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())
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(isList(X)) -> active(isList(X))
 mark(isNeList(X)) -> active(isNeList(X))
 mark(isQid(X)) -> active(isQid(X))
 mark(isNePal(X)) -> active(isNePal(X))
 mark(isPal(X)) -> active(isPal(X))
 mark(a()) -> active(a())
 mark(e()) -> active(e())
 mark(i()) -> active(i())
 mark(o()) -> active(o())
 mark(u()) -> active(u())
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 __(active(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 isList(mark(X)) -> isList(X)
 isList(active(X)) -> isList(X)
 isNeList(mark(X)) -> isNeList(X)
 isNeList(active(X)) -> isNeList(X)
 isQid(mark(X)) -> isQid(X)
 isQid(active(X)) -> isQid(X)
 isNePal(mark(X)) -> isNePal(X)
 isNePal(active(X)) -> isNePal(X)
 isPal(mark(X)) -> isPal(X)
 isPal(active(X)) -> isPal(X)

Proof:
 Open