Input TRS:
    1: azzzz(zz(X,Y),Z) -> azzzz(mark(X),azzzz(mark(Y),mark(Z)))
    2: azzzz(X,nil()) -> mark(X)
    3: azzzz(nil(),X) -> mark(X)
    4: azzU11(tt()) -> tt()
    5: azzU21(tt(),V2) -> azzU22(azzisList(V2))
    6: azzU22(tt()) -> tt()
    7: azzU31(tt()) -> tt()
    8: azzU41(tt(),V2) -> azzU42(azzisNeList(V2))
    9: azzU42(tt()) -> tt()
    10: azzU51(tt(),V2) -> azzU52(azzisList(V2))
    11: azzU52(tt()) -> tt()
    12: azzU61(tt()) -> tt()
    13: azzU71(tt(),P) -> azzU72(azzisPal(P))
    14: azzU72(tt()) -> tt()
    15: azzU81(tt()) -> tt()
    16: azzisList(V) -> azzU11(azzisNeList(V))
    17: azzisList(nil()) -> tt()
    18: azzisList(zz(V1,V2)) -> azzU21(azzisList(V1),V2)
    19: azzisNeList(V) -> azzU31(azzisQid(V))
    20: azzisNeList(zz(V1,V2)) -> azzU41(azzisList(V1),V2)
    21: azzisNeList(zz(V1,V2)) -> azzU51(azzisNeList(V1),V2)
    22: azzisNePal(V) -> azzU61(azzisQid(V))
    23: azzisNePal(zz(I,zz(P,I))) -> azzU71(azzisQid(I),P)
    24: azzisPal(V) -> azzU81(azzisNePal(V))
    25: azzisPal(nil()) -> tt()
    26: azzisQid(a()) -> tt()
    27: azzisQid(e()) -> tt()
    28: azzisQid(i()) -> tt()
    29: azzisQid(o()) -> tt()
    30: azzisQid(u()) -> tt()
    31: mark(zz(X1,X2)) -> azzzz(mark(X1),mark(X2))
    32: mark(U11(X)) -> azzU11(mark(X))
    33: mark(U21(X1,X2)) -> azzU21(mark(X1),X2)
    34: mark(U22(X)) -> azzU22(mark(X))
    35: mark(isList(X)) -> azzisList(X)
    36: mark(U31(X)) -> azzU31(mark(X))
    37: mark(U41(X1,X2)) -> azzU41(mark(X1),X2)
    38: mark(U42(X)) -> azzU42(mark(X))
    39: mark(isNeList(X)) -> azzisNeList(X)
    40: mark(U51(X1,X2)) -> azzU51(mark(X1),X2)
    41: mark(U52(X)) -> azzU52(mark(X))
    42: mark(U61(X)) -> azzU61(mark(X))
    43: mark(U71(X1,X2)) -> azzU71(mark(X1),X2)
    44: mark(U72(X)) -> azzU72(mark(X))
    45: mark(isPal(X)) -> azzisPal(X)
    46: mark(U81(X)) -> azzU81(mark(X))
    47: mark(isQid(X)) -> azzisQid(X)
    48: mark(isNePal(X)) -> azzisNePal(X)
    49: mark(nil()) -> nil()
    50: mark(tt()) -> tt()
    51: mark(a()) -> a()
    52: mark(e()) -> e()
    53: mark(i()) -> i()
    54: mark(o()) -> o()
    55: mark(u()) -> u()
    56: azzzz(X1,X2) -> zz(X1,X2)
    57: azzU11(X) -> U11(X)
    58: azzU21(X1,X2) -> U21(X1,X2)
    59: azzU22(X) -> U22(X)
    60: azzisList(X) -> isList(X)
    61: azzU31(X) -> U31(X)
    62: azzU41(X1,X2) -> U41(X1,X2)
    63: azzU42(X) -> U42(X)
    64: azzisNeList(X) -> isNeList(X)
    65: azzU51(X1,X2) -> U51(X1,X2)
    66: azzU52(X) -> U52(X)
    67: azzU61(X) -> U61(X)
    68: azzU71(X1,X2) -> U71(X1,X2)
    69: azzU72(X) -> U72(X)
    70: azzisPal(X) -> isPal(X)
    71: azzU81(X) -> U81(X)
    72: azzisQid(X) -> isQid(X)
    73: azzisNePal(X) -> isNePal(X)
Number of Rules: 73
Direct QWPOS(Pol) ... orients all.
	I(azzU22) = x1 + 3	sigma(azzU22) = [1]
	I(tt) = 2
	I(U61) = 2 * x1	sigma(U61) = [1]
	I(azzU31) = x1 + 2	sigma(azzU31) = [1]
	I(mark) = x1	sigma(mark) = [1]
	I(U71) = 3 * x1 + 3 * x2 + 1	sigma(U71) = [1,2]
	I(U72) = x1	sigma(U72) = [1]
	I(azzU41) = 3 * x1 + 3 * x2 + 3	sigma(azzU41) = [1,2]
	I(azzU42) = x1 + 3	sigma(azzU42) = [1]
	I(azzisNeList) = 3 * x1 + 3	sigma(azzisNeList) = [1]
	I(U81) = x1 + 3	sigma(U81) = [1]
	I(azzU51) = 3 * x1 + 3 * x2 + 2	sigma(azzU51) = [1,2]
	I(azzisList) = 3 * x1 + 3	sigma(azzisList) = [1]
	I(azzU52) = x1	sigma(azzU52) = [1]
	I(azzU61) = 2 * x1	sigma(azzU61) = [1]
	I(nil) = 0
	I(azzU71) = 3 * x1 + 3 * x2 + 1	sigma(azzU71) = [1,2]
	I(azzU72) = x1	sigma(azzU72) = [1]
	I(a) = 3
	I(e) = 3
	I(i) = 3
	I(o) = 3
	I(isList) = 3 * x1 + 3	sigma(isList) = [1]
	I(azzU81) = x1 + 3	sigma(azzU81) = [1]
	I(u) = 3
	I(zz) = 3 * x1 + x2 + 3	sigma(zz) = [1,2]
	I(isQid) = x1	sigma(isQid) = [1]
	I(isPal) = 3 * x1 + 3	sigma(isPal) = [1]
	I(U11) = x1	sigma(U11) = [1]
	I(isNeList) = 3 * x1 + 3	sigma(isNeList) = [1]
	I(azzzz) = 3 * x1 + x2 + 3	sigma(azzzz) = [1,2]
	I(U21) = 3 * x1 + 3 * x2 + 3	sigma(U21) = [1,2]
	I(U22) = x1 + 3	sigma(U22) = [1]
	I(azzisQid) = x1	sigma(azzisQid) = [1]
	I(azzisPal) = 3 * x1 + 3	sigma(azzisPal) = [1]
	I(U31) = x1 + 2	sigma(U31) = [1]
	I(azzisNePal) = 2 * x1	sigma(azzisNePal) = [1]
	I(U41) = 3 * x1 + 3 * x2 + 3	sigma(U41) = [1,2]
	I(U42) = x1 + 3	sigma(U42) = [1]
	I(azzU11) = x1	sigma(azzU11) = [1]
	I(isNePal) = 2 * x1	sigma(isNePal) = [1]
	I(U51) = 3 * x1 + 3 * x2 + 2	sigma(U51) = [1,2]
	I(U52) = x1	sigma(U52) = [1]
	I(azzU21) = 3 * x1 + 3 * x2 + 3	sigma(azzU21) = [1,2]
    PREC: mark > azzU52 = azzisPal > azzU51 > azzU72 > U72 = azzU71 > azzisList > azzU11 > U52 = azzU21 > nil = a = e = i = o = u > azzU22 = tt = azzU31 = isPal > isList = U21 > azzisNePal > U71 = azzisNeList = U11 > azzzz = U51 > azzU41 > azzU42 > zz = U31 = isNePal > isNeList = U22 > azzU61 > U41 > azzU81 > U61 = azzisQid > U81 = isQid = U42
Number of Rules: 0