MAYBE

Problem:
 active(dbl(0())) -> mark(0())
 active(dbl(s(X))) -> mark(s(s(dbl(X))))
 active(dbls(nil())) -> mark(nil())
 active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
 active(sel(0(),cons(X,Y))) -> mark(X)
 active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
 active(indx(nil(),X)) -> mark(nil())
 active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(dbl(X)) -> dbl(active(X))
 active(dbls(X)) -> dbls(active(X))
 active(sel(X1,X2)) -> sel(active(X1),X2)
 active(sel(X1,X2)) -> sel(X1,active(X2))
 active(indx(X1,X2)) -> indx(active(X1),X2)
 dbl(mark(X)) -> mark(dbl(X))
 dbls(mark(X)) -> mark(dbls(X))
 sel(mark(X1),X2) -> mark(sel(X1,X2))
 sel(X1,mark(X2)) -> mark(sel(X1,X2))
 indx(mark(X1),X2) -> mark(indx(X1,X2))
 proper(dbl(X)) -> dbl(proper(X))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(dbls(X)) -> dbls(proper(X))
 proper(nil()) -> ok(nil())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
 proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 dbl(ok(X)) -> ok(dbl(X))
 s(ok(X)) -> ok(s(X))
 dbls(ok(X)) -> ok(dbls(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
 indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
 from(ok(X)) -> ok(from(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(dbl(s(X))) -> dbl#(X)
   active#(dbl(s(X))) -> s#(dbl(X))
   active#(dbl(s(X))) -> s#(s(dbl(X)))
   active#(dbls(cons(X,Y))) -> dbls#(Y)
   active#(dbls(cons(X,Y))) -> dbl#(X)
   active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
   active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
   active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
   active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
   active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(dbl(X)) -> active#(X)
   active#(dbl(X)) -> dbl#(active(X))
   active#(dbls(X)) -> active#(X)
   active#(dbls(X)) -> dbls#(active(X))
   active#(sel(X1,X2)) -> active#(X1)
   active#(sel(X1,X2)) -> sel#(active(X1),X2)
   active#(sel(X1,X2)) -> active#(X2)
   active#(sel(X1,X2)) -> sel#(X1,active(X2))
   active#(indx(X1,X2)) -> active#(X1)
   active#(indx(X1,X2)) -> indx#(active(X1),X2)
   dbl#(mark(X)) -> dbl#(X)
   dbls#(mark(X)) -> dbls#(X)
   sel#(mark(X1),X2) -> sel#(X1,X2)
   sel#(X1,mark(X2)) -> sel#(X1,X2)
   indx#(mark(X1),X2) -> indx#(X1,X2)
   proper#(dbl(X)) -> proper#(X)
   proper#(dbl(X)) -> dbl#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(dbls(X)) -> proper#(X)
   proper#(dbls(X)) -> dbls#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(sel(X1,X2)) -> proper#(X2)
   proper#(sel(X1,X2)) -> proper#(X1)
   proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
   proper#(indx(X1,X2)) -> proper#(X2)
   proper#(indx(X1,X2)) -> proper#(X1)
   proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
   proper#(from(X)) -> proper#(X)
   proper#(from(X)) -> from#(proper(X))
   dbl#(ok(X)) -> dbl#(X)
   s#(ok(X)) -> s#(X)
   dbls#(ok(X)) -> dbls#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
   indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
   from#(ok(X)) -> from#(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(dbl(0())) -> mark(0())
   active(dbl(s(X))) -> mark(s(s(dbl(X))))
   active(dbls(nil())) -> mark(nil())
   active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
   active(sel(0(),cons(X,Y))) -> mark(X)
   active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
   active(indx(nil(),X)) -> mark(nil())
   active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(dbl(X)) -> dbl(active(X))
   active(dbls(X)) -> dbls(active(X))
   active(sel(X1,X2)) -> sel(active(X1),X2)
   active(sel(X1,X2)) -> sel(X1,active(X2))
   active(indx(X1,X2)) -> indx(active(X1),X2)
   dbl(mark(X)) -> mark(dbl(X))
   dbls(mark(X)) -> mark(dbls(X))
   sel(mark(X1),X2) -> mark(sel(X1,X2))
   sel(X1,mark(X2)) -> mark(sel(X1,X2))
   indx(mark(X1),X2) -> mark(indx(X1,X2))
   proper(dbl(X)) -> dbl(proper(X))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   proper(dbls(X)) -> dbls(proper(X))
   proper(nil()) -> ok(nil())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
   proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   dbl(ok(X)) -> ok(dbl(X))
   s(ok(X)) -> ok(s(X))
   dbls(ok(X)) -> ok(dbls(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
   indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
   from(ok(X)) -> ok(from(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(dbl(s(X))) -> dbl#(X)
    active#(dbl(s(X))) -> s#(dbl(X))
    active#(dbl(s(X))) -> s#(s(dbl(X)))
    active#(dbls(cons(X,Y))) -> dbls#(Y)
    active#(dbls(cons(X,Y))) -> dbl#(X)
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    active#(from(X)) -> s#(X)
    active#(from(X)) -> from#(s(X))
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(dbl(X)) -> active#(X)
    active#(dbl(X)) -> dbl#(active(X))
    active#(dbls(X)) -> active#(X)
    active#(dbls(X)) -> dbls#(active(X))
    active#(sel(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X2)
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(indx(X1,X2)) -> active#(X1)
    active#(indx(X1,X2)) -> indx#(active(X1),X2)
    dbl#(mark(X)) -> dbl#(X)
    dbls#(mark(X)) -> dbls#(X)
    sel#(mark(X1),X2) -> sel#(X1,X2)
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    indx#(mark(X1),X2) -> indx#(X1,X2)
    proper#(dbl(X)) -> proper#(X)
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(dbls(X)) -> proper#(X)
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X))
    dbl#(ok(X)) -> dbl#(X)
    s#(ok(X)) -> s#(X)
    dbls#(ok(X)) -> dbls#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    from#(ok(X)) -> from#(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(dbl(0())) -> mark(0())
    active(dbl(s(X))) -> mark(s(s(dbl(X))))
    active(dbls(nil())) -> mark(nil())
    active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
    active(sel(0(),cons(X,Y))) -> mark(X)
    active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
    active(indx(nil(),X)) -> mark(nil())
    active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(dbl(X)) -> dbl(active(X))
    active(dbls(X)) -> dbls(active(X))
    active(sel(X1,X2)) -> sel(active(X1),X2)
    active(sel(X1,X2)) -> sel(X1,active(X2))
    active(indx(X1,X2)) -> indx(active(X1),X2)
    dbl(mark(X)) -> mark(dbl(X))
    dbls(mark(X)) -> mark(dbls(X))
    sel(mark(X1),X2) -> mark(sel(X1,X2))
    sel(X1,mark(X2)) -> mark(sel(X1,X2))
    indx(mark(X1),X2) -> mark(indx(X1,X2))
    proper(dbl(X)) -> dbl(proper(X))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    proper(dbls(X)) -> dbls(proper(X))
    proper(nil()) -> ok(nil())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
    proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    dbl(ok(X)) -> ok(dbl(X))
    s(ok(X)) -> ok(s(X))
    dbls(ok(X)) -> ok(dbls(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
    indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
    from(ok(X)) -> ok(from(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#(indx(X1,X2)) -> indx#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(indx(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(dbls(X)) -> dbls#(active(X))
    top#(ok(X)) -> active#(X) -> active#(dbls(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(dbl(X)) -> dbl#(active(X))
    top#(ok(X)) -> active#(X) -> active#(dbl(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#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    top#(ok(X)) -> active#(X) -> active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    top#(ok(X)) -> active#(X) -> active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    top#(ok(X)) -> active#(X) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    top#(ok(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    top#(ok(X)) -> active#(X) -> active#(dbls(cons(X,Y))) -> dbl#(X)
    top#(ok(X)) -> active#(X) -> active#(dbls(cons(X,Y))) -> dbls#(Y)
    top#(ok(X)) -> active#(X) -> active#(dbl(s(X))) -> s#(s(dbl(X)))
    top#(ok(X)) -> active#(X) -> active#(dbl(s(X))) -> s#(dbl(X))
    top#(ok(X)) -> active#(X) -> active#(dbl(s(X))) -> dbl#(X)
    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#(from(X)) -> from#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(indx(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(indx(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) -> proper#(dbls(X)) -> dbls#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(dbls(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#(dbl(X)) -> dbl#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(dbl(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#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(dbls(X)) -> proper#(X)
    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#(dbl(X)) -> dbl#(proper(X))
    proper#(from(X)) -> proper#(X) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X)) ->
    from#(ok(X)) -> from#(X)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(dbls(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X2) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(dbls(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(indx(X1,X2)) -> proper#(X1) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2)) ->
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2)) ->
    indx#(mark(X1),X2) -> indx#(X1,X2)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(dbls(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(dbls(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(dbls(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#(dbl(X)) -> dbl#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(dbl(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#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(dbls(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#(dbl(X)) -> dbl#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(dbls(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(dbls(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(dbls(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(dbls(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(dbls(X)) -> proper#(X) -> proper#(dbls(X)) -> proper#(X)
    proper#(dbls(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(dbls(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(dbls(X)) -> proper#(X) ->
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(dbls(X)) -> proper#(X) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(dbls(X)) -> dbls#(proper(X)) ->
    dbls#(ok(X)) -> dbls#(X)
    proper#(dbls(X)) -> dbls#(proper(X)) -> dbls#(mark(X)) -> dbls#(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#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(indx(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(indx(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) -> proper#(dbls(X)) -> dbls#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(dbls(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#(dbl(X)) -> dbl#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(dbl(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(dbl(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> indx#(proper(X1),proper(X2))
    proper#(dbl(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> proper#(X1)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(indx(X1,X2)) -> proper#(X2)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(dbl(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(dbl(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(dbls(X)) -> dbls#(proper(X))
    proper#(dbl(X)) -> proper#(X) -> proper#(dbls(X)) -> proper#(X)
    proper#(dbl(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(dbl(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(dbl(X)) -> proper#(X) ->
    proper#(dbl(X)) -> dbl#(proper(X))
    proper#(dbl(X)) -> proper#(X) ->
    proper#(dbl(X)) -> proper#(X)
    proper#(dbl(X)) -> dbl#(proper(X)) -> dbl#(ok(X)) -> dbl#(X)
    proper#(dbl(X)) -> dbl#(proper(X)) -> dbl#(mark(X)) -> dbl#(X)
    from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2) ->
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2) ->
    indx#(mark(X1),X2) -> indx#(X1,X2)
    indx#(mark(X1),X2) -> indx#(X1,X2) ->
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    indx#(mark(X1),X2) -> indx#(X1,X2) ->
    indx#(mark(X1),X2) -> indx#(X1,X2)
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    sel#(mark(X1),X2) -> sel#(X1,X2) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    sel#(mark(X1),X2) -> sel#(X1,X2) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    sel#(mark(X1),X2) -> sel#(X1,X2) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    sel#(X1,mark(X2)) -> sel#(X1,X2) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    sel#(X1,mark(X2)) -> sel#(X1,X2) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    sel#(X1,mark(X2)) -> sel#(X1,X2) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    dbls#(ok(X)) -> dbls#(X) -> dbls#(ok(X)) -> dbls#(X)
    dbls#(ok(X)) -> dbls#(X) -> dbls#(mark(X)) -> dbls#(X)
    dbls#(mark(X)) -> dbls#(X) -> dbls#(ok(X)) -> dbls#(X)
    dbls#(mark(X)) -> dbls#(X) -> dbls#(mark(X)) -> dbls#(X)
    s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    dbl#(ok(X)) -> dbl#(X) -> dbl#(ok(X)) -> dbl#(X)
    dbl#(ok(X)) -> dbl#(X) -> dbl#(mark(X)) -> dbl#(X)
    dbl#(mark(X)) -> dbl#(X) -> dbl#(ok(X)) -> dbl#(X)
    dbl#(mark(X)) -> dbl#(X) -> dbl#(mark(X)) -> dbl#(X)
    active#(from(X)) -> from#(s(X)) ->
    from#(ok(X)) -> from#(X)
    active#(from(X)) -> cons#(X,from(s(X))) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(from(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z) ->
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z) ->
    indx#(mark(X1),X2) -> indx#(X1,X2)
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(indx(X1,X2)) -> indx#(active(X1),X2) ->
    indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    active#(indx(X1,X2)) -> indx#(active(X1),X2) ->
    indx#(mark(X1),X2) -> indx#(X1,X2)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(indx(X1,X2)) -> indx#(active(X1),X2)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(indx(X1,X2)) -> active#(X1)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> active#(X2)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> active#(X1)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbls(X)) -> dbls#(active(X))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbls(X)) -> active#(X)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbl(X)) -> dbl#(active(X))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbl(X)) -> active#(X)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbls(cons(X,Y))) -> dbl#(X)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbls(cons(X,Y))) -> dbls#(Y)
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbl(s(X))) -> s#(s(dbl(X)))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbl(s(X))) -> s#(dbl(X))
    active#(indx(X1,X2)) -> active#(X1) ->
    active#(dbl(s(X))) -> dbl#(X)
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> sel#(active(X1),X2) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> sel#(active(X1),X2) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> sel#(active(X1),X2) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> sel#(X1,active(X2)) ->
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> sel#(X1,active(X2)) ->
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> sel#(X1,active(X2)) ->
    sel#(mark(X1),X2) -> sel#(X1,X2)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(indx(X1,X2)) -> indx#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(indx(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(sel(X1,X2)) -> active#(X2)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(sel(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbls(X)) -> dbls#(active(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbls(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbl(X)) -> dbl#(active(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbl(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(s(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> s#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbls(cons(X,Y))) -> dbl#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbls(cons(X,Y))) -> dbls#(Y)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbl(s(X))) -> s#(s(dbl(X)))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbl(s(X))) -> s#(dbl(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(dbl(s(X))) -> dbl#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(indx(X1,X2)) -> indx#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(indx(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> active#(X2)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbls(X)) -> dbls#(active(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbls(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbl(X)) -> dbl#(active(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbl(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbls(cons(X,Y))) -> dbl#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbls(cons(X,Y))) -> dbls#(Y)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbl(s(X))) -> s#(s(dbl(X)))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbl(s(X))) -> s#(dbl(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(dbl(s(X))) -> dbl#(X)
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(dbls(cons(X,Y))) -> dbls#(Y) ->
    dbls#(ok(X)) -> dbls#(X)
    active#(dbls(cons(X,Y))) -> dbls#(Y) ->
    dbls#(mark(X)) -> dbls#(X)
    active#(dbls(cons(X,Y))) -> dbl#(X) ->
    dbl#(ok(X)) -> dbl#(X)
    active#(dbls(cons(X,Y))) -> dbl#(X) ->
    dbl#(mark(X)) -> dbl#(X)
    active#(dbls(X)) -> dbls#(active(X)) ->
    dbls#(ok(X)) -> dbls#(X)
    active#(dbls(X)) -> dbls#(active(X)) ->
    dbls#(mark(X)) -> dbls#(X)
    active#(dbls(X)) -> active#(X) ->
    active#(indx(X1,X2)) -> indx#(active(X1),X2)
    active#(dbls(X)) -> active#(X) ->
    active#(indx(X1,X2)) -> active#(X1)
    active#(dbls(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(dbls(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> active#(X2)
    active#(dbls(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(dbls(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> active#(X1)
    active#(dbls(X)) -> active#(X) ->
    active#(dbls(X)) -> dbls#(active(X))
    active#(dbls(X)) -> active#(X) -> active#(dbls(X)) -> active#(X)
    active#(dbls(X)) -> active#(X) ->
    active#(dbl(X)) -> dbl#(active(X))
    active#(dbls(X)) -> active#(X) -> active#(dbl(X)) -> active#(X)
    active#(dbls(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(dbls(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(dbls(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(dbls(X)) -> active#(X) ->
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    active#(dbls(X)) -> active#(X) ->
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    active#(dbls(X)) -> active#(X) ->
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    active#(dbls(X)) -> active#(X) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(dbls(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    active#(dbls(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> dbl#(X)
    active#(dbls(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> dbls#(Y)
    active#(dbls(X)) -> active#(X) ->
    active#(dbl(s(X))) -> s#(s(dbl(X)))
    active#(dbls(X)) -> active#(X) ->
    active#(dbl(s(X))) -> s#(dbl(X))
    active#(dbls(X)) -> active#(X) ->
    active#(dbl(s(X))) -> dbl#(X)
    active#(dbl(s(X))) -> s#(s(dbl(X))) -> s#(ok(X)) -> s#(X)
    active#(dbl(s(X))) -> s#(dbl(X)) -> s#(ok(X)) -> s#(X)
    active#(dbl(s(X))) -> dbl#(X) -> dbl#(ok(X)) -> dbl#(X)
    active#(dbl(s(X))) -> dbl#(X) -> dbl#(mark(X)) -> dbl#(X)
    active#(dbl(X)) -> dbl#(active(X)) -> dbl#(ok(X)) -> dbl#(X)
    active#(dbl(X)) -> dbl#(active(X)) -> dbl#(mark(X)) -> dbl#(X)
    active#(dbl(X)) -> active#(X) ->
    active#(indx(X1,X2)) -> indx#(active(X1),X2)
    active#(dbl(X)) -> active#(X) ->
    active#(indx(X1,X2)) -> active#(X1)
    active#(dbl(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(dbl(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> active#(X2)
    active#(dbl(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(dbl(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> active#(X1)
    active#(dbl(X)) -> active#(X) ->
    active#(dbls(X)) -> dbls#(active(X))
    active#(dbl(X)) -> active#(X) -> active#(dbls(X)) -> active#(X)
    active#(dbl(X)) -> active#(X) ->
    active#(dbl(X)) -> dbl#(active(X))
    active#(dbl(X)) -> active#(X) -> active#(dbl(X)) -> active#(X)
    active#(dbl(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(dbl(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(dbl(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(dbl(X)) -> active#(X) ->
    active#(indx(cons(X,Y),Z)) -> cons#(sel(X,Z),indx(Y,Z))
    active#(dbl(X)) -> active#(X) ->
    active#(indx(cons(X,Y),Z)) -> sel#(X,Z)
    active#(dbl(X)) -> active#(X) ->
    active#(indx(cons(X,Y),Z)) -> indx#(Y,Z)
    active#(dbl(X)) -> active#(X) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(dbl(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> cons#(dbl(X),dbls(Y))
    active#(dbl(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> dbl#(X)
    active#(dbl(X)) -> active#(X) ->
    active#(dbls(cons(X,Y))) -> dbls#(Y)
    active#(dbl(X)) -> active#(X) ->
    active#(dbl(s(X))) -> s#(s(dbl(X)))
    active#(dbl(X)) -> active#(X) -> active#(dbl(s(X))) -> s#(dbl(X))
    active#(dbl(X)) -> active#(X) -> active#(dbl(s(X))) -> dbl#(X)
   SCC Processor:
    #sccs: 10
    #rules: 29
    #arcs: 402/3136
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(dbl(X)) -> active#(X)
     active#(dbls(X)) -> active#(X)
     active#(sel(X1,X2)) -> active#(X1)
     active#(sel(X1,X2)) -> active#(X2)
     active#(indx(X1,X2)) -> active#(X1)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(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(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(dbl(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X)
     proper#(dbls(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(sel(X1,X2)) -> proper#(X2)
     proper#(sel(X1,X2)) -> proper#(X1)
     proper#(indx(X1,X2)) -> proper#(X2)
     proper#(indx(X1,X2)) -> proper#(X1)
     proper#(from(X)) -> proper#(X)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(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(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     from#(ok(X)) -> from#(X)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(from#) = 0
     problem:
      DPs:
       
      TRS:
       active(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     indx#(mark(X1),X2) -> indx#(X1,X2)
     indx#(ok(X1),ok(X2)) -> indx#(X1,X2)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(indx#) = 1
     problem:
      DPs:
       indx#(mark(X1),X2) -> indx#(X1,X2)
      TRS:
       active(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(indx#) = 0
      problem:
       DPs:
        
       TRS:
        active(dbl(0())) -> mark(0())
        active(dbl(s(X))) -> mark(s(s(dbl(X))))
        active(dbls(nil())) -> mark(nil())
        active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
        active(sel(0(),cons(X,Y))) -> mark(X)
        active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
        active(indx(nil(),X)) -> mark(nil())
        active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(dbl(X)) -> dbl(active(X))
        active(dbls(X)) -> dbls(active(X))
        active(sel(X1,X2)) -> sel(active(X1),X2)
        active(sel(X1,X2)) -> sel(X1,active(X2))
        active(indx(X1,X2)) -> indx(active(X1),X2)
        dbl(mark(X)) -> mark(dbl(X))
        dbls(mark(X)) -> mark(dbls(X))
        sel(mark(X1),X2) -> mark(sel(X1,X2))
        sel(X1,mark(X2)) -> mark(sel(X1,X2))
        indx(mark(X1),X2) -> mark(indx(X1,X2))
        proper(dbl(X)) -> dbl(proper(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(dbls(X)) -> dbls(proper(X))
        proper(nil()) -> ok(nil())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
        proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        dbl(ok(X)) -> ok(dbl(X))
        s(ok(X)) -> ok(s(X))
        dbls(ok(X)) -> ok(dbls(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
        indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
        from(ok(X)) -> ok(from(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     sel#(mark(X1),X2) -> sel#(X1,X2)
     sel#(X1,mark(X2)) -> sel#(X1,X2)
     sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(sel#) = 1
     problem:
      DPs:
       sel#(mark(X1),X2) -> sel#(X1,X2)
      TRS:
       active(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(sel#) = 0
      problem:
       DPs:
        
       TRS:
        active(dbl(0())) -> mark(0())
        active(dbl(s(X))) -> mark(s(s(dbl(X))))
        active(dbls(nil())) -> mark(nil())
        active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
        active(sel(0(),cons(X,Y))) -> mark(X)
        active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
        active(indx(nil(),X)) -> mark(nil())
        active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(dbl(X)) -> dbl(active(X))
        active(dbls(X)) -> dbls(active(X))
        active(sel(X1,X2)) -> sel(active(X1),X2)
        active(sel(X1,X2)) -> sel(X1,active(X2))
        active(indx(X1,X2)) -> indx(active(X1),X2)
        dbl(mark(X)) -> mark(dbl(X))
        dbls(mark(X)) -> mark(dbls(X))
        sel(mark(X1),X2) -> mark(sel(X1,X2))
        sel(X1,mark(X2)) -> mark(sel(X1,X2))
        indx(mark(X1),X2) -> mark(indx(X1,X2))
        proper(dbl(X)) -> dbl(proper(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(dbls(X)) -> dbls(proper(X))
        proper(nil()) -> ok(nil())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
        proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
        dbl(ok(X)) -> ok(dbl(X))
        s(ok(X)) -> ok(s(X))
        dbls(ok(X)) -> ok(dbls(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
        indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
        from(ok(X)) -> ok(from(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(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(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(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     dbls#(mark(X)) -> dbls#(X)
     dbls#(ok(X)) -> dbls#(X)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(dbls#) = 0
     problem:
      DPs:
       
      TRS:
       active(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     s#(ok(X)) -> s#(X)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(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(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     dbl#(mark(X)) -> dbl#(X)
     dbl#(ok(X)) -> dbl#(X)
    TRS:
     active(dbl(0())) -> mark(0())
     active(dbl(s(X))) -> mark(s(s(dbl(X))))
     active(dbls(nil())) -> mark(nil())
     active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(indx(nil(),X)) -> mark(nil())
     active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(dbl(X)) -> dbl(active(X))
     active(dbls(X)) -> dbls(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     active(indx(X1,X2)) -> indx(active(X1),X2)
     dbl(mark(X)) -> mark(dbl(X))
     dbls(mark(X)) -> mark(dbls(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     indx(mark(X1),X2) -> mark(indx(X1,X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(dbls(X)) -> dbls(proper(X))
     proper(nil()) -> ok(nil())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     dbl(ok(X)) -> ok(dbl(X))
     s(ok(X)) -> ok(s(X))
     dbls(ok(X)) -> ok(dbls(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
     from(ok(X)) -> ok(from(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(dbl#) = 0
     problem:
      DPs:
       
      TRS:
       active(dbl(0())) -> mark(0())
       active(dbl(s(X))) -> mark(s(s(dbl(X))))
       active(dbls(nil())) -> mark(nil())
       active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(indx(nil(),X)) -> mark(nil())
       active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(dbl(X)) -> dbl(active(X))
       active(dbls(X)) -> dbls(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       active(indx(X1,X2)) -> indx(active(X1),X2)
       dbl(mark(X)) -> mark(dbl(X))
       dbls(mark(X)) -> mark(dbls(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       indx(mark(X1),X2) -> mark(indx(X1,X2))
       proper(dbl(X)) -> dbl(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(dbls(X)) -> dbls(proper(X))
       proper(nil()) -> ok(nil())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       dbl(ok(X)) -> ok(dbl(X))
       s(ok(X)) -> ok(s(X))
       dbls(ok(X)) -> ok(dbls(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed