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))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [top#](x0) = 4x0,
      
      [top](x0) = 4,
      
      [ok](x0) = 4x0 + 4,
      
      [proper](x0) = 0,
      
      [s](x0) = x0,
      
      [from](x0) = x0,
      
      [mark](x0) = 1,
      
      [active](x0) = 4x0 + 2,
      
      [2nd](x0) = x0,
      
      [cons1](x0, x1) = x0 + x1,
      
      [cons](x0, x1) = x0
     orientation:
      top#(ok(X)) = 16X + 16 >= 16X + 8 = top#(active(X))
      
      top#(mark(X)) = 4 >= 0 = top#(proper(X))
      
      active(2nd(cons1(X,cons(Y,Z)))) = 4X + 4Y + 2 >= 1 = mark(Y)
      
      active(2nd(cons(X,X1))) = 4X + 2 >= 1 = mark(2nd(cons1(X,X1)))
      
      active(from(X)) = 4X + 2 >= 1 = mark(cons(X,from(s(X))))
      
      active(2nd(X)) = 4X + 2 >= 4X + 2 = 2nd(active(X))
      
      active(cons(X1,X2)) = 4X1 + 2 >= 4X1 + 2 = cons(active(X1),X2)
      
      active(from(X)) = 4X + 2 >= 4X + 2 = from(active(X))
      
      active(s(X)) = 4X + 2 >= 4X + 2 = s(active(X))
      
      active(cons1(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + X2 + 2 = cons1(active(X1),X2)
      
      active(cons1(X1,X2)) = 4X1 + 4X2 + 2 >= X1 + 4X2 + 2 = cons1(X1,active(X2))
      
      2nd(mark(X)) = 1 >= 1 = mark(2nd(X))
      
      cons(mark(X1),X2) = 1 >= 1 = mark(cons(X1,X2))
      
      from(mark(X)) = 1 >= 1 = mark(from(X))
      
      s(mark(X)) = 1 >= 1 = mark(s(X))
      
      cons1(mark(X1),X2) = X2 + 1 >= 1 = mark(cons1(X1,X2))
      
      cons1(X1,mark(X2)) = X1 + 1 >= 1 = mark(cons1(X1,X2))
      
      proper(2nd(X)) = 0 >= 0 = 2nd(proper(X))
      
      proper(cons(X1,X2)) = 0 >= 0 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = 0 >= 0 = from(proper(X))
      
      proper(s(X)) = 0 >= 0 = s(proper(X))
      
      proper(cons1(X1,X2)) = 0 >= 0 = cons1(proper(X1),proper(X2))
      
      2nd(ok(X)) = 4X + 4 >= 4X + 4 = ok(2nd(X))
      
      cons(ok(X1),ok(X2)) = 4X1 + 4 >= 4X1 + 4 = ok(cons(X1,X2))
      
      from(ok(X)) = 4X + 4 >= 4X + 4 = ok(from(X))
      
      s(ok(X)) = 4X + 4 >= 4X + 4 = ok(s(X))
      
      cons1(ok(X1),ok(X2)) = 4X1 + 4X2 + 8 >= 4X1 + 4X2 + 4 = ok(cons1(X1,X2))
      
      top(mark(X)) = 4 >= 4 = top(proper(X))
      
      top(ok(X)) = 4 >= 4 = top(active(X))
     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))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [active#](x0) = x0,
      
      [top](x0) = 2,
      
      [ok](x0) = x0,
      
      [proper](x0) = x0,
      
      [s](x0) = 2x0 + 1,
      
      [from](x0) = 4x0 + 1,
      
      [mark](x0) = 1,
      
      [active](x0) = x0,
      
      [2nd](x0) = x0 + 5,
      
      [cons1](x0, x1) = 3x0 + 6x1 + 3,
      
      [cons](x0, x1) = 4x0 + 1
     orientation:
      active#(2nd(X)) = X + 5 >= X = active#(X)
      
      active#(cons(X1,X2)) = 4X1 + 1 >= X1 = active#(X1)
      
      active#(from(X)) = 4X + 1 >= X = active#(X)
      
      active#(s(X)) = 2X + 1 >= X = active#(X)
      
      active#(cons1(X1,X2)) = 3X1 + 6X2 + 3 >= X1 = active#(X1)
      
      active#(cons1(X1,X2)) = 3X1 + 6X2 + 3 >= X2 = active#(X2)
      
      active(2nd(cons1(X,cons(Y,Z)))) = 3X + 24Y + 14 >= 1 = mark(Y)
      
      active(2nd(cons(X,X1))) = 4X + 6 >= 1 = mark(2nd(cons1(X,X1)))
      
      active(from(X)) = 4X + 1 >= 1 = mark(cons(X,from(s(X))))
      
      active(2nd(X)) = X + 5 >= X + 5 = 2nd(active(X))
      
      active(cons(X1,X2)) = 4X1 + 1 >= 4X1 + 1 = cons(active(X1),X2)
      
      active(from(X)) = 4X + 1 >= 4X + 1 = from(active(X))
      
      active(s(X)) = 2X + 1 >= 2X + 1 = s(active(X))
      
      active(cons1(X1,X2)) = 3X1 + 6X2 + 3 >= 3X1 + 6X2 + 3 = cons1(active(X1),X2)
      
      active(cons1(X1,X2)) = 3X1 + 6X2 + 3 >= 3X1 + 6X2 + 3 = cons1(X1,active(X2))
      
      2nd(mark(X)) = 6 >= 1 = mark(2nd(X))
      
      cons(mark(X1),X2) = 5 >= 1 = mark(cons(X1,X2))
      
      from(mark(X)) = 5 >= 1 = mark(from(X))
      
      s(mark(X)) = 3 >= 1 = mark(s(X))
      
      cons1(mark(X1),X2) = 6X2 + 6 >= 1 = mark(cons1(X1,X2))
      
      cons1(X1,mark(X2)) = 3X1 + 9 >= 1 = mark(cons1(X1,X2))
      
      proper(2nd(X)) = X + 5 >= X + 5 = 2nd(proper(X))
      
      proper(cons(X1,X2)) = 4X1 + 1 >= 4X1 + 1 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = 4X + 1 >= 4X + 1 = from(proper(X))
      
      proper(s(X)) = 2X + 1 >= 2X + 1 = s(proper(X))
      
      proper(cons1(X1,X2)) = 3X1 + 6X2 + 3 >= 3X1 + 6X2 + 3 = cons1(proper(X1),proper(X2))
      
      2nd(ok(X)) = X + 5 >= X + 5 = ok(2nd(X))
      
      cons(ok(X1),ok(X2)) = 4X1 + 1 >= 4X1 + 1 = ok(cons(X1,X2))
      
      from(ok(X)) = 4X + 1 >= 4X + 1 = ok(from(X))
      
      s(ok(X)) = 2X + 1 >= 2X + 1 = ok(s(X))
      
      cons1(ok(X1),ok(X2)) = 3X1 + 6X2 + 3 >= 3X1 + 6X2 + 3 = ok(cons1(X1,X2))
      
      top(mark(X)) = 2 >= 2 = top(proper(X))
      
      top(ok(X)) = 2 >= 2 = top(active(X))
     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))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [proper#](x0) = x0,
      
      [top](x0) = 3,
      
      [ok](x0) = x0,
      
      [proper](x0) = x0,
      
      [s](x0) = 3x0 + 1,
      
      [from](x0) = 6x0 + 4,
      
      [mark](x0) = 1,
      
      [active](x0) = 2x0,
      
      [2nd](x0) = 4x0 + 1,
      
      [cons1](x0, x1) = 4x0 + x1 + 1,
      
      [cons](x0, x1) = x0 + x1 + 2
     orientation:
      proper#(2nd(X)) = 4X + 1 >= X = proper#(X)
      
      proper#(cons(X1,X2)) = X1 + X2 + 2 >= X2 = proper#(X2)
      
      proper#(cons(X1,X2)) = X1 + X2 + 2 >= X1 = proper#(X1)
      
      proper#(from(X)) = 6X + 4 >= X = proper#(X)
      
      proper#(s(X)) = 3X + 1 >= X = proper#(X)
      
      proper#(cons1(X1,X2)) = 4X1 + X2 + 1 >= X2 = proper#(X2)
      
      proper#(cons1(X1,X2)) = 4X1 + X2 + 1 >= X1 = proper#(X1)
      
      active(2nd(cons1(X,cons(Y,Z)))) = 32X + 8Y + 8Z + 26 >= 1 = mark(Y)
      
      active(2nd(cons(X,X1))) = 8X + 8X1 + 18 >= 1 = mark(2nd(cons1(X,X1)))
      
      active(from(X)) = 12X + 8 >= 1 = mark(cons(X,from(s(X))))
      
      active(2nd(X)) = 8X + 2 >= 8X + 1 = 2nd(active(X))
      
      active(cons(X1,X2)) = 2X1 + 2X2 + 4 >= 2X1 + X2 + 2 = cons(active(X1),X2)
      
      active(from(X)) = 12X + 8 >= 12X + 4 = from(active(X))
      
      active(s(X)) = 6X + 2 >= 6X + 1 = s(active(X))
      
      active(cons1(X1,X2)) = 8X1 + 2X2 + 2 >= 8X1 + X2 + 1 = cons1(active(X1),X2)
      
      active(cons1(X1,X2)) = 8X1 + 2X2 + 2 >= 4X1 + 2X2 + 1 = cons1(X1,active(X2))
      
      2nd(mark(X)) = 5 >= 1 = mark(2nd(X))
      
      cons(mark(X1),X2) = X2 + 3 >= 1 = mark(cons(X1,X2))
      
      from(mark(X)) = 10 >= 1 = mark(from(X))
      
      s(mark(X)) = 4 >= 1 = mark(s(X))
      
      cons1(mark(X1),X2) = X2 + 5 >= 1 = mark(cons1(X1,X2))
      
      cons1(X1,mark(X2)) = 4X1 + 2 >= 1 = mark(cons1(X1,X2))
      
      proper(2nd(X)) = 4X + 1 >= 4X + 1 = 2nd(proper(X))
      
      proper(cons(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = 6X + 4 >= 6X + 4 = from(proper(X))
      
      proper(s(X)) = 3X + 1 >= 3X + 1 = s(proper(X))
      
      proper(cons1(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = cons1(proper(X1),proper(X2))
      
      2nd(ok(X)) = 4X + 1 >= 4X + 1 = ok(2nd(X))
      
      cons(ok(X1),ok(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = ok(cons(X1,X2))
      
      from(ok(X)) = 6X + 4 >= 6X + 4 = ok(from(X))
      
      s(ok(X)) = 3X + 1 >= 3X + 1 = ok(s(X))
      
      cons1(ok(X1),ok(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = ok(cons1(X1,X2))
      
      top(mark(X)) = 3 >= 3 = top(proper(X))
      
      top(ok(X)) = 3 >= 3 = top(active(X))
     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))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [cons1#](x0, x1) = x0 + x1 + 1,
     
     [top](x0) = 7,
     
     [ok](x0) = 2x0 + 1,
     
     [proper](x0) = 4x0,
     
     [s](x0) = x0,
     
     [from](x0) = 4x0 + 2,
     
     [mark](x0) = x0 + 1,
     
     [active](x0) = 4x0,
     
     [2nd](x0) = x0,
     
     [cons1](x0, x1) = 4x0 + x1,
     
     [cons](x0, x1) = 2x0 + 2x1 + 2
    orientation:
     cons1#(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 1 = cons1#(X1,X2)
     
     cons1#(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 1 = cons1#(X1,X2)
     
     cons1#(ok(X1),ok(X2)) = 2X1 + 2X2 + 3 >= X1 + X2 + 1 = cons1#(X1,X2)
     
     active(2nd(cons1(X,cons(Y,Z)))) = 16X + 8Y + 8Z + 8 >= Y + 1 = mark(Y)
     
     active(2nd(cons(X,X1))) = 8X + 8X1 + 8 >= 4X + X1 + 1 = mark(2nd(cons1(X,X1)))
     
     active(from(X)) = 16X + 8 >= 10X + 7 = mark(cons(X,from(s(X))))
     
     active(2nd(X)) = 4X >= 4X = 2nd(active(X))
     
     active(cons(X1,X2)) = 8X1 + 8X2 + 8 >= 8X1 + 2X2 + 2 = cons(active(X1),X2)
     
     active(from(X)) = 16X + 8 >= 16X + 2 = from(active(X))
     
     active(s(X)) = 4X >= 4X = s(active(X))
     
     active(cons1(X1,X2)) = 16X1 + 4X2 >= 16X1 + X2 = cons1(active(X1),X2)
     
     active(cons1(X1,X2)) = 16X1 + 4X2 >= 4X1 + 4X2 = cons1(X1,active(X2))
     
     2nd(mark(X)) = X + 1 >= X + 1 = mark(2nd(X))
     
     cons(mark(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 3 = mark(cons(X1,X2))
     
     from(mark(X)) = 4X + 6 >= 4X + 3 = mark(from(X))
     
     s(mark(X)) = X + 1 >= X + 1 = mark(s(X))
     
     cons1(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 1 = mark(cons1(X1,X2))
     
     cons1(X1,mark(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = mark(cons1(X1,X2))
     
     proper(2nd(X)) = 4X >= 4X = 2nd(proper(X))
     
     proper(cons(X1,X2)) = 8X1 + 8X2 + 8 >= 8X1 + 8X2 + 2 = cons(proper(X1),proper(X2))
     
     proper(from(X)) = 16X + 8 >= 16X + 2 = from(proper(X))
     
     proper(s(X)) = 4X >= 4X = s(proper(X))
     
     proper(cons1(X1,X2)) = 16X1 + 4X2 >= 16X1 + 4X2 = cons1(proper(X1),proper(X2))
     
     2nd(ok(X)) = 2X + 1 >= 2X + 1 = ok(2nd(X))
     
     cons(ok(X1),ok(X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 5 = ok(cons(X1,X2))
     
     from(ok(X)) = 8X + 6 >= 8X + 5 = ok(from(X))
     
     s(ok(X)) = 2X + 1 >= 2X + 1 = ok(s(X))
     
     cons1(ok(X1),ok(X2)) = 8X1 + 2X2 + 5 >= 8X1 + 2X2 + 1 = ok(cons1(X1,X2))
     
     top(mark(X)) = 7 >= 7 = top(proper(X))
     
     top(ok(X)) = 7 >= 7 = top(active(X))
    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))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [s#](x0) = 3x0,
     
     [top](x0) = 0,
     
     [ok](x0) = x0 + 7,
     
     [proper](x0) = x0,
     
     [s](x0) = x0,
     
     [from](x0) = 4x0 + 3,
     
     [mark](x0) = x0 + 4,
     
     [active](x0) = 3x0 + 2,
     
     [2nd](x0) = 4x0 + 3,
     
     [cons1](x0, x1) = x0 + x1,
     
     [cons](x0, x1) = 2x0 + 2x1 + 1
    orientation:
     s#(mark(X)) = 3X + 12 >= 3X = s#(X)
     
     s#(ok(X)) = 3X + 21 >= 3X = s#(X)
     
     active(2nd(cons1(X,cons(Y,Z)))) = 12X + 24Y + 24Z + 23 >= Y + 4 = mark(Y)
     
     active(2nd(cons(X,X1))) = 24X + 24X1 + 23 >= 4X + 4X1 + 7 = mark(2nd(cons1(X,X1)))
     
     active(from(X)) = 12X + 11 >= 10X + 11 = mark(cons(X,from(s(X))))
     
     active(2nd(X)) = 12X + 11 >= 12X + 11 = 2nd(active(X))
     
     active(cons(X1,X2)) = 6X1 + 6X2 + 5 >= 6X1 + 2X2 + 5 = cons(active(X1),X2)
     
     active(from(X)) = 12X + 11 >= 12X + 11 = from(active(X))
     
     active(s(X)) = 3X + 2 >= 3X + 2 = s(active(X))
     
     active(cons1(X1,X2)) = 3X1 + 3X2 + 2 >= 3X1 + X2 + 2 = cons1(active(X1),X2)
     
     active(cons1(X1,X2)) = 3X1 + 3X2 + 2 >= X1 + 3X2 + 2 = cons1(X1,active(X2))
     
     2nd(mark(X)) = 4X + 19 >= 4X + 7 = mark(2nd(X))
     
     cons(mark(X1),X2) = 2X1 + 2X2 + 9 >= 2X1 + 2X2 + 5 = mark(cons(X1,X2))
     
     from(mark(X)) = 4X + 19 >= 4X + 7 = mark(from(X))
     
     s(mark(X)) = X + 4 >= X + 4 = mark(s(X))
     
     cons1(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(cons1(X1,X2))
     
     cons1(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(cons1(X1,X2))
     
     proper(2nd(X)) = 4X + 3 >= 4X + 3 = 2nd(proper(X))
     
     proper(cons(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = cons(proper(X1),proper(X2))
     
     proper(from(X)) = 4X + 3 >= 4X + 3 = from(proper(X))
     
     proper(s(X)) = X >= X = s(proper(X))
     
     proper(cons1(X1,X2)) = X1 + X2 >= X1 + X2 = cons1(proper(X1),proper(X2))
     
     2nd(ok(X)) = 4X + 31 >= 4X + 10 = ok(2nd(X))
     
     cons(ok(X1),ok(X2)) = 2X1 + 2X2 + 29 >= 2X1 + 2X2 + 8 = ok(cons(X1,X2))
     
     from(ok(X)) = 4X + 31 >= 4X + 10 = ok(from(X))
     
     s(ok(X)) = X + 7 >= X + 7 = ok(s(X))
     
     cons1(ok(X1),ok(X2)) = X1 + X2 + 14 >= X1 + X2 + 7 = ok(cons1(X1,X2))
     
     top(mark(X)) = 0 >= 0 = top(proper(X))
     
     top(ok(X)) = 0 >= 0 = top(active(X))
    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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [from#](x0) = 3x0,
    
    [top](x0) = 0,
    
    [ok](x0) = x0 + 7,
    
    [proper](x0) = x0,
    
    [s](x0) = x0,
    
    [from](x0) = 4x0 + 3,
    
    [mark](x0) = x0 + 4,
    
    [active](x0) = 3x0 + 2,
    
    [2nd](x0) = 4x0 + 3,
    
    [cons1](x0, x1) = x0 + x1,
    
    [cons](x0, x1) = 2x0 + 2x1 + 1
   orientation:
    from#(mark(X)) = 3X + 12 >= 3X = from#(X)
    
    from#(ok(X)) = 3X + 21 >= 3X = from#(X)
    
    active(2nd(cons1(X,cons(Y,Z)))) = 12X + 24Y + 24Z + 23 >= Y + 4 = mark(Y)
    
    active(2nd(cons(X,X1))) = 24X + 24X1 + 23 >= 4X + 4X1 + 7 = mark(2nd(cons1(X,X1)))
    
    active(from(X)) = 12X + 11 >= 10X + 11 = mark(cons(X,from(s(X))))
    
    active(2nd(X)) = 12X + 11 >= 12X + 11 = 2nd(active(X))
    
    active(cons(X1,X2)) = 6X1 + 6X2 + 5 >= 6X1 + 2X2 + 5 = cons(active(X1),X2)
    
    active(from(X)) = 12X + 11 >= 12X + 11 = from(active(X))
    
    active(s(X)) = 3X + 2 >= 3X + 2 = s(active(X))
    
    active(cons1(X1,X2)) = 3X1 + 3X2 + 2 >= 3X1 + X2 + 2 = cons1(active(X1),X2)
    
    active(cons1(X1,X2)) = 3X1 + 3X2 + 2 >= X1 + 3X2 + 2 = cons1(X1,active(X2))
    
    2nd(mark(X)) = 4X + 19 >= 4X + 7 = mark(2nd(X))
    
    cons(mark(X1),X2) = 2X1 + 2X2 + 9 >= 2X1 + 2X2 + 5 = mark(cons(X1,X2))
    
    from(mark(X)) = 4X + 19 >= 4X + 7 = mark(from(X))
    
    s(mark(X)) = X + 4 >= X + 4 = mark(s(X))
    
    cons1(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(cons1(X1,X2))
    
    cons1(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(cons1(X1,X2))
    
    proper(2nd(X)) = 4X + 3 >= 4X + 3 = 2nd(proper(X))
    
    proper(cons(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = 4X + 3 >= 4X + 3 = from(proper(X))
    
    proper(s(X)) = X >= X = s(proper(X))
    
    proper(cons1(X1,X2)) = X1 + X2 >= X1 + X2 = cons1(proper(X1),proper(X2))
    
    2nd(ok(X)) = 4X + 31 >= 4X + 10 = ok(2nd(X))
    
    cons(ok(X1),ok(X2)) = 2X1 + 2X2 + 29 >= 2X1 + 2X2 + 8 = ok(cons(X1,X2))
    
    from(ok(X)) = 4X + 31 >= 4X + 10 = ok(from(X))
    
    s(ok(X)) = X + 7 >= X + 7 = ok(s(X))
    
    cons1(ok(X1),ok(X2)) = X1 + X2 + 14 >= X1 + X2 + 7 = ok(cons1(X1,X2))
    
    top(mark(X)) = 0 >= 0 = top(proper(X))
    
    top(ok(X)) = 0 >= 0 = top(active(X))
   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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [cons#](x0, x1) = 3x0,
    
    [top](x0) = 6,
    
    [ok](x0) = 2x0 + 7,
    
    [proper](x0) = 4x0,
    
    [s](x0) = 2x0 + 1,
    
    [from](x0) = 3x0 + 3,
    
    [mark](x0) = x0 + 1,
    
    [active](x0) = 4x0 + 2,
    
    [2nd](x0) = 4x0 + 2,
    
    [cons1](x0, x1) = x0 + x1,
    
    [cons](x0, x1) = x0 + x1
   orientation:
    cons#(mark(X1),X2) = 3X1 + 3 >= 3X1 = cons#(X1,X2)
    
    cons#(ok(X1),ok(X2)) = 6X1 + 21 >= 3X1 = cons#(X1,X2)
    
    active(2nd(cons1(X,cons(Y,Z)))) = 16X + 16Y + 16Z + 10 >= Y + 1 = mark(Y)
    
    active(2nd(cons(X,X1))) = 16X + 16X1 + 10 >= 4X + 4X1 + 3 = mark(2nd(cons1(X,X1)))
    
    active(from(X)) = 12X + 14 >= 7X + 7 = mark(cons(X,from(s(X))))
    
    active(2nd(X)) = 16X + 10 >= 16X + 10 = 2nd(active(X))
    
    active(cons(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + X2 + 2 = cons(active(X1),X2)
    
    active(from(X)) = 12X + 14 >= 12X + 9 = from(active(X))
    
    active(s(X)) = 8X + 6 >= 8X + 5 = s(active(X))
    
    active(cons1(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + X2 + 2 = cons1(active(X1),X2)
    
    active(cons1(X1,X2)) = 4X1 + 4X2 + 2 >= X1 + 4X2 + 2 = cons1(X1,active(X2))
    
    2nd(mark(X)) = 4X + 6 >= 4X + 3 = mark(2nd(X))
    
    cons(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(cons(X1,X2))
    
    from(mark(X)) = 3X + 6 >= 3X + 4 = mark(from(X))
    
    s(mark(X)) = 2X + 3 >= 2X + 2 = mark(s(X))
    
    cons1(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(cons1(X1,X2))
    
    cons1(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(cons1(X1,X2))
    
    proper(2nd(X)) = 16X + 8 >= 16X + 2 = 2nd(proper(X))
    
    proper(cons(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = 12X + 12 >= 12X + 3 = from(proper(X))
    
    proper(s(X)) = 8X + 4 >= 8X + 1 = s(proper(X))
    
    proper(cons1(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons1(proper(X1),proper(X2))
    
    2nd(ok(X)) = 8X + 30 >= 8X + 11 = ok(2nd(X))
    
    cons(ok(X1),ok(X2)) = 2X1 + 2X2 + 14 >= 2X1 + 2X2 + 7 = ok(cons(X1,X2))
    
    from(ok(X)) = 6X + 24 >= 6X + 13 = ok(from(X))
    
    s(ok(X)) = 4X + 15 >= 4X + 9 = ok(s(X))
    
    cons1(ok(X1),ok(X2)) = 2X1 + 2X2 + 14 >= 2X1 + 2X2 + 7 = ok(cons1(X1,X2))
    
    top(mark(X)) = 6 >= 6 = top(proper(X))
    
    top(ok(X)) = 6 >= 6 = top(active(X))
   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))
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [2nd#](x0) = x0,
   
   [top](x0) = 1,
   
   [ok](x0) = x0 + 2,
   
   [proper](x0) = x0,
   
   [s](x0) = x0 + 1,
   
   [from](x0) = 2x0 + 2,
   
   [mark](x0) = x0 + 1/2,
   
   [active](x0) = 3x0 + 5/2,
   
   [2nd](x0) = x0 + 7/2,
   
   [cons1](x0, x1) = 3x0 + 3x1 + 5/2,
   
   [cons](x0, x1) = x0 + 2x1
  orientation:
   2nd#(mark(X)) = X + 1/2 >= X = 2nd#(X)
   
   2nd#(ok(X)) = X + 2 >= X = 2nd#(X)
   
   active(2nd(cons1(X,cons(Y,Z)))) = 9X + 9Y + 18Z + 41/2 >= Y + 1/2 = mark(Y)
   
   active(2nd(cons(X,X1))) = 3X + 6X1 + 13 >= 3X + 3X1 + 13/2 = mark(2nd(cons1(X,X1)))
   
   active(from(X)) = 6X + 17/2 >= 5X + 17/2 = mark(cons(X,from(s(X))))
   
   active(2nd(X)) = 3X + 13 >= 3X + 6 = 2nd(active(X))
   
   active(cons(X1,X2)) = 3X1 + 6X2 + 5/2 >= 3X1 + 2X2 + 5/2 = cons(active(X1),X2)
   
   active(from(X)) = 6X + 17/2 >= 6X + 7 = from(active(X))
   
   active(s(X)) = 3X + 11/2 >= 3X + 7/2 = s(active(X))
   
   active(cons1(X1,X2)) = 9X1 + 9X2 + 10 >= 9X1 + 3X2 + 10 = cons1(active(X1),X2)
   
   active(cons1(X1,X2)) = 9X1 + 9X2 + 10 >= 3X1 + 9X2 + 10 = cons1(X1,active(X2))
   
   2nd(mark(X)) = X + 4 >= X + 4 = mark(2nd(X))
   
   cons(mark(X1),X2) = X1 + 2X2 + 1/2 >= X1 + 2X2 + 1/2 = mark(cons(X1,X2))
   
   from(mark(X)) = 2X + 3 >= 2X + 5/2 = mark(from(X))
   
   s(mark(X)) = X + 3/2 >= X + 3/2 = mark(s(X))
   
   cons1(mark(X1),X2) = 3X1 + 3X2 + 4 >= 3X1 + 3X2 + 3 = mark(cons1(X1,X2))
   
   cons1(X1,mark(X2)) = 3X1 + 3X2 + 4 >= 3X1 + 3X2 + 3 = mark(cons1(X1,X2))
   
   proper(2nd(X)) = X + 7/2 >= X + 7/2 = 2nd(proper(X))
   
   proper(cons(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = cons(proper(X1),proper(X2))
   
   proper(from(X)) = 2X + 2 >= 2X + 2 = from(proper(X))
   
   proper(s(X)) = X + 1 >= X + 1 = s(proper(X))
   
   proper(cons1(X1,X2)) = 3X1 + 3X2 + 5/2 >= 3X1 + 3X2 + 5/2 = cons1(proper(X1),proper(X2))
   
   2nd(ok(X)) = X + 11/2 >= X + 11/2 = ok(2nd(X))
   
   cons(ok(X1),ok(X2)) = X1 + 2X2 + 6 >= X1 + 2X2 + 2 = ok(cons(X1,X2))
   
   from(ok(X)) = 2X + 6 >= 2X + 4 = ok(from(X))
   
   s(ok(X)) = X + 3 >= X + 3 = ok(s(X))
   
   cons1(ok(X1),ok(X2)) = 3X1 + 3X2 + 29/2 >= 3X1 + 3X2 + 9/2 = ok(cons1(X1,X2))
   
   top(mark(X)) = 1 >= 1 = top(proper(X))
   
   top(ok(X)) = 1 >= 1 = top(active(X))
  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