YES

Problem:
 a__fst(0(),Z) -> nil()
 a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
 a__from(X) -> cons(mark(X),from(s(X)))
 a__add(0(),X) -> mark(X)
 a__add(s(X),Y) -> s(add(X,Y))
 a__len(nil()) -> 0()
 a__len(cons(X,Z)) -> s(len(Z))
 mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
 mark(len(X)) -> a__len(mark(X))
 mark(0()) -> 0()
 mark(s(X)) -> s(X)
 mark(nil()) -> nil()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 a__fst(X1,X2) -> fst(X1,X2)
 a__from(X) -> from(X)
 a__add(X1,X2) -> add(X1,X2)
 a__len(X) -> len(X)

Proof:
 DP Processor:
  DPs:
   a__fst#(s(X),cons(Y,Z)) -> mark#(Y)
   a__from#(X) -> mark#(X)
   a__add#(0(),X) -> mark#(X)
   mark#(fst(X1,X2)) -> mark#(X2)
   mark#(fst(X1,X2)) -> mark#(X1)
   mark#(fst(X1,X2)) -> a__fst#(mark(X1),mark(X2))
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(add(X1,X2)) -> mark#(X2)
   mark#(add(X1,X2)) -> mark#(X1)
   mark#(add(X1,X2)) -> a__add#(mark(X1),mark(X2))
   mark#(len(X)) -> mark#(X)
   mark#(len(X)) -> a__len#(mark(X))
   mark#(cons(X1,X2)) -> mark#(X1)
  TRS:
   a__fst(0(),Z) -> nil()
   a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
   a__from(X) -> cons(mark(X),from(s(X)))
   a__add(0(),X) -> mark(X)
   a__add(s(X),Y) -> s(add(X,Y))
   a__len(nil()) -> 0()
   a__len(cons(X,Z)) -> s(len(Z))
   mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
   mark(from(X)) -> a__from(mark(X))
   mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
   mark(len(X)) -> a__len(mark(X))
   mark(0()) -> 0()
   mark(s(X)) -> s(X)
   mark(nil()) -> nil()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   a__fst(X1,X2) -> fst(X1,X2)
   a__from(X) -> from(X)
   a__add(X1,X2) -> add(X1,X2)
   a__len(X) -> len(X)
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    a__fst(0(),Z) -> nil()
    a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
    a__from(X) -> cons(mark(X),from(s(X)))
    a__add(0(),X) -> mark(X)
    a__add(s(X),Y) -> s(add(X,Y))
    a__len(nil()) -> 0()
    a__len(cons(X,Z)) -> s(len(Z))
    mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
    mark(from(X)) -> a__from(mark(X))
    mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
    mark(len(X)) -> a__len(mark(X))
    mark(0()) -> 0()
    mark(s(X)) -> s(X)
    mark(nil()) -> nil()
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    a__fst(X1,X2) -> fst(X1,X2)
    a__from(X) -> from(X)
    a__add(X1,X2) -> add(X1,X2)
    a__len(X) -> len(X)
   interpretation:
    [a__len#](x0) = 2x0,
    
    [a__add#](x0, x1) = x1 + 3,
    
    [a__from#](x0) = x0 + 1,
    
    [mark#](x0) = x0,
    
    [a__fst#](x0, x1) = x1,
    
    [len](x0) = 2x0 + 1,
    
    [a__len](x0) = 2x0 + 1,
    
    [add](x0, x1) = x0 + 4x1 + 4,
    
    [a__add](x0, x1) = x0 + 4x1 + 4,
    
    [from](x0) = x0 + 3,
    
    [a__from](x0) = x0 + 3,
    
    [fst](x0, x1) = 4x0 + 3x1 + 1,
    
    [mark](x0) = x0,
    
    [cons](x0, x1) = x0 + 3,
    
    [s](x0) = 2,
    
    [nil] = 2,
    
    [a__fst](x0, x1) = 4x0 + 3x1 + 1,
    
    [0] = 4
   orientation:
    a__fst#(s(X),cons(Y,Z)) = Y + 3 >= Y = mark#(Y)
    
    a__from#(X) = X + 1 >= X = mark#(X)
    
    a__add#(0(),X) = X + 3 >= X = mark#(X)
    
    mark#(fst(X1,X2)) = 4X1 + 3X2 + 1 >= X2 = mark#(X2)
    
    mark#(fst(X1,X2)) = 4X1 + 3X2 + 1 >= X1 = mark#(X1)
    
    mark#(fst(X1,X2)) = 4X1 + 3X2 + 1 >= X2 = a__fst#(mark(X1),mark(X2))
    
    mark#(from(X)) = X + 3 >= X = mark#(X)
    
    mark#(from(X)) = X + 3 >= X + 1 = a__from#(mark(X))
    
    mark#(add(X1,X2)) = X1 + 4X2 + 4 >= X2 = mark#(X2)
    
    mark#(add(X1,X2)) = X1 + 4X2 + 4 >= X1 = mark#(X1)
    
    mark#(add(X1,X2)) = X1 + 4X2 + 4 >= X2 + 3 = a__add#(mark(X1),mark(X2))
    
    mark#(len(X)) = 2X + 1 >= X = mark#(X)
    
    mark#(len(X)) = 2X + 1 >= 2X = a__len#(mark(X))
    
    mark#(cons(X1,X2)) = X1 + 3 >= X1 = mark#(X1)
    
    a__fst(0(),Z) = 3Z + 17 >= 2 = nil()
    
    a__fst(s(X),cons(Y,Z)) = 3Y + 18 >= Y + 3 = cons(mark(Y),fst(X,Z))
    
    a__from(X) = X + 3 >= X + 3 = cons(mark(X),from(s(X)))
    
    a__add(0(),X) = 4X + 8 >= X = mark(X)
    
    a__add(s(X),Y) = 4Y + 6 >= 2 = s(add(X,Y))
    
    a__len(nil()) = 5 >= 4 = 0()
    
    a__len(cons(X,Z)) = 2X + 7 >= 2 = s(len(Z))
    
    mark(fst(X1,X2)) = 4X1 + 3X2 + 1 >= 4X1 + 3X2 + 1 = a__fst(mark(X1),mark(X2))
    
    mark(from(X)) = X + 3 >= X + 3 = a__from(mark(X))
    
    mark(add(X1,X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = a__add(mark(X1),mark(X2))
    
    mark(len(X)) = 2X + 1 >= 2X + 1 = a__len(mark(X))
    
    mark(0()) = 4 >= 4 = 0()
    
    mark(s(X)) = 2 >= 2 = s(X)
    
    mark(nil()) = 2 >= 2 = nil()
    
    mark(cons(X1,X2)) = X1 + 3 >= X1 + 3 = cons(mark(X1),X2)
    
    a__fst(X1,X2) = 4X1 + 3X2 + 1 >= 4X1 + 3X2 + 1 = fst(X1,X2)
    
    a__from(X) = X + 3 >= X + 3 = from(X)
    
    a__add(X1,X2) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = add(X1,X2)
    
    a__len(X) = 2X + 1 >= 2X + 1 = len(X)
   problem:
    DPs:
     
    TRS:
     a__fst(0(),Z) -> nil()
     a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
     a__from(X) -> cons(mark(X),from(s(X)))
     a__add(0(),X) -> mark(X)
     a__add(s(X),Y) -> s(add(X,Y))
     a__len(nil()) -> 0()
     a__len(cons(X,Z)) -> s(len(Z))
     mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
     mark(from(X)) -> a__from(mark(X))
     mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
     mark(len(X)) -> a__len(mark(X))
     mark(0()) -> 0()
     mark(s(X)) -> s(X)
     mark(nil()) -> nil()
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     a__fst(X1,X2) -> fst(X1,X2)
     a__from(X) -> from(X)
     a__add(X1,X2) -> add(X1,X2)
     a__len(X) -> len(X)
   Qed