YES

Problem:
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(2nd(X)) -> 2nd(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(from(X)) -> from(active(X))
 active(s(X)) -> s(active(X))
 active(cons1(X1,X2)) -> cons1(active(X1),X2)
 active(cons1(X1,X2)) -> cons1(X1,active(X2))
 2nd(mark(X)) -> mark(2nd(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 from(mark(X)) -> mark(from(X))
 s(mark(X)) -> mark(s(X))
 cons1(mark(X1),X2) -> mark(cons1(X1,X2))
 cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
 proper(2nd(X)) -> 2nd(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 proper(s(X)) -> s(proper(X))
 proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
 2nd(ok(X)) -> ok(2nd(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 from(ok(X)) -> ok(from(X))
 s(ok(X)) -> ok(s(X))
 cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(2nd(cons(X,X1))) -> cons1#(X,X1)
   active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(2nd(X)) -> active#(X)
   active#(2nd(X)) -> 2nd#(active(X))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(from(X)) -> active#(X)
   active#(from(X)) -> from#(active(X))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(cons1(X1,X2)) -> active#(X1)
   active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
   active#(cons1(X1,X2)) -> active#(X2)
   active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
   2nd#(mark(X)) -> 2nd#(X)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   from#(mark(X)) -> from#(X)
   s#(mark(X)) -> s#(X)
   cons1#(mark(X1),X2) -> cons1#(X1,X2)
   cons1#(X1,mark(X2)) -> cons1#(X1,X2)
   proper#(2nd(X)) -> proper#(X)
   proper#(2nd(X)) -> 2nd#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(from(X)) -> proper#(X)
   proper#(from(X)) -> from#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(cons1(X1,X2)) -> proper#(X2)
   proper#(cons1(X1,X2)) -> proper#(X1)
   proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
   2nd#(ok(X)) -> 2nd#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   from#(ok(X)) -> from#(X)
   s#(ok(X)) -> s#(X)
   cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
   active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(2nd(X)) -> 2nd(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(from(X)) -> from(active(X))
   active(s(X)) -> s(active(X))
   active(cons1(X1,X2)) -> cons1(active(X1),X2)
   active(cons1(X1,X2)) -> cons1(X1,active(X2))
   2nd(mark(X)) -> mark(2nd(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   from(mark(X)) -> mark(from(X))
   s(mark(X)) -> mark(s(X))
   cons1(mark(X1),X2) -> mark(cons1(X1,X2))
   cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
   proper(2nd(X)) -> 2nd(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(s(X)) -> s(proper(X))
   proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
   2nd(ok(X)) -> ok(2nd(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   from(ok(X)) -> ok(from(X))
   s(ok(X)) -> ok(s(X))
   cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(from(X)) -> s#(X)
    active#(from(X)) -> from#(s(X))
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(2nd(X)) -> active#(X)
    active#(2nd(X)) -> 2nd#(active(X))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(from(X)) -> active#(X)
    active#(from(X)) -> from#(active(X))
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(cons1(X1,X2)) -> active#(X1)
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(cons1(X1,X2)) -> active#(X2)
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    2nd#(mark(X)) -> 2nd#(X)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    from#(mark(X)) -> from#(X)
    s#(mark(X)) -> s#(X)
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    proper#(2nd(X)) -> proper#(X)
    proper#(2nd(X)) -> 2nd#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X2)
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    2nd#(ok(X)) -> 2nd#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    from#(ok(X)) -> from#(X)
    s#(ok(X)) -> s#(X)
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
    active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(2nd(X)) -> 2nd(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(from(X)) -> from(active(X))
    active(s(X)) -> s(active(X))
    active(cons1(X1,X2)) -> cons1(active(X1),X2)
    active(cons1(X1,X2)) -> cons1(X1,active(X2))
    2nd(mark(X)) -> mark(2nd(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    from(mark(X)) -> mark(from(X))
    s(mark(X)) -> mark(s(X))
    cons1(mark(X1),X2) -> mark(cons1(X1,X2))
    cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
    proper(2nd(X)) -> 2nd(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    proper(s(X)) -> s(proper(X))
    proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
    2nd(ok(X)) -> ok(2nd(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    from(ok(X)) -> ok(from(X))
    s(ok(X)) -> ok(s(X))
    cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
    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#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    top#(ok(X)) -> active#(X) -> active#(cons1(X1,X2)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(cons1(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    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#(cons(X1,X2)) -> cons#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X))
    top#(ok(X)) -> active#(X) -> active#(2nd(X)) -> active#(X)
    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#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    top#(ok(X)) -> active#(X) ->
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    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#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(cons1(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(cons1(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)
    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#(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#(2nd(X)) -> 2nd#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(cons1(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)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    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#(2nd(X)) -> 2nd#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons1(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)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    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#(2nd(X)) -> 2nd#(proper(X))
    proper#(from(X)) -> proper#(X) ->
    proper#(2nd(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#(2nd(X)) -> proper#(X) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(2nd(X)) -> proper#(X) ->
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(2nd(X)) -> proper#(X) ->
    proper#(cons1(X1,X2)) -> proper#(X2)
    proper#(2nd(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(2nd(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(2nd(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(2nd(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(2nd(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(2nd(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(2nd(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(2nd(X)) -> proper#(X) ->
    proper#(2nd(X)) -> 2nd#(proper(X))
    proper#(2nd(X)) -> proper#(X) ->
    proper#(2nd(X)) -> proper#(X)
    proper#(2nd(X)) -> 2nd#(proper(X)) -> 2nd#(ok(X)) -> 2nd#(X)
    proper#(2nd(X)) -> 2nd#(proper(X)) ->
    2nd#(mark(X)) -> 2nd#(X)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(cons1(X1,X2)) -> proper#(X2)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(2nd(X)) -> 2nd#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X2) ->
    proper#(2nd(X)) -> proper#(X)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(cons1(X1,X2)) -> proper#(X2)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(2nd(X)) -> 2nd#(proper(X))
    proper#(cons1(X1,X2)) -> proper#(X1) ->
    proper#(2nd(X)) -> proper#(X)
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2)) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2)) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2)) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons1(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#(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#(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#(2nd(X)) -> 2nd#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(2nd(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons1(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons1(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)) -> 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#(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#(2nd(X)) -> 2nd#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(2nd(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)
    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)
    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)
    s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
    s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
    2nd#(ok(X)) -> 2nd#(X) -> 2nd#(ok(X)) -> 2nd#(X)
    2nd#(ok(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X)
    2nd#(mark(X)) -> 2nd#(X) -> 2nd#(ok(X)) -> 2nd#(X)
    2nd#(mark(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X)
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    cons1#(mark(X1),X2) -> cons1#(X1,X2) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    cons1#(mark(X1),X2) -> cons1#(X1,X2) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    cons1#(mark(X1),X2) -> cons1#(X1,X2) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    cons1#(X1,mark(X2)) -> cons1#(X1,X2) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    cons1#(X1,mark(X2)) -> cons1#(X1,X2) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    cons1#(X1,mark(X2)) -> cons1#(X1,X2) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
    active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
    active#(s(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    active#(s(X)) -> active#(X) -> active#(cons1(X1,X2)) -> active#(X2)
    active#(s(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(cons1(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
    active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(s(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X))
    active#(s(X)) -> active#(X) -> active#(2nd(X)) -> active#(X)
    active#(s(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(s(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(s(X)) -> active#(X) ->
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(s(X)) -> active#(X) ->
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    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)) -> 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)) -> s#(X) -> s#(mark(X)) -> s#(X)
    active#(from(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    active#(from(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> active#(X2)
    active#(from(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    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#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(2nd(X)) -> 2nd#(active(X))
    active#(from(X)) -> active#(X) -> active#(2nd(X)) -> active#(X)
    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#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(from(X)) -> active#(X) ->
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1)) ->
    2nd#(ok(X)) -> 2nd#(X)
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1)) ->
    2nd#(mark(X)) -> 2nd#(X)
    active#(2nd(cons(X,X1))) -> cons1#(X,X1) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    active#(2nd(cons(X,X1))) -> cons1#(X,X1) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    active#(2nd(cons(X,X1))) -> cons1#(X,X1) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    active#(2nd(X)) -> 2nd#(active(X)) -> 2nd#(ok(X)) -> 2nd#(X)
    active#(2nd(X)) -> 2nd#(active(X)) -> 2nd#(mark(X)) -> 2nd#(X)
    active#(2nd(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    active#(2nd(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> active#(X2)
    active#(2nd(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(2nd(X)) -> active#(X) ->
    active#(cons1(X1,X2)) -> active#(X1)
    active#(2nd(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(2nd(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(2nd(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(2nd(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(2nd(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(2nd(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(2nd(X)) -> active#(X) ->
    active#(2nd(X)) -> 2nd#(active(X))
    active#(2nd(X)) -> active#(X) -> active#(2nd(X)) -> active#(X)
    active#(2nd(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(2nd(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(2nd(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(2nd(X)) -> active#(X) ->
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(2nd(X)) -> active#(X) ->
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2)) ->
    cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2)) ->
    cons1#(X1,mark(X2)) -> cons1#(X1,X2)
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2)) ->
    cons1#(mark(X1),X2) -> cons1#(X1,X2)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(cons1(X1,X2)) -> active#(X2)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(cons1(X1,X2)) -> active#(X1)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> s#(active(X))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> active#(X)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(active(X))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> active#(X)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(2nd(X)) -> 2nd#(active(X))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(2nd(X)) -> active#(X)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(s(X))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> s#(X)
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(cons1(X1,X2)) -> active#(X2) ->
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> active#(X2)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> active#(X1)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(2nd(X)) -> 2nd#(active(X))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(2nd(X)) -> active#(X)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(cons1(X1,X2)) -> active#(X1) ->
    active#(2nd(cons(X,X1))) -> cons1#(X,X1)
    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#(cons1(X1,X2)) -> cons1#(X1,active(X2))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> active#(X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons1(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    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#(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#(2nd(X)) -> 2nd#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(2nd(X)) -> active#(X)
    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#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
    active#(cons(X1,X2)) -> active#(X1) -> active#(2nd(cons(X,X1))) -> cons1#(X,X1)
   SCC Processor:
    #sccs: 8
    #rules: 26
    #arcs: 284/1936
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [top#](x0) = x0,
      
      [top](x0) = x0 + 0,
      
      [ok](x0) = 3x0 + 4,
      
      [proper](x0) = x0,
      
      [s](x0) = 1x0 + 1,
      
      [from](x0) = x0 + 0,
      
      [mark](x0) = x0,
      
      [active](x0) = 2x0,
      
      [2nd](x0) = x0 + 0,
      
      [cons1](x0, x1) = x0 + 1x1,
      
      [cons](x0, x1) = x0 + 1x1 + 0
     orientation:
      top#(ok(X)) = 3X + 4 >= 2X = top#(active(X))
      
      top#(mark(X)) = X >= X = top#(proper(X))
      
      active(2nd(cons1(X,cons(Y,Z)))) = 2X + 3Y + 4Z + 3 >= Y = mark(Y)
      
      active(2nd(cons(X,X1))) = 2X + 3X1 + 2 >= X + 1X1 + 0 = mark(2nd(cons1(X,X1)))
      
      active(from(X)) = 2X + 2 >= 2X + 2 = mark(cons(X,from(s(X))))
      
      active(2nd(X)) = 2X + 2 >= 2X + 0 = 2nd(active(X))
      
      active(cons(X1,X2)) = 2X1 + 3X2 + 2 >= 2X1 + 1X2 + 0 = cons(active(X1),X2)
      
      active(from(X)) = 2X + 2 >= 2X + 0 = from(active(X))
      
      active(s(X)) = 3X + 3 >= 3X + 1 = s(active(X))
      
      active(cons1(X1,X2)) = 2X1 + 3X2 >= 2X1 + 1X2 = cons1(active(X1),X2)
      
      active(cons1(X1,X2)) = 2X1 + 3X2 >= X1 + 3X2 = cons1(X1,active(X2))
      
      2nd(mark(X)) = X + 0 >= X + 0 = mark(2nd(X))
      
      cons(mark(X1),X2) = X1 + 1X2 + 0 >= X1 + 1X2 + 0 = mark(cons(X1,X2))
      
      from(mark(X)) = X + 0 >= X + 0 = mark(from(X))
      
      s(mark(X)) = 1X + 1 >= 1X + 1 = mark(s(X))
      
      cons1(mark(X1),X2) = X1 + 1X2 >= X1 + 1X2 = mark(cons1(X1,X2))
      
      cons1(X1,mark(X2)) = X1 + 1X2 >= X1 + 1X2 = mark(cons1(X1,X2))
      
      proper(2nd(X)) = X + 0 >= X + 0 = 2nd(proper(X))
      
      proper(cons(X1,X2)) = X1 + 1X2 + 0 >= X1 + 1X2 + 0 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = X + 0 >= X + 0 = from(proper(X))
      
      proper(s(X)) = 1X + 1 >= 1X + 1 = s(proper(X))
      
      proper(cons1(X1,X2)) = X1 + 1X2 >= X1 + 1X2 = cons1(proper(X1),proper(X2))
      
      2nd(ok(X)) = 3X + 4 >= 3X + 4 = ok(2nd(X))
      
      cons(ok(X1),ok(X2)) = 3X1 + 4X2 + 5 >= 3X1 + 4X2 + 4 = ok(cons(X1,X2))
      
      from(ok(X)) = 3X + 4 >= 3X + 4 = ok(from(X))
      
      s(ok(X)) = 4X + 5 >= 4X + 4 = ok(s(X))
      
      cons1(ok(X1),ok(X2)) = 3X1 + 4X2 + 5 >= 3X1 + 4X2 + 4 = ok(cons1(X1,X2))
      
      top(mark(X)) = X + 0 >= X + 0 = top(proper(X))
      
      top(ok(X)) = 3X + 4 >= 2X + 0 = top(active(X))
     problem:
      DPs:
       top#(mark(X)) -> top#(proper(X))
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     LPO Processor:
      argument filtering:
       pi(cons) = [0,1]
       pi(cons1) = [0,1]
       pi(2nd) = 0
       pi(active) = [0]
       pi(mark) = [0]
       pi(from) = 0
       pi(s) = 0
       pi(proper) = 0
       pi(ok) = []
       pi(top) = []
       pi(top#) = 0
      precedence:
       active > cons1 ~ cons > top# ~ top ~ ok ~ proper ~ s ~ from ~ mark ~ 2nd
      problem:
       DPs:
        
       TRS:
        active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
        active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(2nd(X)) -> 2nd(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(from(X)) -> from(active(X))
        active(s(X)) -> s(active(X))
        active(cons1(X1,X2)) -> cons1(active(X1),X2)
        active(cons1(X1,X2)) -> cons1(X1,active(X2))
        2nd(mark(X)) -> mark(2nd(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        from(mark(X)) -> mark(from(X))
        s(mark(X)) -> mark(s(X))
        cons1(mark(X1),X2) -> mark(cons1(X1,X2))
        cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
        proper(2nd(X)) -> 2nd(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
        2nd(ok(X)) -> ok(2nd(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        from(ok(X)) -> ok(from(X))
        s(ok(X)) -> ok(s(X))
        cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     active#(2nd(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1)
     active#(from(X)) -> active#(X)
     active#(s(X)) -> active#(X)
     active#(cons1(X1,X2)) -> active#(X1)
     active#(cons1(X1,X2)) -> active#(X2)
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(2nd(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(from(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X)
     proper#(cons1(X1,X2)) -> proper#(X2)
     proper#(cons1(X1,X2)) -> proper#(X1)
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     cons1#(mark(X1),X2) -> cons1#(X1,X2)
     cons1#(X1,mark(X2)) -> cons1#(X1,X2)
     cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(cons1#) = 1
     problem:
      DPs:
       cons1#(mark(X1),X2) -> cons1#(X1,X2)
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(cons1#) = 0
      problem:
       DPs:
        
       TRS:
        active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
        active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(2nd(X)) -> 2nd(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(from(X)) -> from(active(X))
        active(s(X)) -> s(active(X))
        active(cons1(X1,X2)) -> cons1(active(X1),X2)
        active(cons1(X1,X2)) -> cons1(X1,active(X2))
        2nd(mark(X)) -> mark(2nd(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        from(mark(X)) -> mark(from(X))
        s(mark(X)) -> mark(s(X))
        cons1(mark(X1),X2) -> mark(cons1(X1,X2))
        cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
        proper(2nd(X)) -> 2nd(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
        2nd(ok(X)) -> ok(2nd(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        from(ok(X)) -> ok(from(X))
        s(ok(X)) -> ok(s(X))
        cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     s#(mark(X)) -> s#(X)
     s#(ok(X)) -> s#(X)
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(s#) = 0
     problem:
      DPs:
       
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       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(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(from#) = 0
     problem:
      DPs:
       
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       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(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     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(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(cons#) = 0
      problem:
       DPs:
        
       TRS:
        active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
        active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(2nd(X)) -> 2nd(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(from(X)) -> from(active(X))
        active(s(X)) -> s(active(X))
        active(cons1(X1,X2)) -> cons1(active(X1),X2)
        active(cons1(X1,X2)) -> cons1(X1,active(X2))
        2nd(mark(X)) -> mark(2nd(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        from(mark(X)) -> mark(from(X))
        s(mark(X)) -> mark(s(X))
        cons1(mark(X1),X2) -> mark(cons1(X1,X2))
        cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
        proper(2nd(X)) -> 2nd(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
        2nd(ok(X)) -> ok(2nd(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        from(ok(X)) -> ok(from(X))
        s(ok(X)) -> ok(s(X))
        cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     2nd#(mark(X)) -> 2nd#(X)
     2nd#(ok(X)) -> 2nd#(X)
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(2nd#) = 0
     problem:
      DPs:
       
      TRS:
       active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
       active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(2nd(X)) -> 2nd(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons1(X1,X2)) -> cons1(active(X1),X2)
       active(cons1(X1,X2)) -> cons1(X1,active(X2))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
       2nd(ok(X)) -> ok(2nd(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed