MAYBE

Problem:
 active(f(X)) -> mark(cons(X,f(g(X))))
 active(g(0())) -> mark(s(0()))
 active(g(s(X))) -> mark(s(s(g(X))))
 active(sel(0(),cons(X,Y))) -> mark(X)
 active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
 active(f(X)) -> f(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(g(X)) -> g(active(X))
 active(s(X)) -> s(active(X))
 active(sel(X1,X2)) -> sel(active(X1),X2)
 active(sel(X1,X2)) -> sel(X1,active(X2))
 f(mark(X)) -> mark(f(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 g(mark(X)) -> mark(g(X))
 s(mark(X)) -> mark(s(X))
 sel(mark(X1),X2) -> mark(sel(X1,X2))
 sel(X1,mark(X2)) -> mark(sel(X1,X2))
 proper(f(X)) -> f(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(g(X)) -> g(proper(X))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
 f(ok(X)) -> ok(f(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 g(ok(X)) -> ok(g(X))
 s(ok(X)) -> ok(s(X))
 sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(f(X)) -> g#(X)
   active#(f(X)) -> f#(g(X))
   active#(f(X)) -> cons#(X,f(g(X)))
   active#(g(0())) -> s#(0())
   active#(g(s(X))) -> g#(X)
   active#(g(s(X))) -> s#(g(X))
   active#(g(s(X))) -> s#(s(g(X)))
   active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
   active#(f(X)) -> active#(X)
   active#(f(X)) -> f#(active(X))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(g(X)) -> active#(X)
   active#(g(X)) -> g#(active(X))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(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))
   f#(mark(X)) -> f#(X)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   g#(mark(X)) -> g#(X)
   s#(mark(X)) -> s#(X)
   sel#(mark(X1),X2) -> sel#(X1,X2)
   sel#(X1,mark(X2)) -> sel#(X1,X2)
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(sel(X1,X2)) -> proper#(X2)
   proper#(sel(X1,X2)) -> proper#(X1)
   proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
   f#(ok(X)) -> f#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   g#(ok(X)) -> g#(X)
   s#(ok(X)) -> s#(X)
   sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(f(X)) -> mark(cons(X,f(g(X))))
   active(g(0())) -> mark(s(0()))
   active(g(s(X))) -> mark(s(s(g(X))))
   active(sel(0(),cons(X,Y))) -> mark(X)
   active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
   active(f(X)) -> f(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(g(X)) -> g(active(X))
   active(s(X)) -> s(active(X))
   active(sel(X1,X2)) -> sel(active(X1),X2)
   active(sel(X1,X2)) -> sel(X1,active(X2))
   f(mark(X)) -> mark(f(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   g(mark(X)) -> mark(g(X))
   s(mark(X)) -> mark(s(X))
   sel(mark(X1),X2) -> mark(sel(X1,X2))
   sel(X1,mark(X2)) -> mark(sel(X1,X2))
   proper(f(X)) -> f(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(g(X)) -> g(proper(X))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
   f(ok(X)) -> ok(f(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   g(ok(X)) -> ok(g(X))
   s(ok(X)) -> ok(s(X))
   sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(f(X)) -> g#(X)
    active#(f(X)) -> f#(g(X))
    active#(f(X)) -> cons#(X,f(g(X)))
    active#(g(0())) -> s#(0())
    active#(g(s(X))) -> g#(X)
    active#(g(s(X))) -> s#(g(X))
    active#(g(s(X))) -> s#(s(g(X)))
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(f(X)) -> active#(X)
    active#(f(X)) -> f#(active(X))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(g(X)) -> active#(X)
    active#(g(X)) -> g#(active(X))
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(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))
    f#(mark(X)) -> f#(X)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    g#(mark(X)) -> g#(X)
    s#(mark(X)) -> s#(X)
    sel#(mark(X1),X2) -> sel#(X1,X2)
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2)
    proper#(sel(X1,X2)) -> proper#(X1)
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    f#(ok(X)) -> f#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    g#(ok(X)) -> g#(X)
    s#(ok(X)) -> s#(X)
    sel#(ok(X1),ok(X2)) -> sel#(X1,X2)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(f(X)) -> mark(cons(X,f(g(X))))
    active(g(0())) -> mark(s(0()))
    active(g(s(X))) -> mark(s(s(g(X))))
    active(sel(0(),cons(X,Y))) -> mark(X)
    active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
    active(f(X)) -> f(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(g(X)) -> g(active(X))
    active(s(X)) -> s(active(X))
    active(sel(X1,X2)) -> sel(active(X1),X2)
    active(sel(X1,X2)) -> sel(X1,active(X2))
    f(mark(X)) -> mark(f(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    g(mark(X)) -> mark(g(X))
    s(mark(X)) -> mark(s(X))
    sel(mark(X1),X2) -> mark(sel(X1,X2))
    sel(X1,mark(X2)) -> mark(sel(X1,X2))
    proper(f(X)) -> f(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(g(X)) -> g(proper(X))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
    f(ok(X)) -> ok(f(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    g(ok(X)) -> ok(g(X))
    s(ok(X)) -> ok(s(X))
    sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) ->
    active#(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#(s(X)) -> s#(active(X))
    top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    top#(ok(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    top#(ok(X)) -> active#(X) -> active#(g(s(X))) -> s#(s(g(X)))
    top#(ok(X)) -> active#(X) -> active#(g(s(X))) -> s#(g(X))
    top#(ok(X)) -> active#(X) -> active#(g(s(X))) -> g#(X)
    top#(ok(X)) -> active#(X) -> active#(g(0())) -> s#(0())
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> cons#(X,f(g(X)))
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> f#(g(X))
    top#(ok(X)) -> active#(X) -> active#(f(X)) -> g#(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#(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#(s(X)) -> s#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(g(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#(f(X)) -> f#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    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#(s(X)) -> s#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(g(X)) -> g#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(g(X)) -> proper#(X)
    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#(f(X)) -> f#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X2) ->
    proper#(f(X)) -> proper#(X)
    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#(s(X)) -> s#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(g(X)) -> g#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(g(X)) -> proper#(X)
    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#(f(X)) -> f#(proper(X))
    proper#(sel(X1,X2)) -> proper#(X1) ->
    proper#(f(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#(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#(s(X)) -> s#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(g(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#(f(X)) -> f#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
    proper#(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#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(g(X)) -> g#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(g(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#(f(X)) -> f#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(f(X)) -> proper#(X)
    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#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(g(X)) -> g#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(g(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#(f(X)) -> f#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(f(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    proper#(g(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(g(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1)
    proper#(g(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2)
    proper#(g(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(g(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(g(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(X)
    proper#(f(X)) -> proper#(X) ->
    proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2))
    proper#(f(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1)
    proper#(f(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2)
    proper#(f(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(f(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(f(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
    proper#(f(X)) -> f#(proper(X)) -> f#(mark(X)) -> f#(X)
    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)
    s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
    s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2)
    f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    f#(ok(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(ok(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(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#(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#(s(X)) -> s#(active(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(g(X)) -> g#(active(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(g(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(f(X)) -> f#(active(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(f(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(g(s(X))) -> s#(s(g(X)))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(g(s(X))) -> s#(g(X))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(g(s(X))) -> g#(X)
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(g(0())) -> s#(0())
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(f(X)) -> cons#(X,f(g(X)))
    active#(sel(X1,X2)) -> active#(X2) ->
    active#(f(X)) -> f#(g(X))
    active#(sel(X1,X2)) -> active#(X2) -> active#(f(X)) -> g#(X)
    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#(s(X)) -> s#(active(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(g(X)) -> g#(active(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(g(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> f#(active(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> active#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(g(s(X))) -> s#(s(g(X)))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(g(s(X))) -> s#(g(X))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(g(s(X))) -> g#(X)
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(g(0())) -> s#(0())
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> cons#(X,f(g(X)))
    active#(sel(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> f#(g(X))
    active#(sel(X1,X2)) -> active#(X1) -> active#(f(X)) -> g#(X)
    active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
    active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
    active#(s(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2)
    active#(s(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(s(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    active#(s(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(s(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    active#(s(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    active#(s(X)) -> active#(X) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(s(X)) -> active#(X) -> active#(g(s(X))) -> s#(s(g(X)))
    active#(s(X)) -> active#(X) -> active#(g(s(X))) -> s#(g(X))
    active#(s(X)) -> active#(X) -> active#(g(s(X))) -> g#(X)
    active#(s(X)) -> active#(X) -> active#(g(0())) -> s#(0())
    active#(s(X)) -> active#(X) -> active#(f(X)) -> cons#(X,f(g(X)))
    active#(s(X)) -> active#(X) -> active#(f(X)) -> f#(g(X))
    active#(s(X)) -> active#(X) ->
    active#(f(X)) -> g#(X)
    active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> active#(X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sel(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(g(X)) -> g#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(g(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> f#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(g(s(X))) -> s#(s(g(X)))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(g(s(X))) -> s#(g(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(g(s(X))) -> g#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(g(0())) -> s#(0())
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> cons#(X,f(g(X)))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(f(X)) -> f#(g(X))
    active#(cons(X1,X2)) -> active#(X1) -> active#(f(X)) -> g#(X)
    active#(g(s(X))) -> s#(s(g(X))) -> s#(ok(X)) -> s#(X)
    active#(g(s(X))) -> s#(s(g(X))) -> s#(mark(X)) -> s#(X)
    active#(g(s(X))) -> s#(g(X)) -> s#(ok(X)) -> s#(X)
    active#(g(s(X))) -> s#(g(X)) -> s#(mark(X)) -> s#(X)
    active#(g(s(X))) -> g#(X) -> g#(ok(X)) -> g#(X)
    active#(g(s(X))) -> g#(X) -> g#(mark(X)) -> g#(X)
    active#(g(0())) -> s#(0()) -> s#(ok(X)) -> s#(X)
    active#(g(0())) -> s#(0()) -> s#(mark(X)) -> s#(X)
    active#(g(X)) -> g#(active(X)) -> g#(ok(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X)
    active#(g(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(g(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2)
    active#(g(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(g(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1)
    active#(g(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(g(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(g(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    active#(g(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(g(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(g(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    active#(g(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    active#(g(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    active#(g(X)) -> active#(X) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(g(X)) -> active#(X) -> active#(g(s(X))) -> s#(s(g(X)))
    active#(g(X)) -> active#(X) -> active#(g(s(X))) -> s#(g(X))
    active#(g(X)) -> active#(X) -> active#(g(s(X))) -> g#(X)
    active#(g(X)) -> active#(X) -> active#(g(0())) -> s#(0())
    active#(g(X)) -> active#(X) -> active#(f(X)) -> cons#(X,f(g(X)))
    active#(g(X)) -> active#(X) -> active#(f(X)) -> f#(g(X))
    active#(g(X)) -> active#(X) -> active#(f(X)) -> g#(X)
    active#(f(X)) -> cons#(X,f(g(X))) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(f(X)) -> cons#(X,f(g(X))) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    active#(f(X)) -> f#(g(X)) -> f#(ok(X)) -> f#(X)
    active#(f(X)) -> f#(g(X)) -> f#(mark(X)) -> f#(X)
    active#(f(X)) -> f#(active(X)) -> f#(ok(X)) -> f#(X)
    active#(f(X)) -> f#(active(X)) -> f#(mark(X)) -> f#(X)
    active#(f(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    active#(f(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    active#(f(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(X1,active(X2))
    active#(f(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2)
    active#(f(X)) -> active#(X) ->
    active#(sel(X1,X2)) -> sel#(active(X1),X2)
    active#(f(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1)
    active#(f(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(f(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(f(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    active#(f(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(f(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(f(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    active#(f(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
    active#(f(X)) -> active#(X) -> active#(f(X)) -> active#(X)
    active#(f(X)) -> active#(X) ->
    active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z)
    active#(f(X)) -> active#(X) -> active#(g(s(X))) -> s#(s(g(X)))
    active#(f(X)) -> active#(X) -> active#(g(s(X))) -> s#(g(X))
    active#(f(X)) -> active#(X) -> active#(g(s(X))) -> g#(X)
    active#(f(X)) -> active#(X) -> active#(g(0())) -> s#(0())
    active#(f(X)) -> active#(X) -> active#(f(X)) -> cons#(X,f(g(X)))
    active#(f(X)) -> active#(X) -> active#(f(X)) -> f#(g(X))
    active#(f(X)) -> active#(X) -> active#(f(X)) -> g#(X)
   SCC Processor:
    #sccs: 8
    #rules: 26
    #arcs: 311/2209
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(f(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1)
     active#(g(X)) -> active#(X)
     active#(s(X)) -> active#(X)
     active#(sel(X1,X2)) -> active#(X1)
     active#(sel(X1,X2)) -> active#(X2)
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(f(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(g(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X)
     proper#(sel(X1,X2)) -> proper#(X2)
     proper#(sel(X1,X2)) -> proper#(X1)
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       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(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     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(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(sel#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(X)) -> mark(cons(X,f(g(X))))
        active(g(0())) -> mark(s(0()))
        active(g(s(X))) -> mark(s(s(g(X))))
        active(sel(0(),cons(X,Y))) -> mark(X)
        active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(g(X)) -> g(active(X))
        active(s(X)) -> s(active(X))
        active(sel(X1,X2)) -> sel(active(X1),X2)
        active(sel(X1,X2)) -> sel(X1,active(X2))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        g(mark(X)) -> mark(g(X))
        s(mark(X)) -> mark(s(X))
        sel(mark(X1),X2) -> mark(sel(X1,X2))
        sel(X1,mark(X2)) -> mark(sel(X1,X2))
        proper(f(X)) -> f(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(g(X)) -> g(proper(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        g(ok(X)) -> ok(g(X))
        s(ok(X)) -> ok(s(X))
        sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     s#(mark(X)) -> s#(X)
     s#(ok(X)) -> s#(X)
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(s#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     g#(mark(X)) -> g#(X)
     g#(ok(X)) -> g#(X)
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     cons#(mark(X1),X2) -> cons#(X1,X2)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(cons#) = 1
     problem:
      DPs:
       cons#(mark(X1),X2) -> cons#(X1,X2)
      TRS:
       active(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(cons#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(X)) -> mark(cons(X,f(g(X))))
        active(g(0())) -> mark(s(0()))
        active(g(s(X))) -> mark(s(s(g(X))))
        active(sel(0(),cons(X,Y))) -> mark(X)
        active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(g(X)) -> g(active(X))
        active(s(X)) -> s(active(X))
        active(sel(X1,X2)) -> sel(active(X1),X2)
        active(sel(X1,X2)) -> sel(X1,active(X2))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        g(mark(X)) -> mark(g(X))
        s(mark(X)) -> mark(s(X))
        sel(mark(X1),X2) -> mark(sel(X1,X2))
        sel(X1,mark(X2)) -> mark(sel(X1,X2))
        proper(f(X)) -> f(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(g(X)) -> g(proper(X))
        proper(0()) -> ok(0())
        proper(s(X)) -> s(proper(X))
        proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        g(ok(X)) -> ok(g(X))
        s(ok(X)) -> ok(s(X))
        sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
    
    DPs:
     f#(mark(X)) -> f#(X)
     f#(ok(X)) -> f#(X)
    TRS:
     active(f(X)) -> mark(cons(X,f(g(X))))
     active(g(0())) -> mark(s(0()))
     active(g(s(X))) -> mark(s(s(g(X))))
     active(sel(0(),cons(X,Y))) -> mark(X)
     active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(g(X)) -> g(active(X))
     active(s(X)) -> s(active(X))
     active(sel(X1,X2)) -> sel(active(X1),X2)
     active(sel(X1,X2)) -> sel(X1,active(X2))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     g(mark(X)) -> mark(g(X))
     s(mark(X)) -> mark(s(X))
     sel(mark(X1),X2) -> mark(sel(X1,X2))
     sel(X1,mark(X2)) -> mark(sel(X1,X2))
     proper(f(X)) -> f(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     g(ok(X)) -> ok(g(X))
     s(ok(X)) -> ok(s(X))
     sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X)) -> mark(cons(X,f(g(X))))
       active(g(0())) -> mark(s(0()))
       active(g(s(X))) -> mark(s(s(g(X))))
       active(sel(0(),cons(X,Y))) -> mark(X)
       active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
       active(f(X)) -> f(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(g(X)) -> g(active(X))
       active(s(X)) -> s(active(X))
       active(sel(X1,X2)) -> sel(active(X1),X2)
       active(sel(X1,X2)) -> sel(X1,active(X2))
       f(mark(X)) -> mark(f(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       g(mark(X)) -> mark(g(X))
       s(mark(X)) -> mark(s(X))
       sel(mark(X1),X2) -> mark(sel(X1,X2))
       sel(X1,mark(X2)) -> mark(sel(X1,X2))
       proper(f(X)) -> f(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(g(X)) -> g(proper(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
       f(ok(X)) -> ok(f(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       g(ok(X)) -> ok(g(X))
       s(ok(X)) -> ok(s(X))
       sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed