MAYBE
MAYBE
TRS:
 {
                  __(X1, mark(X2)) -> mark(__(X1, X2)),
                  __(mark(X1), X2) -> mark(__(X1, X2)),
                __(ok(X1), ok(X2)) -> ok(__(X1, X2)),
              active(__(X, nil())) -> mark(X),
                active(__(X1, X2)) -> __(X1, active(X2)),
                active(__(X1, X2)) -> __(active(X1), X2),
           active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))),
              active(__(nil(), X)) -> mark(X),
               active(and(X1, X2)) -> and(active(X1), X2),
              active(and(tt(), X)) -> mark(X),
               active(isNeList(V)) -> mark(isQid(V)),
      active(isNeList(__(V1, V2))) -> mark(and(isNeList(V1), isList(V2))),
      active(isNeList(__(V1, V2))) -> mark(and(isList(V1), isNeList(V2))),
                 active(isList(V)) -> mark(isNeList(V)),
        active(isList(__(V1, V2))) -> mark(and(isList(V1), isList(V2))),
             active(isList(nil())) -> mark(tt()),
                active(isQid(a())) -> mark(tt()),
                active(isQid(e())) -> mark(tt()),
                active(isQid(i())) -> mark(tt()),
                active(isQid(o())) -> mark(tt()),
                active(isQid(u())) -> mark(tt()),
                active(isNePal(V)) -> mark(isQid(V)),
  active(isNePal(__(I, __(P, I)))) -> mark(and(isQid(I), isPal(P))),
                  active(isPal(V)) -> mark(isNePal(V)),
              active(isPal(nil())) -> mark(tt()),
                 and(mark(X1), X2) -> mark(and(X1, X2)),
               and(ok(X1), ok(X2)) -> ok(and(X1, X2)),
                   isNeList(ok(X)) -> ok(isNeList(X)),
                     isList(ok(X)) -> ok(isList(X)),
                      isQid(ok(X)) -> ok(isQid(X)),
                    isNePal(ok(X)) -> ok(isNePal(X)),
                      isPal(ok(X)) -> ok(isPal(X)),
                proper(__(X1, X2)) -> __(proper(X1), proper(X2)),
                     proper(nil()) -> ok(nil()),
               proper(and(X1, X2)) -> and(proper(X1), proper(X2)),
                      proper(tt()) -> ok(tt()),
               proper(isNeList(X)) -> isNeList(proper(X)),
                 proper(isList(X)) -> isList(proper(X)),
                  proper(isQid(X)) -> isQid(proper(X)),
                proper(isNePal(X)) -> isNePal(proper(X)),
                  proper(isPal(X)) -> isPal(proper(X)),
                       proper(a()) -> ok(a()),
                       proper(e()) -> ok(e()),
                       proper(i()) -> ok(i()),
                       proper(o()) -> ok(o()),
                       proper(u()) -> ok(u()),
                      top(mark(X)) -> top(proper(X)),
                        top(ok(X)) -> top(active(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                    __(X1, mark(X2)) -> mark(__(X1, X2)),
                    __(mark(X1), X2) -> mark(__(X1, X2)),
                  __(ok(X1), ok(X2)) -> ok(__(X1, X2)),
                active(__(X, nil())) -> mark(X),
                  active(__(X1, X2)) -> __(X1, active(X2)),
                  active(__(X1, X2)) -> __(active(X1), X2),
             active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))),
                active(__(nil(), X)) -> mark(X),
                 active(and(X1, X2)) -> and(active(X1), X2),
                active(and(tt(), X)) -> mark(X),
                 active(isNeList(V)) -> mark(isQid(V)),
        active(isNeList(__(V1, V2))) -> mark(and(isNeList(V1), isList(V2))),
        active(isNeList(__(V1, V2))) -> mark(and(isList(V1), isNeList(V2))),
                   active(isList(V)) -> mark(isNeList(V)),
          active(isList(__(V1, V2))) -> mark(and(isList(V1), isList(V2))),
               active(isList(nil())) -> mark(tt()),
                  active(isQid(a())) -> mark(tt()),
                  active(isQid(e())) -> mark(tt()),
                  active(isQid(i())) -> mark(tt()),
                  active(isQid(o())) -> mark(tt()),
                  active(isQid(u())) -> mark(tt()),
                  active(isNePal(V)) -> mark(isQid(V)),
    active(isNePal(__(I, __(P, I)))) -> mark(and(isQid(I), isPal(P))),
                    active(isPal(V)) -> mark(isNePal(V)),
                active(isPal(nil())) -> mark(tt()),
                   and(mark(X1), X2) -> mark(and(X1, X2)),
                 and(ok(X1), ok(X2)) -> ok(and(X1, X2)),
                     isNeList(ok(X)) -> ok(isNeList(X)),
                       isList(ok(X)) -> ok(isList(X)),
                        isQid(ok(X)) -> ok(isQid(X)),
                      isNePal(ok(X)) -> ok(isNePal(X)),
                        isPal(ok(X)) -> ok(isPal(X)),
                  proper(__(X1, X2)) -> __(proper(X1), proper(X2)),
                       proper(nil()) -> ok(nil()),
                 proper(and(X1, X2)) -> and(proper(X1), proper(X2)),
                        proper(tt()) -> ok(tt()),
                 proper(isNeList(X)) -> isNeList(proper(X)),
                   proper(isList(X)) -> isList(proper(X)),
                    proper(isQid(X)) -> isQid(proper(X)),
                  proper(isNePal(X)) -> isNePal(proper(X)),
                    proper(isPal(X)) -> isPal(proper(X)),
                         proper(a()) -> ok(a()),
                         proper(e()) -> ok(e()),
                         proper(i()) -> ok(i()),
                         proper(o()) -> ok(o()),
                         proper(u()) -> ok(u()),
                        top(mark(X)) -> top(proper(X)),
                          top(ok(X)) -> top(active(X))
   }
  Fail