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
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [len#](x0) = x0 + 1/2,
      
      [add#](x0, x1) = x0 + 1/2x1,
      
      [activate#](x0) = 1/2x0 + 2,
      
      [fst#](x0, x1) = x0 + x1 + 2,
      
      [n__len](x0) = 2x0,
      
      [len](x0) = 2x0 + 1/2,
      
      [n__add](x0, x1) = 3x0 + x1,
      
      [add](x0, x1) = 3x0 + x1 + 2,
      
      [n__from](x0) = 1,
      
      [from](x0) = 5/2,
      
      [n__fst](x0, x1) = 2x0 + 2x1 + 1,
      
      [activate](x0) = x0 + 2,
      
      [cons](x0, x1) = 1/2x1 + 2,
      
      [s](x0) = 1/2x0 + 5/2,
      
      [nil] = 2,
      
      [fst](x0, x1) = 2x0 + 2x1 + 2,
      
      [0] = 3/2
     orientation:
      len#(cons(X,Z)) = 1/2Z + 5/2 >= 1/2Z + 2 = activate#(Z)
      
      activate#(n__fst(X1,X2)) = X1 + X2 + 5/2 >= X1 + X2 + 2 = fst#(X1,X2)
      
      fst#(s(X),cons(Y,Z)) = 1/2X + 1/2Z + 13/2 >= 1/2Z + 2 = activate#(Z)
      
      activate#(n__add(X1,X2)) = 3/2X1 + 1/2X2 + 2 >= X1 + 1/2X2 = add#(X1,X2)
      
      add#(s(X),Y) = 1/2X + 1/2Y + 5/2 >= 1/2X + 2 = activate#(X)
      
      activate#(n__len(X)) = X + 2 >= X + 1/2 = len#(X)
      
      fst#(s(X),cons(Y,Z)) = 1/2X + 1/2Z + 13/2 >= 1/2X + 2 = activate#(X)
      
      fst(0(),Z) = 2Z + 5 >= 2 = nil()
      
      fst(s(X),cons(Y,Z)) = X + Z + 11 >= X + Z + 13/2 = cons(Y,n__fst(activate(X),activate(Z)))
      
      from(X) = 5/2 >= 5/2 = cons(X,n__from(s(X)))
      
      add(0(),X) = X + 13/2 >= X = X
      
      add(s(X),Y) = 3/2X + Y + 19/2 >= 3/2X + 1/2Y + 11/2 = s(n__add(activate(X),Y))
      
      len(nil()) = 9/2 >= 3/2 = 0()
      
      len(cons(X,Z)) = Z + 9/2 >= Z + 9/2 = s(n__len(activate(Z)))
      
      fst(X1,X2) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 1 = n__fst(X1,X2)
      
      from(X) = 5/2 >= 1 = n__from(X)
      
      add(X1,X2) = 3X1 + X2 + 2 >= 3X1 + X2 = n__add(X1,X2)
      
      len(X) = 2X + 1/2 >= 2X = n__len(X)
      
      activate(n__fst(X1,X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 2 = fst(X1,X2)
      
      activate(n__from(X)) = 3 >= 5/2 = from(X)
      
      activate(n__add(X1,X2)) = 3X1 + X2 + 2 >= 3X1 + X2 + 2 = add(X1,X2)
      
      activate(n__len(X)) = 2X + 2 >= 2X + 1/2 = len(X)
      
      activate(X) = X + 2 >= X = X
     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