YES

Problem:
 active(fst(0(),Z)) -> mark(nil())
 active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(add(0(),X)) -> mark(X)
 active(add(s(X),Y)) -> mark(s(add(X,Y)))
 active(len(nil())) -> mark(0())
 active(len(cons(X,Z))) -> mark(s(len(Z)))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(fst(X1,X2)) -> fst(active(X1),X2)
 active(fst(X1,X2)) -> fst(X1,active(X2))
 active(from(X)) -> from(active(X))
 active(add(X1,X2)) -> add(active(X1),X2)
 active(add(X1,X2)) -> add(X1,active(X2))
 active(len(X)) -> len(active(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 fst(mark(X1),X2) -> mark(fst(X1,X2))
 fst(X1,mark(X2)) -> mark(fst(X1,X2))
 from(mark(X)) -> mark(from(X))
 add(mark(X1),X2) -> mark(add(X1,X2))
 add(X1,mark(X2)) -> mark(add(X1,X2))
 len(mark(X)) -> mark(len(X))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(nil()) -> ok(nil())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 proper(add(X1,X2)) -> add(proper(X1),proper(X2))
 proper(len(X)) -> len(proper(X))
 s(ok(X)) -> ok(s(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
 from(ok(X)) -> ok(from(X))
 add(ok(X1),ok(X2)) -> ok(add(X1,X2))
 len(ok(X)) -> ok(len(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
   active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(add(s(X),Y)) -> add#(X,Y)
   active#(add(s(X),Y)) -> s#(add(X,Y))
   active#(len(cons(X,Z))) -> len#(Z)
   active#(len(cons(X,Z))) -> s#(len(Z))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(fst(X1,X2)) -> active#(X1)
   active#(fst(X1,X2)) -> fst#(active(X1),X2)
   active#(fst(X1,X2)) -> active#(X2)
   active#(fst(X1,X2)) -> fst#(X1,active(X2))
   active#(from(X)) -> active#(X)
   active#(from(X)) -> from#(active(X))
   active#(add(X1,X2)) -> active#(X1)
   active#(add(X1,X2)) -> add#(active(X1),X2)
   active#(add(X1,X2)) -> active#(X2)
   active#(add(X1,X2)) -> add#(X1,active(X2))
   active#(len(X)) -> active#(X)
   active#(len(X)) -> len#(active(X))
   cons#(mark(X1),X2) -> cons#(X1,X2)
   fst#(mark(X1),X2) -> fst#(X1,X2)
   fst#(X1,mark(X2)) -> fst#(X1,X2)
   from#(mark(X)) -> from#(X)
   add#(mark(X1),X2) -> add#(X1,X2)
   add#(X1,mark(X2)) -> add#(X1,X2)
   len#(mark(X)) -> len#(X)
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(fst(X1,X2)) -> proper#(X2)
   proper#(fst(X1,X2)) -> proper#(X1)
   proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
   proper#(from(X)) -> proper#(X)
   proper#(from(X)) -> from#(proper(X))
   proper#(add(X1,X2)) -> proper#(X2)
   proper#(add(X1,X2)) -> proper#(X1)
   proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
   proper#(len(X)) -> proper#(X)
   proper#(len(X)) -> len#(proper(X))
   s#(ok(X)) -> s#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
   from#(ok(X)) -> from#(X)
   add#(ok(X1),ok(X2)) -> add#(X1,X2)
   len#(ok(X)) -> len#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(fst(0(),Z)) -> mark(nil())
   active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(add(0(),X)) -> mark(X)
   active(add(s(X),Y)) -> mark(s(add(X,Y)))
   active(len(nil())) -> mark(0())
   active(len(cons(X,Z))) -> mark(s(len(Z)))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(fst(X1,X2)) -> fst(active(X1),X2)
   active(fst(X1,X2)) -> fst(X1,active(X2))
   active(from(X)) -> from(active(X))
   active(add(X1,X2)) -> add(active(X1),X2)
   active(add(X1,X2)) -> add(X1,active(X2))
   active(len(X)) -> len(active(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   fst(mark(X1),X2) -> mark(fst(X1,X2))
   fst(X1,mark(X2)) -> mark(fst(X1,X2))
   from(mark(X)) -> mark(from(X))
   add(mark(X1),X2) -> mark(add(X1,X2))
   add(X1,mark(X2)) -> mark(add(X1,X2))
   len(mark(X)) -> mark(len(X))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   proper(nil()) -> ok(nil())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(add(X1,X2)) -> add(proper(X1),proper(X2))
   proper(len(X)) -> len(proper(X))
   s(ok(X)) -> ok(s(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
   from(ok(X)) -> ok(from(X))
   add(ok(X1),ok(X2)) -> ok(add(X1,X2))
   len(ok(X)) -> ok(len(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(from(X)) -> s#(X)
    active#(from(X)) -> from#(s(X))
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(len(cons(X,Z))) -> len#(Z)
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X2)
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(from(X)) -> active#(X)
    active#(from(X)) -> from#(active(X))
    active#(add(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X2)
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(len(X)) -> active#(X)
    active#(len(X)) -> len#(active(X))
    cons#(mark(X1),X2) -> cons#(X1,X2)
    fst#(mark(X1),X2) -> fst#(X1,X2)
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    from#(mark(X)) -> from#(X)
    add#(mark(X1),X2) -> add#(X1,X2)
    add#(X1,mark(X2)) -> add#(X1,X2)
    len#(mark(X)) -> len#(X)
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X))
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(len(X)) -> proper#(X)
    proper#(len(X)) -> len#(proper(X))
    s#(ok(X)) -> s#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    from#(ok(X)) -> from#(X)
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    len#(ok(X)) -> len#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(fst(0(),Z)) -> mark(nil())
    active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(add(0(),X)) -> mark(X)
    active(add(s(X),Y)) -> mark(s(add(X,Y)))
    active(len(nil())) -> mark(0())
    active(len(cons(X,Z))) -> mark(s(len(Z)))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(fst(X1,X2)) -> fst(active(X1),X2)
    active(fst(X1,X2)) -> fst(X1,active(X2))
    active(from(X)) -> from(active(X))
    active(add(X1,X2)) -> add(active(X1),X2)
    active(add(X1,X2)) -> add(X1,active(X2))
    active(len(X)) -> len(active(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    fst(mark(X1),X2) -> mark(fst(X1,X2))
    fst(X1,mark(X2)) -> mark(fst(X1,X2))
    from(mark(X)) -> mark(from(X))
    add(mark(X1),X2) -> mark(add(X1,X2))
    add(X1,mark(X2)) -> mark(add(X1,X2))
    len(mark(X)) -> mark(len(X))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    proper(nil()) -> ok(nil())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    proper(add(X1,X2)) -> add(proper(X1),proper(X2))
    proper(len(X)) -> len(proper(X))
    s(ok(X)) -> ok(s(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
    from(ok(X)) -> ok(from(X))
    add(ok(X1),ok(X2)) -> ok(add(X1,X2))
    len(ok(X)) -> ok(len(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) -> active#(len(X)) -> len#(active(X))
    top#(ok(X)) -> active#(X) -> active#(len(X)) -> active#(X)
    top#(ok(X)) -> active#(X) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    top#(ok(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    top#(ok(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    top#(ok(X)) -> active#(X) -> active#(fst(X1,X2)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(fst(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(len(cons(X,Z))) -> s#(len(Z))
    top#(ok(X)) -> active#(X) -> active#(len(cons(X,Z))) -> len#(Z)
    top#(ok(X)) -> active#(X) -> active#(add(s(X),Y)) -> s#(add(X,Y))
    top#(ok(X)) -> active#(X) -> active#(add(s(X),Y)) -> add#(X,Y)
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X)))
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    top#(ok(X)) -> active#(X) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    top#(ok(X)) -> active#(X) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(len(X)) -> len#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(len(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(fst(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(fst(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(len(X)) -> proper#(X) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(len(X)) -> proper#(X) -> proper#(len(X)) -> proper#(X)
    proper#(len(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(len(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(len(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(len(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(len(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(len(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(len(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(len(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(len(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(len(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(len(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(len(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(len(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(len(X)) -> len#(proper(X)) -> len#(ok(X)) -> len#(X)
    proper#(len(X)) -> len#(proper(X)) ->
    len#(mark(X)) -> len#(X)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(len(X)) -> proper#(X)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(add(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(len(X)) -> proper#(X)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(add(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) ->
    add#(mark(X1),X2) -> add#(X1,X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(len(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(from(X)) -> proper#(X) ->
    proper#(s(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X)) ->
    from#(ok(X)) -> from#(X)
    proper#(from(X)) -> from#(proper(X)) ->
    from#(mark(X)) -> from#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(len(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(len(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    proper#(s(X)) -> proper#(X) -> proper#(len(X)) -> len#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(len(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(fst(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(fst(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(len(X)) -> proper#(X)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(fst(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(len(X)) -> len#(proper(X))
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(len(X)) -> proper#(X)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> add#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(add(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(fst(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(fst(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2)) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2)) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    proper#(fst(X1,X2)) -> fst#(proper(X1),proper(X2)) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    len#(ok(X)) -> len#(X) -> len#(ok(X)) -> len#(X)
    len#(ok(X)) -> len#(X) -> len#(mark(X)) -> len#(X)
    len#(mark(X)) -> len#(X) -> len#(ok(X)) -> len#(X)
    len#(mark(X)) -> len#(X) -> len#(mark(X)) -> len#(X)
    add#(ok(X1),ok(X2)) -> add#(X1,X2) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    add#(ok(X1),ok(X2)) -> add#(X1,X2) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    add#(ok(X1),ok(X2)) -> add#(X1,X2) ->
    add#(mark(X1),X2) -> add#(X1,X2)
    add#(mark(X1),X2) -> add#(X1,X2) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    add#(mark(X1),X2) -> add#(X1,X2) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    add#(mark(X1),X2) -> add#(X1,X2) ->
    add#(mark(X1),X2) -> add#(X1,X2)
    add#(X1,mark(X2)) -> add#(X1,X2) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    add#(X1,mark(X2)) -> add#(X1,X2) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    add#(X1,mark(X2)) -> add#(X1,X2) -> add#(mark(X1),X2) -> add#(X1,X2)
    from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
    from#(ok(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
    from#(mark(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
    from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
    s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    fst#(mark(X1),X2) -> fst#(X1,X2) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    fst#(mark(X1),X2) -> fst#(X1,X2) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    fst#(mark(X1),X2) -> fst#(X1,X2) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    fst#(X1,mark(X2)) -> fst#(X1,X2) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    fst#(X1,mark(X2)) -> fst#(X1,X2) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    fst#(X1,mark(X2)) -> fst#(X1,X2) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    active#(len(cons(X,Z))) -> len#(Z) -> len#(ok(X)) -> len#(X)
    active#(len(cons(X,Z))) -> len#(Z) ->
    len#(mark(X)) -> len#(X)
    active#(len(cons(X,Z))) -> s#(len(Z)) -> s#(ok(X)) -> s#(X)
    active#(len(X)) -> len#(active(X)) -> len#(ok(X)) -> len#(X)
    active#(len(X)) -> len#(active(X)) -> len#(mark(X)) -> len#(X)
    active#(len(X)) -> active#(X) ->
    active#(len(X)) -> len#(active(X))
    active#(len(X)) -> active#(X) -> active#(len(X)) -> active#(X)
    active#(len(X)) -> active#(X) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(len(X)) -> active#(X) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(len(X)) -> active#(X) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(len(X)) -> active#(X) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(len(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(len(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(len(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(len(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(len(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(len(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(len(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(len(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(len(X)) -> active#(X) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(len(X)) -> active#(X) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(len(X)) -> active#(X) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(len(X)) -> active#(X) -> active#(add(s(X),Y)) -> add#(X,Y)
    active#(len(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(len(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(len(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(len(X)) -> active#(X) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(len(X)) -> active#(X) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(add(s(X),Y)) -> add#(X,Y) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    active#(add(s(X),Y)) -> add#(X,Y) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    active#(add(s(X),Y)) -> add#(X,Y) ->
    add#(mark(X1),X2) -> add#(X1,X2)
    active#(add(s(X),Y)) -> s#(add(X,Y)) ->
    s#(ok(X)) -> s#(X)
    active#(add(X1,X2)) -> add#(active(X1),X2) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    active#(add(X1,X2)) -> add#(active(X1),X2) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    active#(add(X1,X2)) -> add#(active(X1),X2) ->
    add#(mark(X1),X2) -> add#(X1,X2)
    active#(add(X1,X2)) -> add#(X1,active(X2)) ->
    add#(ok(X1),ok(X2)) -> add#(X1,X2)
    active#(add(X1,X2)) -> add#(X1,active(X2)) ->
    add#(X1,mark(X2)) -> add#(X1,X2)
    active#(add(X1,X2)) -> add#(X1,active(X2)) ->
    add#(mark(X1),X2) -> add#(X1,X2)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(len(X)) -> len#(active(X))
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    active#(len(X)) -> active#(X)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(active(X))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> active#(X)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(s(X))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> s#(X)
    active#(add(X1,X2)) -> active#(X2) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(add(X1,X2)) -> active#(X2) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(len(X)) -> len#(active(X))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(len(X)) -> active#(X)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(add(X1,X2)) -> active#(X1) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(add(X1,X2)) -> active#(X1) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(from(X)) -> from#(s(X)) -> from#(ok(X)) -> from#(X)
    active#(from(X)) -> from#(s(X)) ->
    from#(mark(X)) -> from#(X)
    active#(from(X)) -> from#(active(X)) ->
    from#(ok(X)) -> from#(X)
    active#(from(X)) -> from#(active(X)) -> from#(mark(X)) -> from#(X)
    active#(from(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    active#(from(X)) -> cons#(X,from(s(X))) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(from(X)) -> cons#(X,from(s(X))) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    active#(from(X)) -> active#(X) ->
    active#(len(X)) -> len#(active(X))
    active#(from(X)) -> active#(X) -> active#(len(X)) -> active#(X)
    active#(from(X)) -> active#(X) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(from(X)) -> active#(X) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(from(X)) -> active#(X) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(from(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(from(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(from(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(from(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(from(X)) -> active#(X) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(from(X)) -> active#(X) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(from(X)) -> active#(X) ->
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(from(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(from(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(from(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(from(X)) -> active#(X) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(from(X)) -> active#(X) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(len(X)) -> len#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(len(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z)) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> fst#(active(X1),X2) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> fst#(active(X1),X2) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> fst#(active(X1),X2) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> fst#(X1,active(X2)) ->
    fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> fst#(X1,active(X2)) ->
    fst#(X1,mark(X2)) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> fst#(X1,active(X2)) ->
    fst#(mark(X1),X2) -> fst#(X1,X2)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(len(X)) -> len#(active(X))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(len(X)) -> active#(X)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(active(X))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> active#(X)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(s(X))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> s#(X)
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(fst(X1,X2)) -> active#(X2) ->
    active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(len(X)) -> len#(active(X))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(len(X)) -> active#(X)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> add#(X1,active(X2))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> active#(X2)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> add#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(add(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> fst#(X1,active(X2))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> active#(X2)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> fst#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(fst(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(len(cons(X,Z))) -> s#(len(Z))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(len(cons(X,Z))) -> len#(Z)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(add(s(X),Y)) -> s#(add(X,Y))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(add(s(X),Y)) -> add#(X,Y)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(fst(X1,X2)) -> active#(X1) ->
    active#(fst(s(X),cons(Y,Z))) -> cons#(Y,fst(X,Z))
    active#(fst(X1,X2)) -> active#(X1) -> active#(fst(s(X),cons(Y,Z))) -> fst#(X,Z)
   SCC Processor:
    #sccs: 9
    #rules: 31
    #arcs: 421/3025
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(fst) = [0,1]
      pi(active) = 0
      pi(nil) = []
      pi(mark) = [0]
      pi(s) = []
      pi(cons) = 0
      pi(from) = [0]
      pi(add) = [0,1]
      pi(len) = [0]
      pi(proper) = 0
      pi(ok) = 0
      pi(top) = 0
      pi(top#) = 0
     weight function:
      w0 = 1
      w(top#) = w(top) = w(len) = w(from) = w(s) = w(mark) = w(nil) = w(
      fst) = w(0) = 1
      w(ok) = w(proper) = w(add) = w(cons) = w(active) = 0
     precedence:
      len ~ add ~ from ~ 0 > fst > top# ~ top ~ ok ~ proper ~ cons ~ s ~ mark ~ nil ~ active
     problem:
      DPs:
       top#(ok(X)) -> top#(active(X))
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     KBO Processor:
      argument filtering:
       pi(0) = []
       pi(fst) = 1
       pi(active) = [0]
       pi(nil) = []
       pi(mark) = 0
       pi(s) = 0
       pi(cons) = 1
       pi(from) = 0
       pi(add) = 1
       pi(len) = [0]
       pi(proper) = [0]
       pi(ok) = [0]
       pi(top) = []
       pi(top#) = 0
      weight function:
       w0 = 1
       w(top#) = w(top) = w(ok) = w(proper) = w(len) = w(cons) = w(nil) = w(
       0) = 1
       w(add) = w(from) = w(s) = w(mark) = w(active) = w(fst) = 0
      precedence:
       top ~ proper ~ active ~ 0 > len > top# ~ ok ~ add ~ from ~ cons ~ s ~ mark ~ nil ~ fst
      problem:
       DPs:
        
       TRS:
        active(fst(0(),Z)) -> mark(nil())
        active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(add(0(),X)) -> mark(X)
        active(add(s(X),Y)) -> mark(s(add(X,Y)))
        active(len(nil())) -> mark(0())
        active(len(cons(X,Z))) -> mark(s(len(Z)))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(fst(X1,X2)) -> fst(active(X1),X2)
        active(fst(X1,X2)) -> fst(X1,active(X2))
        active(from(X)) -> from(active(X))
        active(add(X1,X2)) -> add(active(X1),X2)
        active(add(X1,X2)) -> add(X1,active(X2))
        active(len(X)) -> len(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        fst(mark(X1),X2) -> mark(fst(X1,X2))
        fst(X1,mark(X2)) -> mark(fst(X1,X2))
        from(mark(X)) -> mark(from(X))
        add(mark(X1),X2) -> mark(add(X1,X2))
        add(X1,mark(X2)) -> mark(add(X1,X2))
        len(mark(X)) -> mark(len(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(nil()) -> ok(nil())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(add(X1,X2)) -> add(proper(X1),proper(X2))
        proper(len(X)) -> len(proper(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
        from(ok(X)) -> ok(from(X))
        add(ok(X1),ok(X2)) -> ok(add(X1,X2))
        len(ok(X)) -> ok(len(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     active#(cons(X1,X2)) -> active#(X1)
     active#(fst(X1,X2)) -> active#(X1)
     active#(fst(X1,X2)) -> active#(X2)
     active#(from(X)) -> active#(X)
     active#(add(X1,X2)) -> active#(X1)
     active#(add(X1,X2)) -> active#(X2)
     active#(len(X)) -> active#(X)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(s(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(fst(X1,X2)) -> proper#(X2)
     proper#(fst(X1,X2)) -> proper#(X1)
     proper#(from(X)) -> proper#(X)
     proper#(add(X1,X2)) -> proper#(X2)
     proper#(add(X1,X2)) -> proper#(X1)
     proper#(len(X)) -> proper#(X)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     len#(mark(X)) -> len#(X)
     len#(ok(X)) -> len#(X)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(len#) = 0
     problem:
      DPs:
       
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     add#(mark(X1),X2) -> add#(X1,X2)
     add#(X1,mark(X2)) -> add#(X1,X2)
     add#(ok(X1),ok(X2)) -> add#(X1,X2)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(add#) = 1
     problem:
      DPs:
       add#(mark(X1),X2) -> add#(X1,X2)
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(add#) = 0
      problem:
       DPs:
        
       TRS:
        active(fst(0(),Z)) -> mark(nil())
        active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(add(0(),X)) -> mark(X)
        active(add(s(X),Y)) -> mark(s(add(X,Y)))
        active(len(nil())) -> mark(0())
        active(len(cons(X,Z))) -> mark(s(len(Z)))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(fst(X1,X2)) -> fst(active(X1),X2)
        active(fst(X1,X2)) -> fst(X1,active(X2))
        active(from(X)) -> from(active(X))
        active(add(X1,X2)) -> add(active(X1),X2)
        active(add(X1,X2)) -> add(X1,active(X2))
        active(len(X)) -> len(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        fst(mark(X1),X2) -> mark(fst(X1,X2))
        fst(X1,mark(X2)) -> mark(fst(X1,X2))
        from(mark(X)) -> mark(from(X))
        add(mark(X1),X2) -> mark(add(X1,X2))
        add(X1,mark(X2)) -> mark(add(X1,X2))
        len(mark(X)) -> mark(len(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(nil()) -> ok(nil())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(add(X1,X2)) -> add(proper(X1),proper(X2))
        proper(len(X)) -> len(proper(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
        from(ok(X)) -> ok(from(X))
        add(ok(X1),ok(X2)) -> ok(add(X1,X2))
        len(ok(X)) -> ok(len(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     from#(mark(X)) -> from#(X)
     from#(ok(X)) -> from#(X)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(from#) = 0
     problem:
      DPs:
       
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     fst#(mark(X1),X2) -> fst#(X1,X2)
     fst#(X1,mark(X2)) -> fst#(X1,X2)
     fst#(ok(X1),ok(X2)) -> fst#(X1,X2)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(fst#) = 1
     problem:
      DPs:
       fst#(mark(X1),X2) -> fst#(X1,X2)
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(fst#) = 0
      problem:
       DPs:
        
       TRS:
        active(fst(0(),Z)) -> mark(nil())
        active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(add(0(),X)) -> mark(X)
        active(add(s(X),Y)) -> mark(s(add(X,Y)))
        active(len(nil())) -> mark(0())
        active(len(cons(X,Z))) -> mark(s(len(Z)))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(fst(X1,X2)) -> fst(active(X1),X2)
        active(fst(X1,X2)) -> fst(X1,active(X2))
        active(from(X)) -> from(active(X))
        active(add(X1,X2)) -> add(active(X1),X2)
        active(add(X1,X2)) -> add(X1,active(X2))
        active(len(X)) -> len(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        fst(mark(X1),X2) -> mark(fst(X1,X2))
        fst(X1,mark(X2)) -> mark(fst(X1,X2))
        from(mark(X)) -> mark(from(X))
        add(mark(X1),X2) -> mark(add(X1,X2))
        add(X1,mark(X2)) -> mark(add(X1,X2))
        len(mark(X)) -> mark(len(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(nil()) -> ok(nil())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(add(X1,X2)) -> add(proper(X1),proper(X2))
        proper(len(X)) -> len(proper(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
        from(ok(X)) -> ok(from(X))
        add(ok(X1),ok(X2)) -> ok(add(X1,X2))
        len(ok(X)) -> ok(len(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     cons#(mark(X1),X2) -> cons#(X1,X2)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(cons#) = 1
     problem:
      DPs:
       cons#(mark(X1),X2) -> cons#(X1,X2)
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(cons#) = 0
      problem:
       DPs:
        
       TRS:
        active(fst(0(),Z)) -> mark(nil())
        active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(add(0(),X)) -> mark(X)
        active(add(s(X),Y)) -> mark(s(add(X,Y)))
        active(len(nil())) -> mark(0())
        active(len(cons(X,Z))) -> mark(s(len(Z)))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(fst(X1,X2)) -> fst(active(X1),X2)
        active(fst(X1,X2)) -> fst(X1,active(X2))
        active(from(X)) -> from(active(X))
        active(add(X1,X2)) -> add(active(X1),X2)
        active(add(X1,X2)) -> add(X1,active(X2))
        active(len(X)) -> len(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        fst(mark(X1),X2) -> mark(fst(X1,X2))
        fst(X1,mark(X2)) -> mark(fst(X1,X2))
        from(mark(X)) -> mark(from(X))
        add(mark(X1),X2) -> mark(add(X1,X2))
        add(X1,mark(X2)) -> mark(add(X1,X2))
        len(mark(X)) -> mark(len(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(nil()) -> ok(nil())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(add(X1,X2)) -> add(proper(X1),proper(X2))
        proper(len(X)) -> len(proper(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
        from(ok(X)) -> ok(from(X))
        add(ok(X1),ok(X2)) -> ok(add(X1,X2))
        len(ok(X)) -> ok(len(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     s#(ok(X)) -> s#(X)
    TRS:
     active(fst(0(),Z)) -> mark(nil())
     active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(add(0(),X)) -> mark(X)
     active(add(s(X),Y)) -> mark(s(add(X,Y)))
     active(len(nil())) -> mark(0())
     active(len(cons(X,Z))) -> mark(s(len(Z)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(fst(X1,X2)) -> fst(active(X1),X2)
     active(fst(X1,X2)) -> fst(X1,active(X2))
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     active(add(X1,X2)) -> add(X1,active(X2))
     active(len(X)) -> len(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     proper(len(X)) -> len(proper(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
     from(ok(X)) -> ok(from(X))
     add(ok(X1),ok(X2)) -> ok(add(X1,X2))
     len(ok(X)) -> ok(len(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(s#) = 0
     problem:
      DPs:
       
      TRS:
       active(fst(0(),Z)) -> mark(nil())
       active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(add(0(),X)) -> mark(X)
       active(add(s(X),Y)) -> mark(s(add(X,Y)))
       active(len(nil())) -> mark(0())
       active(len(cons(X,Z))) -> mark(s(len(Z)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(fst(X1,X2)) -> fst(active(X1),X2)
       active(fst(X1,X2)) -> fst(X1,active(X2))
       active(from(X)) -> from(active(X))
       active(add(X1,X2)) -> add(active(X1),X2)
       active(add(X1,X2)) -> add(X1,active(X2))
       active(len(X)) -> len(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(add(X1,X2)) -> add(proper(X1),proper(X2))
       proper(len(X)) -> len(proper(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
       from(ok(X)) -> ok(from(X))
       add(ok(X1),ok(X2)) -> ok(add(X1,X2))
       len(ok(X)) -> ok(len(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed