MAYBE

Problem:
 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))

Proof:
 Open