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(n__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)
 s(X) -> n__s(X)
 add(X1,X2) -> n__add(X1,X2)
 len(X) -> n__len(X)
 activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(X)
 activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
 activate(n__len(X)) -> len(activate(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)
   add#(s(X),Y) -> s#(n__add(activate(X),Y))
   len#(cons(X,Z)) -> activate#(Z)
   len#(cons(X,Z)) -> s#(n__len(activate(Z)))
   activate#(n__fst(X1,X2)) -> activate#(X2)
   activate#(n__fst(X1,X2)) -> activate#(X1)
   activate#(n__fst(X1,X2)) -> fst#(activate(X1),activate(X2))
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> s#(X)
   activate#(n__add(X1,X2)) -> activate#(X2)
   activate#(n__add(X1,X2)) -> activate#(X1)
   activate#(n__add(X1,X2)) -> add#(activate(X1),activate(X2))
   activate#(n__len(X)) -> activate#(X)
   activate#(n__len(X)) -> len#(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(n__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)
   s(X) -> n__s(X)
   add(X1,X2) -> n__add(X1,X2)
   len(X) -> n__len(X)
   activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(X)
   activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
   activate(n__len(X)) -> len(activate(X))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    fst(0(),Z) -> nil()
    fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
    from(X) -> cons(X,n__from(n__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)
    s(X) -> n__s(X)
    add(X1,X2) -> n__add(X1,X2)
    len(X) -> n__len(X)
    activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(X)
    activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
    activate(n__len(X)) -> len(activate(X))
    activate(X) -> X
   interpretation:
    [len#](x0) = 2x0,
    
    [s#](x0) = 0,
    
    [add#](x0, x1) = 2x0 + x1 + 2,
    
    [from#](x0) = 2x0,
    
    [activate#](x0) = x0 + 1/2,
    
    [fst#](x0, x1) = 2x0 + 2x1 + 1/2,
    
    [n__len](x0) = 2x0 + 1,
    
    [len](x0) = 2x0 + 1,
    
    [n__add](x0, x1) = 2x0 + 3x1 + 2,
    
    [add](x0, x1) = 2x0 + 3x1 + 2,
    
    [n__from](x0) = 2x0 + 1,
    
    [n__s](x0) = 1/2x0,
    
    [from](x0) = 2x0 + 1,
    
    [n__fst](x0, x1) = 2x0 + 2x1 + 1,
    
    [activate](x0) = x0,
    
    [cons](x0, x1) = 1/2x1 + 1/2,
    
    [s](x0) = 1/2x0,
    
    [nil] = 2,
    
    [fst](x0, x1) = 2x0 + 2x1 + 1,
    
    [0] = 5/2
   orientation:
    fst#(s(X),cons(Y,Z)) = X + Z + 3/2 >= Z + 1/2 = activate#(Z)
    
    fst#(s(X),cons(Y,Z)) = X + Z + 3/2 >= X + 1/2 = activate#(X)
    
    add#(s(X),Y) = X + Y + 2 >= X + 1/2 = activate#(X)
    
    add#(s(X),Y) = X + Y + 2 >= 0 = s#(n__add(activate(X),Y))
    
    len#(cons(X,Z)) = Z + 1 >= Z + 1/2 = activate#(Z)
    
    len#(cons(X,Z)) = Z + 1 >= 0 = s#(n__len(activate(Z)))
    
    activate#(n__fst(X1,X2)) = 2X1 + 2X2 + 3/2 >= X2 + 1/2 = activate#(X2)
    
    activate#(n__fst(X1,X2)) = 2X1 + 2X2 + 3/2 >= X1 + 1/2 = activate#(X1)
    
    activate#(n__fst(X1,X2)) = 2X1 + 2X2 + 3/2 >= 2X1 + 2X2 + 1/2 = fst#(activate(X1),activate(X2))
    
    activate#(n__from(X)) = 2X + 3/2 >= X + 1/2 = activate#(X)
    
    activate#(n__from(X)) = 2X + 3/2 >= 2X = from#(activate(X))
    
    activate#(n__s(X)) = 1/2X + 1/2 >= 0 = s#(X)
    
    activate#(n__add(X1,X2)) = 2X1 + 3X2 + 5/2 >= X2 + 1/2 = activate#(X2)
    
    activate#(n__add(X1,X2)) = 2X1 + 3X2 + 5/2 >= X1 + 1/2 = activate#(X1)
    
    activate#(n__add(X1,X2)) = 2X1 + 3X2 + 5/2 >= 2X1 + X2 + 2 = add#(activate(X1),activate(X2))
    
    activate#(n__len(X)) = 2X + 3/2 >= X + 1/2 = activate#(X)
    
    activate#(n__len(X)) = 2X + 3/2 >= 2X = len#(activate(X))
    
    fst(0(),Z) = 2Z + 6 >= 2 = nil()
    
    fst(s(X),cons(Y,Z)) = X + Z + 2 >= X + Z + 1 = cons(Y,n__fst(activate(X),activate(Z)))
    
    from(X) = 2X + 1 >= 1/2X + 1 = cons(X,n__from(n__s(X)))
    
    add(0(),X) = 3X + 7 >= X = X
    
    add(s(X),Y) = X + 3Y + 2 >= X + 3/2Y + 1 = s(n__add(activate(X),Y))
    
    len(nil()) = 5 >= 5/2 = 0()
    
    len(cons(X,Z)) = Z + 2 >= Z + 1/2 = s(n__len(activate(Z)))
    
    fst(X1,X2) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = n__fst(X1,X2)
    
    from(X) = 2X + 1 >= 2X + 1 = n__from(X)
    
    s(X) = 1/2X >= 1/2X = n__s(X)
    
    add(X1,X2) = 2X1 + 3X2 + 2 >= 2X1 + 3X2 + 2 = n__add(X1,X2)
    
    len(X) = 2X + 1 >= 2X + 1 = n__len(X)
    
    activate(n__fst(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = fst(activate(X1),activate(X2))
    
    activate(n__from(X)) = 2X + 1 >= 2X + 1 = from(activate(X))
    
    activate(n__s(X)) = 1/2X >= 1/2X = s(X)
    
    activate(n__add(X1,X2)) = 2X1 + 3X2 + 2 >= 2X1 + 3X2 + 2 = add(activate(X1),activate(X2))
    
    activate(n__len(X)) = 2X + 1 >= 2X + 1 = len(activate(X))
    
    activate(X) = X >= 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(n__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)
     s(X) -> n__s(X)
     add(X1,X2) -> n__add(X1,X2)
     len(X) -> n__len(X)
     activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(X)
     activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
     activate(n__len(X)) -> len(activate(X))
     activate(X) -> X
   Qed