Input TRS:
    1: active(zz(zz(X,Y),Z)) -> mark(zz(X,zz(Y,Z)))
    2: active(zz(X,nil())) -> mark(X)
    3: active(zz(nil(),X)) -> mark(X)
    4: active(and(tt(),X)) -> mark(X)
    5: active(isList(V)) -> mark(isNeList(V))
    6: active(isList(nil())) -> mark(tt())
    7: active(isList(zz(V1,V2))) -> mark(and(isList(V1),isList(V2)))
    8: active(isNeList(V)) -> mark(isQid(V))
    9: active(isNeList(zz(V1,V2))) -> mark(and(isList(V1),isNeList(V2)))
    10: active(isNeList(zz(V1,V2))) -> mark(and(isNeList(V1),isList(V2)))
    11: active(isNePal(V)) -> mark(isQid(V))
    12: active(isNePal(zz(I,zz(P,I)))) -> mark(and(isQid(I),isPal(P)))
    13: active(isPal(V)) -> mark(isNePal(V))
    14: active(isPal(nil())) -> mark(tt())
    15: active(isQid(a())) -> mark(tt())
    16: active(isQid(e())) -> mark(tt())
    17: active(isQid(i())) -> mark(tt())
    18: active(isQid(o())) -> mark(tt())
    19: active(isQid(u())) -> mark(tt())
    20: active(zz(X1,X2)) -> zz(active(X1),X2)
    21: active(zz(X1,X2)) -> zz(X1,active(X2))
    22: active(and(X1,X2)) -> and(active(X1),X2)
    23: zz(mark(X1),X2) -> mark(zz(X1,X2))
    24: zz(X1,mark(X2)) -> mark(zz(X1,X2))
    25: and(mark(X1),X2) -> mark(and(X1,X2))
    26: proper(zz(X1,X2)) -> zz(proper(X1),proper(X2))
    27: proper(nil()) -> ok(nil())
    28: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    29: proper(tt()) -> ok(tt())
    30: proper(isList(X)) -> isList(proper(X))
    31: proper(isNeList(X)) -> isNeList(proper(X))
    32: proper(isQid(X)) -> isQid(proper(X))
    33: proper(isNePal(X)) -> isNePal(proper(X))
    34: proper(isPal(X)) -> isPal(proper(X))
    35: proper(a()) -> ok(a())
    36: proper(e()) -> ok(e())
    37: proper(i()) -> ok(i())
    38: proper(o()) -> ok(o())
    39: proper(u()) -> ok(u())
    40: zz(ok(X1),ok(X2)) -> ok(zz(X1,X2))
    41: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    42: isList(ok(X)) -> ok(isList(X))
    43: isNeList(ok(X)) -> ok(isNeList(X))
    44: isQid(ok(X)) -> ok(isQid(X))
    45: isNePal(ok(X)) -> ok(isNePal(X))
    46: isPal(ok(X)) -> ok(isPal(X))
    47: top(mark(X)) -> top(proper(X))
    48: top(ok(X)) -> top(active(X))
Number of Rules: 48
Direct POLO(mPol) ... failed.