(VAR I P V V1 V2 X X1 X2 Y Z )
(RULES 
        active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
        active(__(X, nil)) -> mark(X)
        active(__(nil, X)) -> mark(X)
        active(and(tt, X)) -> mark(X)
        active(isList(V)) -> mark(isNeList(V))
        active(isList(nil)) -> mark(tt)
        active(isList(__(V1, V2))) -> mark(and(isList(V1), isList(V2)))
        active(isNeList(V)) -> mark(isQid(V))
        active(isNeList(__(V1, V2))) -> mark(and(isList(V1), isNeList(V2)))
        active(isNeList(__(V1, V2))) -> mark(and(isNeList(V1), isList(V2)))
        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)
        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(__(X1, X2)) -> __(active(X1), X2)
        active(__(X1, X2)) -> __(X1, active(X2))
        active(and(X1, X2)) -> and(active(X1), X2)
        __(mark(X1), X2) -> mark(__(X1, X2))
        __(X1, mark(X2)) -> mark(__(X1, X2))
        and(mark(X1), X2) -> mark(and(X1, X2))
        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(isList(X)) -> isList(proper(X))
        proper(isNeList(X)) -> isNeList(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)
        __(ok(X1), ok(X2)) -> ok(__(X1, X2))
        and(ok(X1), ok(X2)) -> ok(and(X1, X2))
        isList(ok(X)) -> ok(isList(X))
        isNeList(ok(X)) -> ok(isNeList(X))
        isQid(ok(X)) -> ok(isQid(X))
        isNePal(ok(X)) -> ok(isNePal(X))
        isPal(ok(X)) -> ok(isPal(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)