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
  Usable Rule 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:
    
   CDG 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:
     
    graph:
     
    Qed