fst(0(),Z) -> nil()
    fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
    from(X) -> cons(X,n__from(s(X)))
    add(0(),X) -> X
    add(s(X),Y) -> s(n__add(activate(X),Y))
    len(nil()) -> 0()
    len(cons(X,Z)) -> s(n__len(activate(Z)))
    fst(X1,X2) -> n__fst(X1,X2)
    from(X) -> n__from(X)
    add(X1,X2) -> n__add(X1,X2)
    len(X) -> n__len(X)
    activate(n__fst(X1,X2)) -> fst(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__add(X1,X2)) -> add(X1,X2)
    activate(n__len(X)) -> len(X)
    activate(X) -> X
   graph:
    len#(cons(X,Z)) -> activate#(Z) ->
    activate#(n__len(X)) -> len#(X)
    len#(cons(X,Z)) -> activate#(Z) ->
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    len#(cons(X,Z)) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(X)
    len#(cons(X,Z)) -> activate#(Z) ->
    activate#(n__fst(X1,X2)) -> fst#(X1,X2)
    add#(s(X),Y) -> activate#(X) -> activate#(n__len(X)) -> len#(X)
    add#(s(X),Y) -> activate#(X) ->
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    add#(s(X),Y) -> activate#(X) -> activate#(n__from(X)) -> from#(X)
    add#(s(X),Y) -> activate#(X) ->
    activate#(n__fst(X1,X2)) -> fst#(X1,X2)
    activate#(n__len(X)) -> len#(X) ->
    len#(cons(X,Z)) -> activate#(Z)
    activate#(n__add(X1,X2)) -> add#(X1,X2) ->
    add#(s(X),Y) -> activate#(X)
    activate#(n__fst(X1,X2)) -> fst#(X1,X2) ->
    fst#(s(X),cons(Y,Z)) -> activate#(X)
    activate#(n__fst(X1,X2)) -> fst#(X1,X2) ->
    fst#(s(X),cons(Y,Z)) -> activate#(Z)
    fst#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__len(X)) -> len#(X)
    fst#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    fst#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(X)
    fst#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__fst(X1,X2)) -> fst#(X1,X2)
    fst#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__len(X)) -> len#(X)
    fst#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    fst#(s(X),cons(Y,Z)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(X)
    fst#(s(X),cons(Y,Z)) -> activate#(X) -> activate#(n__fst(X1,X2)) -> fst#(X1,X2)
   SCC Processor:
    #sccs: 1
    #rules: 7
    #arcs: 20/64
    DPs:
     len#(cons(X,Z)) -> activate#(Z)
     activate#(n__fst(X1,X2)) -> fst#(X1,X2)
     fst#(s(X),cons(Y,Z)) -> activate#(Z)
     activate#(n__add(X1,X2)) -> add#(X1,X2)
     add#(s(X),Y) -> activate#(X)
     activate#(n__len(X)) -> len#(X)
     fst#(s(X),cons(Y,Z)) -> activate#(X)
    TRS:
     fst(0(),Z) -> nil()
     fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
     from(X) -> cons(X,n__from(s(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(n__add(activate(X),Y))
     len(nil()) -> 0()
     len(cons(X,Z)) -> s(n__len(activate(Z)))
     fst(X1,X2) -> n__fst(X1,X2)
     from(X) -> n__from(X)
     add(X1,X2) -> n__add(X1,X2)
     len(X) -> n__len(X)
     activate(n__fst(X1,X2)) -> fst(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__add(X1,X2)) -> add(X1,X2)
     activate(n__len(X)) -> len(X)
     activate(X) -> X
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [len#](x0) = x0 + 0,
      
      [add#](x0, x1) = x0 + x1 + 0,
      
      [activate#](x0) = x0 + 0,
      
      [fst#](x0, x1) = 4x0 + 1x1 + 0,
      
      [n__len](x0) = x0,
      
      [len](x0) = x0,
      
      [n__add](x0, x1) = x0 + x1 + 0,
      
      [add](x0, x1) = x0 + x1 + 0,
      
      [n__from](x0) = x0 + 1,
      
      [from](x0) = x0 + 1,
      
      [n__fst](x0, x1) = 4x0 + 2x1,
      
      [activate](x0) = x0 + 0,
      
      [cons](x0, x1) = x0 + x1 + 0,
      
      [s](x0) = x0 + 0,
      
      [nil] = 4,
      
      [fst](x0, x1) = 4x0 + 2x1,
      
      [0] = 3
     orientation:
      len#(cons(X,Z)) = X + Z + 0 >= Z + 0 = activate#(Z)
      
      activate#(n__fst(X1,X2)) = 4X1 + 2X2 + 0 >= 4X1 + 1X2 + 0 = fst#(X1,X2)
      
      fst#(s(X),cons(Y,Z)) = 4X + 1Y + 1Z + 4 >= Z + 0 = activate#(Z)
      
      activate#(n__add(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = add#(X1,X2)
      
      add#(s(X),Y) = X + Y + 0 >= X + 0 = activate#(X)
      
      activate#(n__len(X)) = X + 0 >= X + 0 = len#(X)
      
      fst#(s(X),cons(Y,Z)) = 4X + 1Y + 1Z + 4 >= X + 0 = activate#(X)
      
      fst(0(),Z) = 2Z + 7 >= 4 = nil()
      
      fst(s(X),cons(Y,Z)) = 4X + 2Y + 2Z + 4 >= 4X + Y + 2Z + 4 = cons(Y,n__fst(activate(X),activate(Z)))
      
      from(X) = X + 1 >= X + 1 = cons(X,n__from(s(X)))
      
      add(0(),X) = X + 3 >= X = X
      
      add(s(X),Y) = X + Y + 0 >= X + Y + 0 = s(n__add(activate(X),Y))
      
      len(nil()) = 4 >= 3 = 0()
      
      len(cons(X,Z)) = X + Z + 0 >= Z + 0 = s(n__len(activate(Z)))
      
      fst(X1,X2) = 4X1 + 2X2 >= 4X1 + 2X2 = n__fst(X1,X2)
      
      from(X) = X + 1 >= X + 1 = n__from(X)
      
      add(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = n__add(X1,X2)
      
      len(X) = X >= X = n__len(X)
      
      activate(n__fst(X1,X2)) = 4X1 + 2X2 + 0 >= 4X1 + 2X2 = fst(X1,X2)
      
      activate(n__from(X)) = X + 1 >= X + 1 = from(X)
      
      activate(n__add(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = add(X1,X2)
      
      activate(n__len(X)) = X + 0 >= X = len(X)
      
      activate(X) = X + 0 >= X = X
     problem:
      DPs:
       len#(cons(X,Z)) -> activate#(Z)
       activate#(n__fst(X1,X2)) -> fst#(X1,X2)
       activate#(n__add(X1,X2)) -> add#(X1,X2)
       add#(s(X),Y) -> activate#(X)
       activate#(n__len(X)) -> len#(X)
      TRS:
       fst(0(),Z) -> nil()
       fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
       from(X) -> cons(X,n__from(s(X)))
       add(0(),X) -> X
       add(s(X),Y) -> s(n__add(activate(X),Y))
       len(nil()) -> 0()
       len(cons(X,Z)) -> s(n__len(activate(Z)))
       fst(X1,X2) -> n__fst(X1,X2)
       from(X) -> n__from(X)
       add(X1,X2) -> n__add(X1,X2)
       len(X) -> n__len(X)
       activate(n__fst(X1,X2)) -> fst(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__add(X1,X2)) -> add(X1,X2)
       activate(n__len(X)) -> len(X)
       activate(X) -> X
     SCC Processor:
      #sccs: 1
      #rules: 4
      #arcs: 16/25
      DPs:
       len#(cons(X,Z)) -> activate#(Z)
       activate#(n__add(X1,X2)) -> add#(X1,X2)
       add#(s(X),Y) -> activate#(X)
       activate#(n__len(X)) -> len#(X)
      TRS:
       fst(0(),Z) -> nil()
       fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
       from(X) -> cons(X,n__from(s(X)))
       add(0(),X) -> X
       add(s(X),Y) -> s(n__add(activate(X),Y))
       len(nil()) -> 0()
       len(cons(X,Z)) -> s(n__len(activate(Z)))
       fst(X1,X2) -> n__fst(X1,X2)
       from(X) -> n__from(X)
       add(X1,X2) -> n__add(X1,X2)
       len(X) -> n__len(X)
       activate(n__fst(X1,X2)) -> fst(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__add(X1,X2)) -> add(X1,X2)
       activate(n__len(X)) -> len(X)
       activate(X) -> X
      Subterm Criterion Processor:
       simple projection:
        pi(activate#) = 0
        pi(add#) = 0
        pi(len#) = 0
       problem:
        DPs:
         
        TRS:
         fst(0(),Z) -> nil()
         fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
         from(X) -> cons(X,n__from(s(X)))
         add(0(),X) -> X
         add(s(X),Y) -> s(n__add(activate(X),Y))
         len(nil()) -> 0()
         len(cons(X,Z)) -> s(n__len(activate(Z)))
         fst(X1,X2) -> n__fst(X1,X2)
         from(X) -> n__from(X)
         add(X1,X2) -> n__add(X1,X2)
         len(X) -> n__len(X)
         activate(n__fst(X1,X2)) -> fst(X1,X2)
         activate(n__from(X)) -> from(X)
         activate(n__add(X1,X2)) -> add(X1,X2)
         activate(n__len(X)) -> len(X)
         activate(X) -> X
       Qed