MAYBE

Problem:
 active(nats()) -> mark(adx(zeros()))
 active(zeros()) -> mark(cons(0(),zeros()))
 active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
 active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
 active(hd(cons(X,Y))) -> mark(X)
 active(tl(cons(X,Y))) -> mark(Y)
 active(adx(X)) -> adx(active(X))
 active(incr(X)) -> incr(active(X))
 active(hd(X)) -> hd(active(X))
 active(tl(X)) -> tl(active(X))
 adx(mark(X)) -> mark(adx(X))
 incr(mark(X)) -> mark(incr(X))
 hd(mark(X)) -> mark(hd(X))
 tl(mark(X)) -> mark(tl(X))
 proper(nats()) -> ok(nats())
 proper(adx(X)) -> adx(proper(X))
 proper(zeros()) -> ok(zeros())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(incr(X)) -> incr(proper(X))
 proper(s(X)) -> s(proper(X))
 proper(hd(X)) -> hd(proper(X))
 proper(tl(X)) -> tl(proper(X))
 adx(ok(X)) -> ok(adx(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 incr(ok(X)) -> ok(incr(X))
 s(ok(X)) -> ok(s(X))
 hd(ok(X)) -> ok(hd(X))
 tl(ok(X)) -> ok(tl(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(nats()) -> adx#(zeros())
   active#(zeros()) -> cons#(0(),zeros())
   active#(incr(cons(X,Y))) -> incr#(Y)
   active#(incr(cons(X,Y))) -> s#(X)
   active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
   active#(adx(cons(X,Y))) -> adx#(Y)
   active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
   active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
   active#(adx(X)) -> active#(X)
   active#(adx(X)) -> adx#(active(X))
   active#(incr(X)) -> active#(X)
   active#(incr(X)) -> incr#(active(X))
   active#(hd(X)) -> active#(X)
   active#(hd(X)) -> hd#(active(X))
   active#(tl(X)) -> active#(X)
   active#(tl(X)) -> tl#(active(X))
   adx#(mark(X)) -> adx#(X)
   incr#(mark(X)) -> incr#(X)
   hd#(mark(X)) -> hd#(X)
   tl#(mark(X)) -> tl#(X)
   proper#(adx(X)) -> proper#(X)
   proper#(adx(X)) -> adx#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(incr(X)) -> proper#(X)
   proper#(incr(X)) -> incr#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(hd(X)) -> proper#(X)
   proper#(hd(X)) -> hd#(proper(X))
   proper#(tl(X)) -> proper#(X)
   proper#(tl(X)) -> tl#(proper(X))
   adx#(ok(X)) -> adx#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   incr#(ok(X)) -> incr#(X)
   s#(ok(X)) -> s#(X)
   hd#(ok(X)) -> hd#(X)
   tl#(ok(X)) -> tl#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(nats()) -> mark(adx(zeros()))
   active(zeros()) -> mark(cons(0(),zeros()))
   active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
   active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
   active(hd(cons(X,Y))) -> mark(X)
   active(tl(cons(X,Y))) -> mark(Y)
   active(adx(X)) -> adx(active(X))
   active(incr(X)) -> incr(active(X))
   active(hd(X)) -> hd(active(X))
   active(tl(X)) -> tl(active(X))
   adx(mark(X)) -> mark(adx(X))
   incr(mark(X)) -> mark(incr(X))
   hd(mark(X)) -> mark(hd(X))
   tl(mark(X)) -> mark(tl(X))
   proper(nats()) -> ok(nats())
   proper(adx(X)) -> adx(proper(X))
   proper(zeros()) -> ok(zeros())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(incr(X)) -> incr(proper(X))
   proper(s(X)) -> s(proper(X))
   proper(hd(X)) -> hd(proper(X))
   proper(tl(X)) -> tl(proper(X))
   adx(ok(X)) -> ok(adx(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   incr(ok(X)) -> ok(incr(X))
   s(ok(X)) -> ok(s(X))
   hd(ok(X)) -> ok(hd(X))
   tl(ok(X)) -> ok(tl(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(nats()) -> adx#(zeros())
    active#(zeros()) -> cons#(0(),zeros())
    active#(incr(cons(X,Y))) -> incr#(Y)
    active#(incr(cons(X,Y))) -> s#(X)
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
    active#(adx(cons(X,Y))) -> adx#(Y)
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
    active#(adx(X)) -> active#(X)
    active#(adx(X)) -> adx#(active(X))
    active#(incr(X)) -> active#(X)
    active#(incr(X)) -> incr#(active(X))
    active#(hd(X)) -> active#(X)
    active#(hd(X)) -> hd#(active(X))
    active#(tl(X)) -> active#(X)
    active#(tl(X)) -> tl#(active(X))
    adx#(mark(X)) -> adx#(X)
    incr#(mark(X)) -> incr#(X)
    hd#(mark(X)) -> hd#(X)
    tl#(mark(X)) -> tl#(X)
    proper#(adx(X)) -> proper#(X)
    proper#(adx(X)) -> adx#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(incr(X)) -> proper#(X)
    proper#(incr(X)) -> incr#(proper(X))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(hd(X)) -> proper#(X)
    proper#(hd(X)) -> hd#(proper(X))
    proper#(tl(X)) -> proper#(X)
    proper#(tl(X)) -> tl#(proper(X))
    adx#(ok(X)) -> adx#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    incr#(ok(X)) -> incr#(X)
    s#(ok(X)) -> s#(X)
    hd#(ok(X)) -> hd#(X)
    tl#(ok(X)) -> tl#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(nats()) -> mark(adx(zeros()))
    active(zeros()) -> mark(cons(0(),zeros()))
    active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
    active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
    active(hd(cons(X,Y))) -> mark(X)
    active(tl(cons(X,Y))) -> mark(Y)
    active(adx(X)) -> adx(active(X))
    active(incr(X)) -> incr(active(X))
    active(hd(X)) -> hd(active(X))
    active(tl(X)) -> tl(active(X))
    adx(mark(X)) -> mark(adx(X))
    incr(mark(X)) -> mark(incr(X))
    hd(mark(X)) -> mark(hd(X))
    tl(mark(X)) -> mark(tl(X))
    proper(nats()) -> ok(nats())
    proper(adx(X)) -> adx(proper(X))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(incr(X)) -> incr(proper(X))
    proper(s(X)) -> s(proper(X))
    proper(hd(X)) -> hd(proper(X))
    proper(tl(X)) -> tl(proper(X))
    adx(ok(X)) -> ok(adx(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    incr(ok(X)) -> ok(incr(X))
    s(ok(X)) -> ok(s(X))
    hd(ok(X)) -> ok(hd(X))
    tl(ok(X)) -> ok(tl(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) -> active#(tl(X)) -> tl#(active(X))
    top#(ok(X)) -> active#(X) -> active#(tl(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(hd(X)) -> hd#(active(X))
    top#(ok(X)) -> active#(X) -> active#(hd(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(incr(X)) -> incr#(active(X))
    top#(ok(X)) -> active#(X) -> active#(incr(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(adx(X)) -> adx#(active(X))
    top#(ok(X)) -> active#(X) -> active#(adx(X)) -> active#(X)
    top#(ok(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
    top#(ok(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
    top#(ok(X)) -> active#(X) -> active#(adx(cons(X,Y))) -> adx#(Y)
    top#(ok(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
    top#(ok(X)) -> active#(X) -> active#(incr(cons(X,Y))) -> s#(X)
    top#(ok(X)) -> active#(X) -> active#(incr(cons(X,Y))) -> incr#(Y)
    top#(ok(X)) -> active#(X) -> active#(zeros()) -> cons#(0(),zeros())
    top#(ok(X)) -> active#(X) -> active#(nats()) -> adx#(zeros())
    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#(tl(X)) -> tl#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(tl(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(hd(X)) -> hd#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(hd(X)) -> proper#(X)
    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#(incr(X)) -> incr#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(incr(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#(adx(X)) -> adx#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(adx(X)) -> proper#(X)
    proper#(tl(X)) -> proper#(X) -> proper#(tl(X)) -> tl#(proper(X))
    proper#(tl(X)) -> proper#(X) -> proper#(tl(X)) -> proper#(X)
    proper#(tl(X)) -> proper#(X) -> proper#(hd(X)) -> hd#(proper(X))
    proper#(tl(X)) -> proper#(X) -> proper#(hd(X)) -> proper#(X)
    proper#(tl(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(tl(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(tl(X)) -> proper#(X) ->
    proper#(incr(X)) -> incr#(proper(X))
    proper#(tl(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X)
    proper#(tl(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(tl(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(tl(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(tl(X)) -> proper#(X) -> proper#(adx(X)) -> adx#(proper(X))
    proper#(tl(X)) -> proper#(X) -> proper#(adx(X)) -> proper#(X)
    proper#(tl(X)) -> tl#(proper(X)) -> tl#(ok(X)) -> tl#(X)
    proper#(tl(X)) -> tl#(proper(X)) -> tl#(mark(X)) -> tl#(X)
    proper#(hd(X)) -> proper#(X) -> proper#(tl(X)) -> tl#(proper(X))
    proper#(hd(X)) -> proper#(X) -> proper#(tl(X)) -> proper#(X)
    proper#(hd(X)) -> proper#(X) -> proper#(hd(X)) -> hd#(proper(X))
    proper#(hd(X)) -> proper#(X) -> proper#(hd(X)) -> proper#(X)
    proper#(hd(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(hd(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(hd(X)) -> proper#(X) ->
    proper#(incr(X)) -> incr#(proper(X))
    proper#(hd(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X)
    proper#(hd(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(hd(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(hd(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(hd(X)) -> proper#(X) -> proper#(adx(X)) -> adx#(proper(X))
    proper#(hd(X)) -> proper#(X) -> proper#(adx(X)) -> proper#(X)
    proper#(hd(X)) -> hd#(proper(X)) -> hd#(ok(X)) -> hd#(X)
    proper#(hd(X)) -> hd#(proper(X)) -> hd#(mark(X)) -> hd#(X)
    proper#(s(X)) -> proper#(X) -> proper#(tl(X)) -> tl#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(tl(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) -> proper#(hd(X)) -> hd#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(hd(X)) -> proper#(X)
    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#(incr(X)) -> incr#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(incr(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#(adx(X)) -> adx#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(adx(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    proper#(incr(X)) -> proper#(X) ->
    proper#(tl(X)) -> tl#(proper(X))
    proper#(incr(X)) -> proper#(X) -> proper#(tl(X)) -> proper#(X)
    proper#(incr(X)) -> proper#(X) ->
    proper#(hd(X)) -> hd#(proper(X))
    proper#(incr(X)) -> proper#(X) -> proper#(hd(X)) -> proper#(X)
    proper#(incr(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(incr(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(incr(X)) -> proper#(X) ->
    proper#(incr(X)) -> incr#(proper(X))
    proper#(incr(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X)
    proper#(incr(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(incr(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(incr(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(incr(X)) -> proper#(X) ->
    proper#(adx(X)) -> adx#(proper(X))
    proper#(incr(X)) -> proper#(X) ->
    proper#(adx(X)) -> proper#(X)
    proper#(incr(X)) -> incr#(proper(X)) ->
    incr#(ok(X)) -> incr#(X)
    proper#(incr(X)) -> incr#(proper(X)) ->
    incr#(mark(X)) -> incr#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(tl(X)) -> tl#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(tl(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(hd(X)) -> hd#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(hd(X)) -> proper#(X)
    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#(incr(X)) -> incr#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(incr(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#(adx(X)) -> adx#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(adx(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(tl(X)) -> tl#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(tl(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(hd(X)) -> hd#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(hd(X)) -> proper#(X)
    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#(incr(X)) -> incr#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(incr(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#(adx(X)) -> adx#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(adx(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    proper#(adx(X)) -> proper#(X) -> proper#(tl(X)) -> tl#(proper(X))
    proper#(adx(X)) -> proper#(X) -> proper#(tl(X)) -> proper#(X)
    proper#(adx(X)) -> proper#(X) -> proper#(hd(X)) -> hd#(proper(X))
    proper#(adx(X)) -> proper#(X) -> proper#(hd(X)) -> proper#(X)
    proper#(adx(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(adx(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(adx(X)) -> proper#(X) ->
    proper#(incr(X)) -> incr#(proper(X))
    proper#(adx(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X)
    proper#(adx(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(adx(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(adx(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(adx(X)) -> proper#(X) ->
    proper#(adx(X)) -> adx#(proper(X))
    proper#(adx(X)) -> proper#(X) ->
    proper#(adx(X)) -> proper#(X)
    proper#(adx(X)) -> adx#(proper(X)) -> adx#(ok(X)) -> adx#(X)
    proper#(adx(X)) -> adx#(proper(X)) -> adx#(mark(X)) -> adx#(X)
    tl#(ok(X)) -> tl#(X) -> tl#(ok(X)) -> tl#(X)
    tl#(ok(X)) -> tl#(X) -> tl#(mark(X)) -> tl#(X)
    tl#(mark(X)) -> tl#(X) -> tl#(ok(X)) -> tl#(X)
    tl#(mark(X)) -> tl#(X) -> tl#(mark(X)) -> tl#(X)
    hd#(ok(X)) -> hd#(X) -> hd#(ok(X)) -> hd#(X)
    hd#(ok(X)) -> hd#(X) -> hd#(mark(X)) -> hd#(X)
    hd#(mark(X)) -> hd#(X) -> hd#(ok(X)) -> hd#(X)
    hd#(mark(X)) -> hd#(X) -> hd#(mark(X)) -> hd#(X)
    s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    incr#(ok(X)) -> incr#(X) -> incr#(ok(X)) -> incr#(X)
    incr#(ok(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X)
    incr#(mark(X)) -> incr#(X) -> incr#(ok(X)) -> incr#(X)
    incr#(mark(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    adx#(ok(X)) -> adx#(X) -> adx#(ok(X)) -> adx#(X)
    adx#(ok(X)) -> adx#(X) -> adx#(mark(X)) -> adx#(X)
    adx#(mark(X)) -> adx#(X) -> adx#(ok(X)) -> adx#(X)
    adx#(mark(X)) -> adx#(X) -> adx#(mark(X)) -> adx#(X)
    active#(tl(X)) -> tl#(active(X)) -> tl#(ok(X)) -> tl#(X)
    active#(tl(X)) -> tl#(active(X)) -> tl#(mark(X)) -> tl#(X)
    active#(tl(X)) -> active#(X) -> active#(tl(X)) -> tl#(active(X))
    active#(tl(X)) -> active#(X) -> active#(tl(X)) -> active#(X)
    active#(tl(X)) -> active#(X) -> active#(hd(X)) -> hd#(active(X))
    active#(tl(X)) -> active#(X) -> active#(hd(X)) -> active#(X)
    active#(tl(X)) -> active#(X) ->
    active#(incr(X)) -> incr#(active(X))
    active#(tl(X)) -> active#(X) -> active#(incr(X)) -> active#(X)
    active#(tl(X)) -> active#(X) -> active#(adx(X)) -> adx#(active(X))
    active#(tl(X)) -> active#(X) -> active#(adx(X)) -> active#(X)
    active#(tl(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
    active#(tl(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
    active#(tl(X)) -> active#(X) -> active#(adx(cons(X,Y))) -> adx#(Y)
    active#(tl(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
    active#(tl(X)) -> active#(X) -> active#(incr(cons(X,Y))) -> s#(X)
    active#(tl(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> incr#(Y)
    active#(tl(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(tl(X)) -> active#(X) ->
    active#(nats()) -> adx#(zeros())
    active#(hd(X)) -> hd#(active(X)) -> hd#(ok(X)) -> hd#(X)
    active#(hd(X)) -> hd#(active(X)) -> hd#(mark(X)) -> hd#(X)
    active#(hd(X)) -> active#(X) -> active#(tl(X)) -> tl#(active(X))
    active#(hd(X)) -> active#(X) -> active#(tl(X)) -> active#(X)
    active#(hd(X)) -> active#(X) -> active#(hd(X)) -> hd#(active(X))
    active#(hd(X)) -> active#(X) -> active#(hd(X)) -> active#(X)
    active#(hd(X)) -> active#(X) ->
    active#(incr(X)) -> incr#(active(X))
    active#(hd(X)) -> active#(X) -> active#(incr(X)) -> active#(X)
    active#(hd(X)) -> active#(X) -> active#(adx(X)) -> adx#(active(X))
    active#(hd(X)) -> active#(X) -> active#(adx(X)) -> active#(X)
    active#(hd(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
    active#(hd(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
    active#(hd(X)) -> active#(X) -> active#(adx(cons(X,Y))) -> adx#(Y)
    active#(hd(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
    active#(hd(X)) -> active#(X) -> active#(incr(cons(X,Y))) -> s#(X)
    active#(hd(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> incr#(Y)
    active#(hd(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(hd(X)) -> active#(X) ->
    active#(nats()) -> adx#(zeros())
    active#(incr(cons(X,Y))) -> s#(X) -> s#(ok(X)) -> s#(X)
    active#(incr(cons(X,Y))) -> incr#(Y) ->
    incr#(ok(X)) -> incr#(X)
    active#(incr(cons(X,Y))) -> incr#(Y) ->
    incr#(mark(X)) -> incr#(X)
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(incr(X)) -> incr#(active(X)) ->
    incr#(ok(X)) -> incr#(X)
    active#(incr(X)) -> incr#(active(X)) ->
    incr#(mark(X)) -> incr#(X)
    active#(incr(X)) -> active#(X) ->
    active#(tl(X)) -> tl#(active(X))
    active#(incr(X)) -> active#(X) -> active#(tl(X)) -> active#(X)
    active#(incr(X)) -> active#(X) ->
    active#(hd(X)) -> hd#(active(X))
    active#(incr(X)) -> active#(X) -> active#(hd(X)) -> active#(X)
    active#(incr(X)) -> active#(X) ->
    active#(incr(X)) -> incr#(active(X))
    active#(incr(X)) -> active#(X) -> active#(incr(X)) -> active#(X)
    active#(incr(X)) -> active#(X) ->
    active#(adx(X)) -> adx#(active(X))
    active#(incr(X)) -> active#(X) -> active#(adx(X)) -> active#(X)
    active#(incr(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
    active#(incr(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
    active#(incr(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> adx#(Y)
    active#(incr(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
    active#(incr(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> s#(X)
    active#(incr(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> incr#(Y)
    active#(incr(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(incr(X)) -> active#(X) ->
    active#(nats()) -> adx#(zeros())
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) ->
    incr#(ok(X)) -> incr#(X)
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) ->
    incr#(mark(X)) -> incr#(X)
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(adx(cons(X,Y))) -> adx#(Y) -> adx#(ok(X)) -> adx#(X)
    active#(adx(cons(X,Y))) -> adx#(Y) ->
    adx#(mark(X)) -> adx#(X)
    active#(adx(X)) -> adx#(active(X)) -> adx#(ok(X)) -> adx#(X)
    active#(adx(X)) -> adx#(active(X)) -> adx#(mark(X)) -> adx#(X)
    active#(adx(X)) -> active#(X) -> active#(tl(X)) -> tl#(active(X))
    active#(adx(X)) -> active#(X) -> active#(tl(X)) -> active#(X)
    active#(adx(X)) -> active#(X) -> active#(hd(X)) -> hd#(active(X))
    active#(adx(X)) -> active#(X) -> active#(hd(X)) -> active#(X)
    active#(adx(X)) -> active#(X) ->
    active#(incr(X)) -> incr#(active(X))
    active#(adx(X)) -> active#(X) -> active#(incr(X)) -> active#(X)
    active#(adx(X)) -> active#(X) ->
    active#(adx(X)) -> adx#(active(X))
    active#(adx(X)) -> active#(X) -> active#(adx(X)) -> active#(X)
    active#(adx(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y)))
    active#(adx(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> cons#(X,adx(Y))
    active#(adx(X)) -> active#(X) ->
    active#(adx(cons(X,Y))) -> adx#(Y)
    active#(adx(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y))
    active#(adx(X)) -> active#(X) -> active#(incr(cons(X,Y))) -> s#(X)
    active#(adx(X)) -> active#(X) ->
    active#(incr(cons(X,Y))) -> incr#(Y)
    active#(adx(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(adx(X)) -> active#(X) ->
    active#(nats()) -> adx#(zeros())
    active#(zeros()) -> cons#(0(),zeros()) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(nats()) -> adx#(zeros()) -> adx#(ok(X)) -> adx#(X)
    active#(nats()) -> adx#(zeros()) -> adx#(mark(X)) -> adx#(X)
   SCC Processor:
    #sccs: 9
    #rules: 23
    #arcs: 240/1849
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(adx(X)) -> active#(X)
     active#(incr(X)) -> active#(X)
     active#(hd(X)) -> active#(X)
     active#(tl(X)) -> active#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(adx(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(incr(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X)
     proper#(hd(X)) -> proper#(X)
     proper#(tl(X)) -> proper#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     tl#(mark(X)) -> tl#(X)
     tl#(ok(X)) -> tl#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(tl#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     hd#(mark(X)) -> hd#(X)
     hd#(ok(X)) -> hd#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(hd#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     s#(ok(X)) -> s#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(s#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     incr#(mark(X)) -> incr#(X)
     incr#(ok(X)) -> incr#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(incr#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(cons#) = 1
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     adx#(mark(X)) -> adx#(X)
     adx#(ok(X)) -> adx#(X)
    TRS:
     active(nats()) -> mark(adx(zeros()))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
     active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
     active(hd(cons(X,Y))) -> mark(X)
     active(tl(cons(X,Y))) -> mark(Y)
     active(adx(X)) -> adx(active(X))
     active(incr(X)) -> incr(active(X))
     active(hd(X)) -> hd(active(X))
     active(tl(X)) -> tl(active(X))
     adx(mark(X)) -> mark(adx(X))
     incr(mark(X)) -> mark(incr(X))
     hd(mark(X)) -> mark(hd(X))
     tl(mark(X)) -> mark(tl(X))
     proper(nats()) -> ok(nats())
     proper(adx(X)) -> adx(proper(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(incr(X)) -> incr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(hd(X)) -> hd(proper(X))
     proper(tl(X)) -> tl(proper(X))
     adx(ok(X)) -> ok(adx(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     incr(ok(X)) -> ok(incr(X))
     s(ok(X)) -> ok(s(X))
     hd(ok(X)) -> ok(hd(X))
     tl(ok(X)) -> ok(tl(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(adx#) = 0
     problem:
      DPs:
       
      TRS:
       active(nats()) -> mark(adx(zeros()))
       active(zeros()) -> mark(cons(0(),zeros()))
       active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
       active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
       active(hd(cons(X,Y))) -> mark(X)
       active(tl(cons(X,Y))) -> mark(Y)
       active(adx(X)) -> adx(active(X))
       active(incr(X)) -> incr(active(X))
       active(hd(X)) -> hd(active(X))
       active(tl(X)) -> tl(active(X))
       adx(mark(X)) -> mark(adx(X))
       incr(mark(X)) -> mark(incr(X))
       hd(mark(X)) -> mark(hd(X))
       tl(mark(X)) -> mark(tl(X))
       proper(nats()) -> ok(nats())
       proper(adx(X)) -> adx(proper(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(incr(X)) -> incr(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(hd(X)) -> hd(proper(X))
       proper(tl(X)) -> tl(proper(X))
       adx(ok(X)) -> ok(adx(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       incr(ok(X)) -> ok(incr(X))
       s(ok(X)) -> ok(s(X))
       hd(ok(X)) -> ok(hd(X))
       tl(ok(X)) -> ok(tl(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed