MAYBE
MAYBE
TRS:
 {
         cons(mark(X1), X2) -> mark(cons(X1, X2)),
       cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
              incr(mark(X)) -> mark(incr(X)),
                incr(ok(X)) -> ok(incr(X)),
       active(cons(X1, X2)) -> cons(active(X1), X2),
            active(incr(X)) -> incr(active(X)),
  active(incr(cons(X, XS))) -> mark(cons(s(X), incr(XS))),
             active(nats()) -> mark(cons(0(), incr(nats()))),
             active(odds()) -> mark(incr(pairs())),
            active(pairs()) -> mark(cons(0(), incr(odds()))),
               active(s(X)) -> s(active(X)),
            active(head(X)) -> head(active(X)),
  active(head(cons(X, XS))) -> mark(X),
            active(tail(X)) -> tail(active(X)),
  active(tail(cons(X, XS))) -> mark(XS),
                 s(mark(X)) -> mark(s(X)),
                   s(ok(X)) -> ok(s(X)),
              head(mark(X)) -> mark(head(X)),
                head(ok(X)) -> ok(head(X)),
              tail(mark(X)) -> mark(tail(X)),
                tail(ok(X)) -> ok(tail(X)),
       proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                proper(0()) -> ok(0()),
            proper(incr(X)) -> incr(proper(X)),
             proper(nats()) -> ok(nats()),
             proper(odds()) -> ok(odds()),
            proper(pairs()) -> ok(pairs()),
               proper(s(X)) -> s(proper(X)),
            proper(head(X)) -> head(proper(X)),
            proper(tail(X)) -> tail(proper(X)),
               top(mark(X)) -> top(proper(X)),
                 top(ok(X)) -> top(active(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
           cons(mark(X1), X2) -> mark(cons(X1, X2)),
         cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                incr(mark(X)) -> mark(incr(X)),
                  incr(ok(X)) -> ok(incr(X)),
         active(cons(X1, X2)) -> cons(active(X1), X2),
              active(incr(X)) -> incr(active(X)),
    active(incr(cons(X, XS))) -> mark(cons(s(X), incr(XS))),
               active(nats()) -> mark(cons(0(), incr(nats()))),
               active(odds()) -> mark(incr(pairs())),
              active(pairs()) -> mark(cons(0(), incr(odds()))),
                 active(s(X)) -> s(active(X)),
              active(head(X)) -> head(active(X)),
    active(head(cons(X, XS))) -> mark(X),
              active(tail(X)) -> tail(active(X)),
    active(tail(cons(X, XS))) -> mark(XS),
                   s(mark(X)) -> mark(s(X)),
                     s(ok(X)) -> ok(s(X)),
                head(mark(X)) -> mark(head(X)),
                  head(ok(X)) -> ok(head(X)),
                tail(mark(X)) -> mark(tail(X)),
                  tail(ok(X)) -> ok(tail(X)),
         proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                  proper(0()) -> ok(0()),
              proper(incr(X)) -> incr(proper(X)),
               proper(nats()) -> ok(nats()),
               proper(odds()) -> ok(odds()),
              proper(pairs()) -> ok(pairs()),
                 proper(s(X)) -> s(proper(X)),
              proper(head(X)) -> head(proper(X)),
              proper(tail(X)) -> tail(proper(X)),
                 top(mark(X)) -> top(proper(X)),
                   top(ok(X)) -> top(active(X))
   }
  Fail