MAYBE
MAYBE
TRS:
 {
               sel(X1, mark(X2)) -> mark(sel(X1, X2)),
               sel(mark(X1), X2) -> mark(sel(X1, X2)),
             sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)),
              fib1(X1, mark(X2)) -> mark(fib1(X1, X2)),
              fib1(mark(X1), X2) -> mark(fib1(X1, X2)),
            fib1(ok(X1), ok(X2)) -> ok(fib1(X1, X2)),
                      s(mark(X)) -> mark(s(X)),
                        s(ok(X)) -> ok(s(X)),
             active(sel(X1, X2)) -> sel(X1, active(X2)),
             active(sel(X1, X2)) -> sel(active(X1), X2),
  active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)),
   active(sel(0(), cons(X, XS))) -> mark(X),
              active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))),
            active(fib1(X1, X2)) -> fib1(X1, active(X2)),
            active(fib1(X1, X2)) -> fib1(active(X1), X2),
                    active(s(X)) -> s(active(X)),
                  active(fib(N)) -> mark(sel(N, fib1(s(0()), s(0())))),
                  active(fib(X)) -> fib(active(X)),
            active(cons(X1, X2)) -> cons(active(X1), X2),
             active(add(X1, X2)) -> add(X1, active(X2)),
             active(add(X1, X2)) -> add(active(X1), X2),
            active(add(s(X), Y)) -> mark(s(add(X, Y))),
             active(add(0(), X)) -> mark(X),
                    fib(mark(X)) -> mark(fib(X)),
                      fib(ok(X)) -> ok(fib(X)),
              cons(mark(X1), X2) -> mark(cons(X1, X2)),
            cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
               add(X1, mark(X2)) -> mark(add(X1, X2)),
               add(mark(X1), X2) -> mark(add(X1, X2)),
             add(ok(X1), ok(X2)) -> ok(add(X1, X2)),
             proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
            proper(fib1(X1, X2)) -> fib1(proper(X1), proper(X2)),
                    proper(s(X)) -> s(proper(X)),
                     proper(0()) -> ok(0()),
                  proper(fib(X)) -> fib(proper(X)),
            proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
             proper(add(X1, X2)) -> add(proper(X1), proper(X2)),
                    top(mark(X)) -> top(proper(X)),
                      top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                 sel(X1, mark(X2)) -> mark(sel(X1, X2)),
                 sel(mark(X1), X2) -> mark(sel(X1, X2)),
               sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)),
                fib1(X1, mark(X2)) -> mark(fib1(X1, X2)),
                fib1(mark(X1), X2) -> mark(fib1(X1, X2)),
              fib1(ok(X1), ok(X2)) -> ok(fib1(X1, X2)),
                        s(mark(X)) -> mark(s(X)),
                          s(ok(X)) -> ok(s(X)),
               active(sel(X1, X2)) -> sel(X1, active(X2)),
               active(sel(X1, X2)) -> sel(active(X1), X2),
    active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)),
     active(sel(0(), cons(X, XS))) -> mark(X),
                active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))),
              active(fib1(X1, X2)) -> fib1(X1, active(X2)),
              active(fib1(X1, X2)) -> fib1(active(X1), X2),
                      active(s(X)) -> s(active(X)),
                    active(fib(N)) -> mark(sel(N, fib1(s(0()), s(0())))),
                    active(fib(X)) -> fib(active(X)),
              active(cons(X1, X2)) -> cons(active(X1), X2),
               active(add(X1, X2)) -> add(X1, active(X2)),
               active(add(X1, X2)) -> add(active(X1), X2),
              active(add(s(X), Y)) -> mark(s(add(X, Y))),
               active(add(0(), X)) -> mark(X),
                      fib(mark(X)) -> mark(fib(X)),
                        fib(ok(X)) -> ok(fib(X)),
                cons(mark(X1), X2) -> mark(cons(X1, X2)),
              cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                 add(X1, mark(X2)) -> mark(add(X1, X2)),
                 add(mark(X1), X2) -> mark(add(X1, X2)),
               add(ok(X1), ok(X2)) -> ok(add(X1, X2)),
               proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
              proper(fib1(X1, X2)) -> fib1(proper(X1), proper(X2)),
                      proper(s(X)) -> s(proper(X)),
                       proper(0()) -> ok(0()),
                    proper(fib(X)) -> fib(proper(X)),
              proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
               proper(add(X1, X2)) -> add(proper(X1), proper(X2)),
                      top(mark(X)) -> top(proper(X)),
                        top(ok(X)) -> top(active(X))
   }
  Fail