MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(isPalListKind(X)) -> a__isPalListKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  , mark(isList(X)) -> a__isList(X)
  , mark(U23(X)) -> a__U23(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U32(X)) -> a__U32(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
  , mark(U43(X)) -> a__U43(mark(X))
  , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  , mark(U53(X)) -> a__U53(mark(X))
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X1, X2) -> U11(X1, X2)
  , a__U11(tt(), V) -> a__U12(a__isNeList(V))
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) ->
    a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isNeList(__(V1, V2)) ->
    a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2)
  , a__U22(X1, X2) -> U22(X1, X2)
  , a__U22(tt(), V2) -> a__U23(a__isList(V2))
  , a__isList(V) -> a__U11(a__isPalListKind(V), V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) ->
    a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isList(nil()) -> tt()
  , a__U23(X) -> U23(X)
  , a__U23(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), V) -> a__U32(a__isQid(V))
  , a__U32(X) -> U32(X)
  , a__U32(tt()) -> tt()
  , a__isQid(X) -> isQid(X)
  , a__isQid(a()) -> tt()
  , a__isQid(e()) -> tt()
  , a__isQid(i()) -> tt()
  , a__isQid(o()) -> tt()
  , a__isQid(u()) -> tt()
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2)
  , a__U42(X1, X2) -> U42(X1, X2)
  , a__U42(tt(), V2) -> a__U43(a__isNeList(V2))
  , a__U43(X) -> U43(X)
  , a__U43(tt()) -> tt()
  , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2)
  , a__U52(X1, X2) -> U52(X1, X2)
  , a__U52(tt(), V2) -> a__U53(a__isList(V2))
  , a__U53(X) -> U53(X)
  , a__U53(tt()) -> tt()
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V) -> a__U62(a__isQid(V))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), V) -> a__U72(a__isNePal(V))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) ->
    a__and(a__and(a__isQid(I), isPalListKind(I)),
           and(isPal(P), isPalListKind(P)))
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isPalListKind(X) -> isPalListKind(X)
  , a__isPalListKind(__(V1, V2)) ->
    a__and(a__isPalListKind(V1), isPalListKind(V2))
  , a__isPalListKind(nil()) -> tt()
  , a__isPalListKind(a()) -> tt()
  , a__isPalListKind(e()) -> tt()
  , a__isPalListKind(i()) -> tt()
  , a__isPalListKind(o()) -> tt()
  , a__isPalListKind(u()) -> tt()
  , a__isPal(V) -> a__U71(a__isPalListKind(V), V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { a____^#(X1, X2) -> c_1()
  , a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
  , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(a()) -> c_11()
  , mark^#(e()) -> c_12()
  , mark^#(i()) -> c_13()
  , mark^#(o()) -> c_14()
  , mark^#(u()) -> c_15()
  , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2), mark^#(X1))
  , mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
  , mark^#(U21(X1, X2, X3)) ->
    c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2), mark^#(X1))
  , mark^#(isList(X)) -> c_21(a__isList^#(X))
  , mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
  , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2), mark^#(X1))
  , mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
  , mark^#(isQid(X)) -> c_25(a__isQid^#(X))
  , mark^#(U41(X1, X2, X3)) ->
    c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2), mark^#(X1))
  , mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
  , mark^#(U51(X1, X2, X3)) ->
    c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2), mark^#(X1))
  , mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
  , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2), mark^#(X1))
  , mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
  , a__isPalListKind^#(X) -> c_90()
  , a__isPalListKind^#(__(V1, V2)) ->
    c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isPalListKind^#(nil()) -> c_92()
  , a__isPalListKind^#(a()) -> c_93()
  , a__isPalListKind^#(e()) -> c_94()
  , a__isPalListKind^#(i()) -> c_95()
  , a__isPalListKind^#(o()) -> c_96()
  , a__isPalListKind^#(u()) -> c_97()
  , a__and^#(X1, X2) -> c_88()
  , a__and^#(tt(), X) -> c_89(mark^#(X))
  , a__isPal^#(V) ->
    c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isPal^#(X) -> c_99()
  , a__isPal^#(nil()) -> c_100()
  , a__U11^#(X1, X2) -> c_37()
  , a__U11^#(tt(), V) ->
    c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
  , a__U12^#(X) -> c_39()
  , a__U12^#(tt()) -> c_40()
  , a__isNeList^#(V) ->
    c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNeList^#(X) -> c_42()
  , a__isNeList^#(__(V1, V2)) ->
    c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U21^#(X1, X2, X3) -> c_45()
  , a__U21^#(tt(), V1, V2) ->
    c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U22^#(X1, X2) -> c_47()
  , a__U22^#(tt(), V2) ->
    c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isList^#(X) -> c_50()
  , a__isList^#(__(V1, V2)) ->
    c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isList^#(nil()) -> c_52()
  , a__U23^#(X) -> c_53()
  , a__U23^#(tt()) -> c_54()
  , a__U31^#(X1, X2) -> c_55()
  , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
  , a__U32^#(X) -> c_57()
  , a__U32^#(tt()) -> c_58()
  , a__isQid^#(X) -> c_59()
  , a__isQid^#(a()) -> c_60()
  , a__isQid^#(e()) -> c_61()
  , a__isQid^#(i()) -> c_62()
  , a__isQid^#(o()) -> c_63()
  , a__isQid^#(u()) -> c_64()
  , a__U41^#(X1, X2, X3) -> c_65()
  , a__U41^#(tt(), V1, V2) ->
    c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U42^#(X1, X2) -> c_67()
  , a__U42^#(tt(), V2) ->
    c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U43^#(X) -> c_69()
  , a__U43^#(tt()) -> c_70()
  , a__U51^#(X1, X2, X3) -> c_71()
  , a__U51^#(tt(), V1, V2) ->
    c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U52^#(X1, X2) -> c_73()
  , a__U52^#(tt(), V2) ->
    c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
  , a__U53^#(X) -> c_75()
  , a__U53^#(tt()) -> c_76()
  , a__U61^#(X1, X2) -> c_77()
  , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
  , a__U62^#(X) -> c_79()
  , a__U62^#(tt()) -> c_80()
  , a__U71^#(X1, X2) -> c_81()
  , a__U71^#(tt(), V) ->
    c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
  , a__U72^#(X) -> c_83()
  , a__U72^#(tt()) -> c_84()
  , a__isNePal^#(V) ->
    c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNePal^#(X) -> c_86()
  , a__isNePal^#(__(I, __(P, I))) ->
    c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I)),
         a__isQid^#(I)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a____^#(X1, X2) -> c_1()
  , a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
  , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(a()) -> c_11()
  , mark^#(e()) -> c_12()
  , mark^#(i()) -> c_13()
  , mark^#(o()) -> c_14()
  , mark^#(u()) -> c_15()
  , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2), mark^#(X1))
  , mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
  , mark^#(U21(X1, X2, X3)) ->
    c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2), mark^#(X1))
  , mark^#(isList(X)) -> c_21(a__isList^#(X))
  , mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
  , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2), mark^#(X1))
  , mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
  , mark^#(isQid(X)) -> c_25(a__isQid^#(X))
  , mark^#(U41(X1, X2, X3)) ->
    c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2), mark^#(X1))
  , mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
  , mark^#(U51(X1, X2, X3)) ->
    c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2), mark^#(X1))
  , mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
  , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2), mark^#(X1))
  , mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
  , a__isPalListKind^#(X) -> c_90()
  , a__isPalListKind^#(__(V1, V2)) ->
    c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isPalListKind^#(nil()) -> c_92()
  , a__isPalListKind^#(a()) -> c_93()
  , a__isPalListKind^#(e()) -> c_94()
  , a__isPalListKind^#(i()) -> c_95()
  , a__isPalListKind^#(o()) -> c_96()
  , a__isPalListKind^#(u()) -> c_97()
  , a__and^#(X1, X2) -> c_88()
  , a__and^#(tt(), X) -> c_89(mark^#(X))
  , a__isPal^#(V) ->
    c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isPal^#(X) -> c_99()
  , a__isPal^#(nil()) -> c_100()
  , a__U11^#(X1, X2) -> c_37()
  , a__U11^#(tt(), V) ->
    c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
  , a__U12^#(X) -> c_39()
  , a__U12^#(tt()) -> c_40()
  , a__isNeList^#(V) ->
    c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNeList^#(X) -> c_42()
  , a__isNeList^#(__(V1, V2)) ->
    c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U21^#(X1, X2, X3) -> c_45()
  , a__U21^#(tt(), V1, V2) ->
    c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U22^#(X1, X2) -> c_47()
  , a__U22^#(tt(), V2) ->
    c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isList^#(X) -> c_50()
  , a__isList^#(__(V1, V2)) ->
    c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isList^#(nil()) -> c_52()
  , a__U23^#(X) -> c_53()
  , a__U23^#(tt()) -> c_54()
  , a__U31^#(X1, X2) -> c_55()
  , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
  , a__U32^#(X) -> c_57()
  , a__U32^#(tt()) -> c_58()
  , a__isQid^#(X) -> c_59()
  , a__isQid^#(a()) -> c_60()
  , a__isQid^#(e()) -> c_61()
  , a__isQid^#(i()) -> c_62()
  , a__isQid^#(o()) -> c_63()
  , a__isQid^#(u()) -> c_64()
  , a__U41^#(X1, X2, X3) -> c_65()
  , a__U41^#(tt(), V1, V2) ->
    c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U42^#(X1, X2) -> c_67()
  , a__U42^#(tt(), V2) ->
    c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U43^#(X) -> c_69()
  , a__U43^#(tt()) -> c_70()
  , a__U51^#(X1, X2, X3) -> c_71()
  , a__U51^#(tt(), V1, V2) ->
    c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U52^#(X1, X2) -> c_73()
  , a__U52^#(tt(), V2) ->
    c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
  , a__U53^#(X) -> c_75()
  , a__U53^#(tt()) -> c_76()
  , a__U61^#(X1, X2) -> c_77()
  , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
  , a__U62^#(X) -> c_79()
  , a__U62^#(tt()) -> c_80()
  , a__U71^#(X1, X2) -> c_81()
  , a__U71^#(tt(), V) ->
    c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
  , a__U72^#(X) -> c_83()
  , a__U72^#(tt()) -> c_84()
  , a__isNePal^#(V) ->
    c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNePal^#(X) -> c_86()
  , a__isNePal^#(__(I, __(P, I))) ->
    c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I)),
         a__isQid^#(I)) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(isPalListKind(X)) -> a__isPalListKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  , mark(isList(X)) -> a__isList(X)
  , mark(U23(X)) -> a__U23(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U32(X)) -> a__U32(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
  , mark(U43(X)) -> a__U43(mark(X))
  , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  , mark(U53(X)) -> a__U53(mark(X))
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X1, X2) -> U11(X1, X2)
  , a__U11(tt(), V) -> a__U12(a__isNeList(V))
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) ->
    a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isNeList(__(V1, V2)) ->
    a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2)
  , a__U22(X1, X2) -> U22(X1, X2)
  , a__U22(tt(), V2) -> a__U23(a__isList(V2))
  , a__isList(V) -> a__U11(a__isPalListKind(V), V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) ->
    a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isList(nil()) -> tt()
  , a__U23(X) -> U23(X)
  , a__U23(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), V) -> a__U32(a__isQid(V))
  , a__U32(X) -> U32(X)
  , a__U32(tt()) -> tt()
  , a__isQid(X) -> isQid(X)
  , a__isQid(a()) -> tt()
  , a__isQid(e()) -> tt()
  , a__isQid(i()) -> tt()
  , a__isQid(o()) -> tt()
  , a__isQid(u()) -> tt()
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2)
  , a__U42(X1, X2) -> U42(X1, X2)
  , a__U42(tt(), V2) -> a__U43(a__isNeList(V2))
  , a__U43(X) -> U43(X)
  , a__U43(tt()) -> tt()
  , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2)
  , a__U52(X1, X2) -> U52(X1, X2)
  , a__U52(tt(), V2) -> a__U53(a__isList(V2))
  , a__U53(X) -> U53(X)
  , a__U53(tt()) -> tt()
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V) -> a__U62(a__isQid(V))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), V) -> a__U72(a__isNePal(V))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) ->
    a__and(a__and(a__isQid(I), isPalListKind(I)),
           and(isPal(P), isPalListKind(P)))
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isPalListKind(X) -> isPalListKind(X)
  , a__isPalListKind(__(V1, V2)) ->
    a__and(a__isPalListKind(V1), isPalListKind(V2))
  , a__isPalListKind(nil()) -> tt()
  , a__isPalListKind(a()) -> tt()
  , a__isPalListKind(e()) -> tt()
  , a__isPalListKind(i()) -> tt()
  , a__isPalListKind(o()) -> tt()
  , a__isPalListKind(u()) -> tt()
  , a__isPal(V) -> a__U71(a__isPalListKind(V), V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of
{1,6,7,11,12,13,14,15,37,39,40,41,42,43,44,45,48,49,50,52,53,55,58,60,63,65,66,67,68,70,71,72,73,74,75,76,77,78,80,82,83,84,86,88,89,90,92,93,94,96,97,99}
by applications of
Pre({1,6,7,11,12,13,14,15,37,39,40,41,42,43,44,45,48,49,50,52,53,55,58,60,63,65,66,67,68,70,71,72,73,74,75,76,77,78,80,82,83,84,86,88,89,90,92,93,94,96,97,99})
=
{2,3,4,5,8,9,10,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,38,46,47,51,54,56,57,59,61,62,64,69,79,81,85,87,91,95,98,100}.
Here rules are labeled as follows:

  DPs:
    { 1: a____^#(X1, X2) -> c_1()
    , 2: a____^#(X, nil()) -> c_2(mark^#(X))
    , 3: a____^#(__(X, Y), Z) ->
         c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
             mark^#(X),
             a____^#(mark(Y), mark(Z)),
             mark^#(Y),
             mark^#(Z))
    , 4: a____^#(nil(), X) -> c_4(mark^#(X))
    , 5: mark^#(__(X1, X2)) ->
         c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 6: mark^#(nil()) -> c_6()
    , 7: mark^#(tt()) -> c_7()
    , 8: mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
    , 9: mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
    , 10: mark^#(isPal(X)) -> c_10(a__isPal^#(X))
    , 11: mark^#(a()) -> c_11()
    , 12: mark^#(e()) -> c_12()
    , 13: mark^#(i()) -> c_13()
    , 14: mark^#(o()) -> c_14()
    , 15: mark^#(u()) -> c_15()
    , 16: mark^#(U11(X1, X2)) ->
          c_16(a__U11^#(mark(X1), X2), mark^#(X1))
    , 17: mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
    , 18: mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
    , 19: mark^#(U21(X1, X2, X3)) ->
          c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
    , 20: mark^#(U22(X1, X2)) ->
          c_20(a__U22^#(mark(X1), X2), mark^#(X1))
    , 21: mark^#(isList(X)) -> c_21(a__isList^#(X))
    , 22: mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
    , 23: mark^#(U31(X1, X2)) ->
          c_23(a__U31^#(mark(X1), X2), mark^#(X1))
    , 24: mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
    , 25: mark^#(isQid(X)) -> c_25(a__isQid^#(X))
    , 26: mark^#(U41(X1, X2, X3)) ->
          c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
    , 27: mark^#(U42(X1, X2)) ->
          c_27(a__U42^#(mark(X1), X2), mark^#(X1))
    , 28: mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
    , 29: mark^#(U51(X1, X2, X3)) ->
          c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
    , 30: mark^#(U52(X1, X2)) ->
          c_30(a__U52^#(mark(X1), X2), mark^#(X1))
    , 31: mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
    , 32: mark^#(U61(X1, X2)) ->
          c_32(a__U61^#(mark(X1), X2), mark^#(X1))
    , 33: mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
    , 34: mark^#(U71(X1, X2)) ->
          c_34(a__U71^#(mark(X1), X2), mark^#(X1))
    , 35: mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
    , 36: mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
    , 37: a__isPalListKind^#(X) -> c_90()
    , 38: a__isPalListKind^#(__(V1, V2)) ->
          c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 39: a__isPalListKind^#(nil()) -> c_92()
    , 40: a__isPalListKind^#(a()) -> c_93()
    , 41: a__isPalListKind^#(e()) -> c_94()
    , 42: a__isPalListKind^#(i()) -> c_95()
    , 43: a__isPalListKind^#(o()) -> c_96()
    , 44: a__isPalListKind^#(u()) -> c_97()
    , 45: a__and^#(X1, X2) -> c_88()
    , 46: a__and^#(tt(), X) -> c_89(mark^#(X))
    , 47: a__isPal^#(V) ->
          c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 48: a__isPal^#(X) -> c_99()
    , 49: a__isPal^#(nil()) -> c_100()
    , 50: a__U11^#(X1, X2) -> c_37()
    , 51: a__U11^#(tt(), V) ->
          c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
    , 52: a__U12^#(X) -> c_39()
    , 53: a__U12^#(tt()) -> c_40()
    , 54: a__isNeList^#(V) ->
          c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 55: a__isNeList^#(X) -> c_42()
    , 56: a__isNeList^#(__(V1, V2)) ->
          c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                        V1,
                        V2),
               a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 57: a__isNeList^#(__(V1, V2)) ->
          c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                        V1,
                        V2),
               a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 58: a__U21^#(X1, X2, X3) -> c_45()
    , 59: a__U21^#(tt(), V1, V2) ->
          c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
    , 60: a__U22^#(X1, X2) -> c_47()
    , 61: a__U22^#(tt(), V2) ->
          c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
    , 62: a__isList^#(V) ->
          c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 63: a__isList^#(X) -> c_50()
    , 64: a__isList^#(__(V1, V2)) ->
          c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                        V1,
                        V2),
               a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 65: a__isList^#(nil()) -> c_52()
    , 66: a__U23^#(X) -> c_53()
    , 67: a__U23^#(tt()) -> c_54()
    , 68: a__U31^#(X1, X2) -> c_55()
    , 69: a__U31^#(tt(), V) ->
          c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
    , 70: a__U32^#(X) -> c_57()
    , 71: a__U32^#(tt()) -> c_58()
    , 72: a__isQid^#(X) -> c_59()
    , 73: a__isQid^#(a()) -> c_60()
    , 74: a__isQid^#(e()) -> c_61()
    , 75: a__isQid^#(i()) -> c_62()
    , 76: a__isQid^#(o()) -> c_63()
    , 77: a__isQid^#(u()) -> c_64()
    , 78: a__U41^#(X1, X2, X3) -> c_65()
    , 79: a__U41^#(tt(), V1, V2) ->
          c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
    , 80: a__U42^#(X1, X2) -> c_67()
    , 81: a__U42^#(tt(), V2) ->
          c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
    , 82: a__U43^#(X) -> c_69()
    , 83: a__U43^#(tt()) -> c_70()
    , 84: a__U51^#(X1, X2, X3) -> c_71()
    , 85: a__U51^#(tt(), V1, V2) ->
          c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
    , 86: a__U52^#(X1, X2) -> c_73()
    , 87: a__U52^#(tt(), V2) ->
          c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
    , 88: a__U53^#(X) -> c_75()
    , 89: a__U53^#(tt()) -> c_76()
    , 90: a__U61^#(X1, X2) -> c_77()
    , 91: a__U61^#(tt(), V) ->
          c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
    , 92: a__U62^#(X) -> c_79()
    , 93: a__U62^#(tt()) -> c_80()
    , 94: a__U71^#(X1, X2) -> c_81()
    , 95: a__U71^#(tt(), V) ->
          c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
    , 96: a__U72^#(X) -> c_83()
    , 97: a__U72^#(tt()) -> c_84()
    , 98: a__isNePal^#(V) ->
          c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 99: a__isNePal^#(X) -> c_86()
    , 100: a__isNePal^#(__(I, __(P, I))) ->
           c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                         and(isPal(P), isPalListKind(P))),
                a__and^#(a__isQid(I), isPalListKind(I)),
                a__isQid^#(I)) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
  , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2), mark^#(X1))
  , mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
  , mark^#(U21(X1, X2, X3)) ->
    c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2), mark^#(X1))
  , mark^#(isList(X)) -> c_21(a__isList^#(X))
  , mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
  , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2), mark^#(X1))
  , mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
  , mark^#(isQid(X)) -> c_25(a__isQid^#(X))
  , mark^#(U41(X1, X2, X3)) ->
    c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2), mark^#(X1))
  , mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
  , mark^#(U51(X1, X2, X3)) ->
    c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2), mark^#(X1))
  , mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
  , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2), mark^#(X1))
  , mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
  , a__isPalListKind^#(__(V1, V2)) ->
    c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__and^#(tt(), X) -> c_89(mark^#(X))
  , a__isPal^#(V) ->
    c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__U11^#(tt(), V) ->
    c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isNeList^#(V) ->
    c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNeList^#(__(V1, V2)) ->
    c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U21^#(tt(), V1, V2) ->
    c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U22^#(tt(), V2) ->
    c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
  , a__U41^#(tt(), V1, V2) ->
    c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U42^#(tt(), V2) ->
    c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U51^#(tt(), V1, V2) ->
    c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U52^#(tt(), V2) ->
    c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
  , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
  , a__U71^#(tt(), V) ->
    c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(V) ->
    c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I)),
         a__isQid^#(I)) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(a()) -> c_11()
  , mark^#(e()) -> c_12()
  , mark^#(i()) -> c_13()
  , mark^#(o()) -> c_14()
  , mark^#(u()) -> c_15()
  , a__isPalListKind^#(X) -> c_90()
  , a__isPalListKind^#(nil()) -> c_92()
  , a__isPalListKind^#(a()) -> c_93()
  , a__isPalListKind^#(e()) -> c_94()
  , a__isPalListKind^#(i()) -> c_95()
  , a__isPalListKind^#(o()) -> c_96()
  , a__isPalListKind^#(u()) -> c_97()
  , a__and^#(X1, X2) -> c_88()
  , a__isPal^#(X) -> c_99()
  , a__isPal^#(nil()) -> c_100()
  , a__U11^#(X1, X2) -> c_37()
  , a__U12^#(X) -> c_39()
  , a__U12^#(tt()) -> c_40()
  , a__isNeList^#(X) -> c_42()
  , a__U21^#(X1, X2, X3) -> c_45()
  , a__U22^#(X1, X2) -> c_47()
  , a__isList^#(X) -> c_50()
  , a__isList^#(nil()) -> c_52()
  , a__U23^#(X) -> c_53()
  , a__U23^#(tt()) -> c_54()
  , a__U31^#(X1, X2) -> c_55()
  , a__U32^#(X) -> c_57()
  , a__U32^#(tt()) -> c_58()
  , a__isQid^#(X) -> c_59()
  , a__isQid^#(a()) -> c_60()
  , a__isQid^#(e()) -> c_61()
  , a__isQid^#(i()) -> c_62()
  , a__isQid^#(o()) -> c_63()
  , a__isQid^#(u()) -> c_64()
  , a__U41^#(X1, X2, X3) -> c_65()
  , a__U42^#(X1, X2) -> c_67()
  , a__U43^#(X) -> c_69()
  , a__U43^#(tt()) -> c_70()
  , a__U51^#(X1, X2, X3) -> c_71()
  , a__U52^#(X1, X2) -> c_73()
  , a__U53^#(X) -> c_75()
  , a__U53^#(tt()) -> c_76()
  , a__U61^#(X1, X2) -> c_77()
  , a__U62^#(X) -> c_79()
  , a__U62^#(tt()) -> c_80()
  , a__U71^#(X1, X2) -> c_81()
  , a__U72^#(X) -> c_83()
  , a__U72^#(tt()) -> c_84()
  , a__isNePal^#(X) -> c_86() }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(isPalListKind(X)) -> a__isPalListKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  , mark(isList(X)) -> a__isList(X)
  , mark(U23(X)) -> a__U23(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U32(X)) -> a__U32(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
  , mark(U43(X)) -> a__U43(mark(X))
  , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  , mark(U53(X)) -> a__U53(mark(X))
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X1, X2) -> U11(X1, X2)
  , a__U11(tt(), V) -> a__U12(a__isNeList(V))
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) ->
    a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isNeList(__(V1, V2)) ->
    a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2)
  , a__U22(X1, X2) -> U22(X1, X2)
  , a__U22(tt(), V2) -> a__U23(a__isList(V2))
  , a__isList(V) -> a__U11(a__isPalListKind(V), V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) ->
    a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isList(nil()) -> tt()
  , a__U23(X) -> U23(X)
  , a__U23(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), V) -> a__U32(a__isQid(V))
  , a__U32(X) -> U32(X)
  , a__U32(tt()) -> tt()
  , a__isQid(X) -> isQid(X)
  , a__isQid(a()) -> tt()
  , a__isQid(e()) -> tt()
  , a__isQid(i()) -> tt()
  , a__isQid(o()) -> tt()
  , a__isQid(u()) -> tt()
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2)
  , a__U42(X1, X2) -> U42(X1, X2)
  , a__U42(tt(), V2) -> a__U43(a__isNeList(V2))
  , a__U43(X) -> U43(X)
  , a__U43(tt()) -> tt()
  , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2)
  , a__U52(X1, X2) -> U52(X1, X2)
  , a__U52(tt(), V2) -> a__U53(a__isList(V2))
  , a__U53(X) -> U53(X)
  , a__U53(tt()) -> tt()
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V) -> a__U62(a__isQid(V))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), V) -> a__U72(a__isNePal(V))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) ->
    a__and(a__and(a__isQid(I), isPalListKind(I)),
           and(isPal(P), isPalListKind(P)))
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isPalListKind(X) -> isPalListKind(X)
  , a__isPalListKind(__(V1, V2)) ->
    a__and(a__isPalListKind(V1), isPalListKind(V2))
  , a__isPalListKind(nil()) -> tt()
  , a__isPalListKind(a()) -> tt()
  , a__isPalListKind(e()) -> tt()
  , a__isPalListKind(i()) -> tt()
  , a__isPalListKind(o()) -> tt()
  , a__isPalListKind(u()) -> tt()
  , a__isPal(V) -> a__U71(a__isPalListKind(V), V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {17,40,45} by applications
of Pre({17,40,45}) =
{1,2,3,4,6,8,9,11,12,14,15,16,18,19,20,21,22,23,24,25,26,27,30,33,47}.
Here rules are labeled as follows:

  DPs:
    { 1: a____^#(X, nil()) -> c_2(mark^#(X))
    , 2: a____^#(__(X, Y), Z) ->
         c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
             mark^#(X),
             a____^#(mark(Y), mark(Z)),
             mark^#(Y),
             mark^#(Z))
    , 3: a____^#(nil(), X) -> c_4(mark^#(X))
    , 4: mark^#(__(X1, X2)) ->
         c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 5: mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
    , 6: mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
    , 7: mark^#(isPal(X)) -> c_10(a__isPal^#(X))
    , 8: mark^#(U11(X1, X2)) ->
         c_16(a__U11^#(mark(X1), X2), mark^#(X1))
    , 9: mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
    , 10: mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
    , 11: mark^#(U21(X1, X2, X3)) ->
          c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
    , 12: mark^#(U22(X1, X2)) ->
          c_20(a__U22^#(mark(X1), X2), mark^#(X1))
    , 13: mark^#(isList(X)) -> c_21(a__isList^#(X))
    , 14: mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
    , 15: mark^#(U31(X1, X2)) ->
          c_23(a__U31^#(mark(X1), X2), mark^#(X1))
    , 16: mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
    , 17: mark^#(isQid(X)) -> c_25(a__isQid^#(X))
    , 18: mark^#(U41(X1, X2, X3)) ->
          c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
    , 19: mark^#(U42(X1, X2)) ->
          c_27(a__U42^#(mark(X1), X2), mark^#(X1))
    , 20: mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
    , 21: mark^#(U51(X1, X2, X3)) ->
          c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
    , 22: mark^#(U52(X1, X2)) ->
          c_30(a__U52^#(mark(X1), X2), mark^#(X1))
    , 23: mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
    , 24: mark^#(U61(X1, X2)) ->
          c_32(a__U61^#(mark(X1), X2), mark^#(X1))
    , 25: mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
    , 26: mark^#(U71(X1, X2)) ->
          c_34(a__U71^#(mark(X1), X2), mark^#(X1))
    , 27: mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
    , 28: mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
    , 29: a__isPalListKind^#(__(V1, V2)) ->
          c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 30: a__and^#(tt(), X) -> c_89(mark^#(X))
    , 31: a__isPal^#(V) ->
          c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 32: a__U11^#(tt(), V) ->
          c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
    , 33: a__isNeList^#(V) ->
          c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 34: a__isNeList^#(__(V1, V2)) ->
          c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                        V1,
                        V2),
               a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 35: a__isNeList^#(__(V1, V2)) ->
          c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                        V1,
                        V2),
               a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 36: a__U21^#(tt(), V1, V2) ->
          c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
    , 37: a__U22^#(tt(), V2) ->
          c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
    , 38: a__isList^#(V) ->
          c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 39: a__isList^#(__(V1, V2)) ->
          c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                        V1,
                        V2),
               a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
               a__isPalListKind^#(V1))
    , 40: a__U31^#(tt(), V) ->
          c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
    , 41: a__U41^#(tt(), V1, V2) ->
          c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
    , 42: a__U42^#(tt(), V2) ->
          c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
    , 43: a__U51^#(tt(), V1, V2) ->
          c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
    , 44: a__U52^#(tt(), V2) ->
          c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
    , 45: a__U61^#(tt(), V) ->
          c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
    , 46: a__U71^#(tt(), V) ->
          c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
    , 47: a__isNePal^#(V) ->
          c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
    , 48: a__isNePal^#(__(I, __(P, I))) ->
          c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                        and(isPal(P), isPalListKind(P))),
               a__and^#(a__isQid(I), isPalListKind(I)),
               a__isQid^#(I))
    , 49: a____^#(X1, X2) -> c_1()
    , 50: mark^#(nil()) -> c_6()
    , 51: mark^#(tt()) -> c_7()
    , 52: mark^#(a()) -> c_11()
    , 53: mark^#(e()) -> c_12()
    , 54: mark^#(i()) -> c_13()
    , 55: mark^#(o()) -> c_14()
    , 56: mark^#(u()) -> c_15()
    , 57: a__isPalListKind^#(X) -> c_90()
    , 58: a__isPalListKind^#(nil()) -> c_92()
    , 59: a__isPalListKind^#(a()) -> c_93()
    , 60: a__isPalListKind^#(e()) -> c_94()
    , 61: a__isPalListKind^#(i()) -> c_95()
    , 62: a__isPalListKind^#(o()) -> c_96()
    , 63: a__isPalListKind^#(u()) -> c_97()
    , 64: a__and^#(X1, X2) -> c_88()
    , 65: a__isPal^#(X) -> c_99()
    , 66: a__isPal^#(nil()) -> c_100()
    , 67: a__U11^#(X1, X2) -> c_37()
    , 68: a__U12^#(X) -> c_39()
    , 69: a__U12^#(tt()) -> c_40()
    , 70: a__isNeList^#(X) -> c_42()
    , 71: a__U21^#(X1, X2, X3) -> c_45()
    , 72: a__U22^#(X1, X2) -> c_47()
    , 73: a__isList^#(X) -> c_50()
    , 74: a__isList^#(nil()) -> c_52()
    , 75: a__U23^#(X) -> c_53()
    , 76: a__U23^#(tt()) -> c_54()
    , 77: a__U31^#(X1, X2) -> c_55()
    , 78: a__U32^#(X) -> c_57()
    , 79: a__U32^#(tt()) -> c_58()
    , 80: a__isQid^#(X) -> c_59()
    , 81: a__isQid^#(a()) -> c_60()
    , 82: a__isQid^#(e()) -> c_61()
    , 83: a__isQid^#(i()) -> c_62()
    , 84: a__isQid^#(o()) -> c_63()
    , 85: a__isQid^#(u()) -> c_64()
    , 86: a__U41^#(X1, X2, X3) -> c_65()
    , 87: a__U42^#(X1, X2) -> c_67()
    , 88: a__U43^#(X) -> c_69()
    , 89: a__U43^#(tt()) -> c_70()
    , 90: a__U51^#(X1, X2, X3) -> c_71()
    , 91: a__U52^#(X1, X2) -> c_73()
    , 92: a__U53^#(X) -> c_75()
    , 93: a__U53^#(tt()) -> c_76()
    , 94: a__U61^#(X1, X2) -> c_77()
    , 95: a__U62^#(X) -> c_79()
    , 96: a__U62^#(tt()) -> c_80()
    , 97: a__U71^#(X1, X2) -> c_81()
    , 98: a__U72^#(X) -> c_83()
    , 99: a__U72^#(tt()) -> c_84()
    , 100: a__isNePal^#(X) -> c_86() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
  , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2), mark^#(X1))
  , mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
  , mark^#(U21(X1, X2, X3)) ->
    c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2), mark^#(X1))
  , mark^#(isList(X)) -> c_21(a__isList^#(X))
  , mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
  , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2), mark^#(X1))
  , mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2, X3)) ->
    c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2), mark^#(X1))
  , mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
  , mark^#(U51(X1, X2, X3)) ->
    c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2), mark^#(X1))
  , mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
  , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2), mark^#(X1))
  , mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
  , a__isPalListKind^#(__(V1, V2)) ->
    c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__and^#(tt(), X) -> c_89(mark^#(X))
  , a__isPal^#(V) ->
    c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__U11^#(tt(), V) ->
    c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isNeList^#(V) ->
    c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNeList^#(__(V1, V2)) ->
    c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U21^#(tt(), V1, V2) ->
    c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U22^#(tt(), V2) ->
    c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U41^#(tt(), V1, V2) ->
    c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U42^#(tt(), V2) ->
    c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U51^#(tt(), V1, V2) ->
    c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U52^#(tt(), V2) ->
    c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), V) ->
    c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(V) ->
    c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I)),
         a__isQid^#(I)) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(a()) -> c_11()
  , mark^#(e()) -> c_12()
  , mark^#(i()) -> c_13()
  , mark^#(o()) -> c_14()
  , mark^#(u()) -> c_15()
  , mark^#(isQid(X)) -> c_25(a__isQid^#(X))
  , a__isPalListKind^#(X) -> c_90()
  , a__isPalListKind^#(nil()) -> c_92()
  , a__isPalListKind^#(a()) -> c_93()
  , a__isPalListKind^#(e()) -> c_94()
  , a__isPalListKind^#(i()) -> c_95()
  , a__isPalListKind^#(o()) -> c_96()
  , a__isPalListKind^#(u()) -> c_97()
  , a__and^#(X1, X2) -> c_88()
  , a__isPal^#(X) -> c_99()
  , a__isPal^#(nil()) -> c_100()
  , a__U11^#(X1, X2) -> c_37()
  , a__U12^#(X) -> c_39()
  , a__U12^#(tt()) -> c_40()
  , a__isNeList^#(X) -> c_42()
  , a__U21^#(X1, X2, X3) -> c_45()
  , a__U22^#(X1, X2) -> c_47()
  , a__isList^#(X) -> c_50()
  , a__isList^#(nil()) -> c_52()
  , a__U23^#(X) -> c_53()
  , a__U23^#(tt()) -> c_54()
  , a__U31^#(X1, X2) -> c_55()
  , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
  , a__U32^#(X) -> c_57()
  , a__U32^#(tt()) -> c_58()
  , a__isQid^#(X) -> c_59()
  , a__isQid^#(a()) -> c_60()
  , a__isQid^#(e()) -> c_61()
  , a__isQid^#(i()) -> c_62()
  , a__isQid^#(o()) -> c_63()
  , a__isQid^#(u()) -> c_64()
  , a__U41^#(X1, X2, X3) -> c_65()
  , a__U42^#(X1, X2) -> c_67()
  , a__U43^#(X) -> c_69()
  , a__U43^#(tt()) -> c_70()
  , a__U51^#(X1, X2, X3) -> c_71()
  , a__U52^#(X1, X2) -> c_73()
  , a__U53^#(X) -> c_75()
  , a__U53^#(tt()) -> c_76()
  , a__U61^#(X1, X2) -> c_77()
  , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
  , a__U62^#(X) -> c_79()
  , a__U62^#(tt()) -> c_80()
  , a__U71^#(X1, X2) -> c_81()
  , a__U72^#(X) -> c_83()
  , a__U72^#(tt()) -> c_84()
  , a__isNePal^#(X) -> c_86() }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(isPalListKind(X)) -> a__isPalListKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  , mark(isList(X)) -> a__isList(X)
  , mark(U23(X)) -> a__U23(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U32(X)) -> a__U32(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
  , mark(U43(X)) -> a__U43(mark(X))
  , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  , mark(U53(X)) -> a__U53(mark(X))
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X1, X2) -> U11(X1, X2)
  , a__U11(tt(), V) -> a__U12(a__isNeList(V))
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) ->
    a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isNeList(__(V1, V2)) ->
    a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2)
  , a__U22(X1, X2) -> U22(X1, X2)
  , a__U22(tt(), V2) -> a__U23(a__isList(V2))
  , a__isList(V) -> a__U11(a__isPalListKind(V), V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) ->
    a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isList(nil()) -> tt()
  , a__U23(X) -> U23(X)
  , a__U23(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), V) -> a__U32(a__isQid(V))
  , a__U32(X) -> U32(X)
  , a__U32(tt()) -> tt()
  , a__isQid(X) -> isQid(X)
  , a__isQid(a()) -> tt()
  , a__isQid(e()) -> tt()
  , a__isQid(i()) -> tt()
  , a__isQid(o()) -> tt()
  , a__isQid(u()) -> tt()
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2)
  , a__U42(X1, X2) -> U42(X1, X2)
  , a__U42(tt(), V2) -> a__U43(a__isNeList(V2))
  , a__U43(X) -> U43(X)
  , a__U43(tt()) -> tt()
  , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2)
  , a__U52(X1, X2) -> U52(X1, X2)
  , a__U52(tt(), V2) -> a__U53(a__isList(V2))
  , a__U53(X) -> U53(X)
  , a__U53(tt()) -> tt()
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V) -> a__U62(a__isQid(V))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), V) -> a__U72(a__isNePal(V))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) ->
    a__and(a__and(a__isQid(I), isPalListKind(I)),
           and(isPal(P), isPalListKind(P)))
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isPalListKind(X) -> isPalListKind(X)
  , a__isPalListKind(__(V1, V2)) ->
    a__and(a__isPalListKind(V1), isPalListKind(V2))
  , a__isPalListKind(nil()) -> tt()
  , a__isPalListKind(a()) -> tt()
  , a__isPalListKind(e()) -> tt()
  , a__isPalListKind(i()) -> tt()
  , a__isPalListKind(o()) -> tt()
  , a__isPalListKind(u()) -> tt()
  , a__isPal(V) -> a__U71(a__isPalListKind(V), V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ a____^#(X1, X2) -> c_1()
, mark^#(nil()) -> c_6()
, mark^#(tt()) -> c_7()
, mark^#(a()) -> c_11()
, mark^#(e()) -> c_12()
, mark^#(i()) -> c_13()
, mark^#(o()) -> c_14()
, mark^#(u()) -> c_15()
, mark^#(isQid(X)) -> c_25(a__isQid^#(X))
, a__isPalListKind^#(X) -> c_90()
, a__isPalListKind^#(nil()) -> c_92()
, a__isPalListKind^#(a()) -> c_93()
, a__isPalListKind^#(e()) -> c_94()
, a__isPalListKind^#(i()) -> c_95()
, a__isPalListKind^#(o()) -> c_96()
, a__isPalListKind^#(u()) -> c_97()
, a__and^#(X1, X2) -> c_88()
, a__isPal^#(X) -> c_99()
, a__isPal^#(nil()) -> c_100()
, a__U11^#(X1, X2) -> c_37()
, a__U12^#(X) -> c_39()
, a__U12^#(tt()) -> c_40()
, a__isNeList^#(X) -> c_42()
, a__U21^#(X1, X2, X3) -> c_45()
, a__U22^#(X1, X2) -> c_47()
, a__isList^#(X) -> c_50()
, a__isList^#(nil()) -> c_52()
, a__U23^#(X) -> c_53()
, a__U23^#(tt()) -> c_54()
, a__U31^#(X1, X2) -> c_55()
, a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V)), a__isQid^#(V))
, a__U32^#(X) -> c_57()
, a__U32^#(tt()) -> c_58()
, a__isQid^#(X) -> c_59()
, a__isQid^#(a()) -> c_60()
, a__isQid^#(e()) -> c_61()
, a__isQid^#(i()) -> c_62()
, a__isQid^#(o()) -> c_63()
, a__isQid^#(u()) -> c_64()
, a__U41^#(X1, X2, X3) -> c_65()
, a__U42^#(X1, X2) -> c_67()
, a__U43^#(X) -> c_69()
, a__U43^#(tt()) -> c_70()
, a__U51^#(X1, X2, X3) -> c_71()
, a__U52^#(X1, X2) -> c_73()
, a__U53^#(X) -> c_75()
, a__U53^#(tt()) -> c_76()
, a__U61^#(X1, X2) -> c_77()
, a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V)), a__isQid^#(V))
, a__U62^#(X) -> c_79()
, a__U62^#(tt()) -> c_80()
, a__U71^#(X1, X2) -> c_81()
, a__U72^#(X) -> c_83()
, a__U72^#(tt()) -> c_84()
, a__isNePal^#(X) -> c_86() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X))
  , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2), mark^#(X1))
  , mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X))
  , mark^#(U21(X1, X2, X3)) ->
    c_19(a__U21^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2), mark^#(X1))
  , mark^#(isList(X)) -> c_21(a__isList^#(X))
  , mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
  , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2), mark^#(X1))
  , mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2, X3)) ->
    c_26(a__U41^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2), mark^#(X1))
  , mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
  , mark^#(U51(X1, X2, X3)) ->
    c_29(a__U51^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2), mark^#(X1))
  , mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
  , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2), mark^#(X1))
  , mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X))
  , a__isPalListKind^#(__(V1, V2)) ->
    c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__and^#(tt(), X) -> c_89(mark^#(X))
  , a__isPal^#(V) ->
    c_98(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__U11^#(tt(), V) ->
    c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isNeList^#(V) ->
    c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNeList^#(__(V1, V2)) ->
    c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U21^#(tt(), V1, V2) ->
    c_46(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U22^#(tt(), V2) ->
    c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_49(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U41^#(tt(), V1, V2) ->
    c_66(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U42^#(tt(), V2) ->
    c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U51^#(tt(), V1, V2) ->
    c_72(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U52^#(tt(), V2) ->
    c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), V) ->
    c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(V) ->
    c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I)),
         a__isQid^#(I)) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(isPalListKind(X)) -> a__isPalListKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  , mark(isList(X)) -> a__isList(X)
  , mark(U23(X)) -> a__U23(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U32(X)) -> a__U32(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
  , mark(U43(X)) -> a__U43(mark(X))
  , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  , mark(U53(X)) -> a__U53(mark(X))
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X1, X2) -> U11(X1, X2)
  , a__U11(tt(), V) -> a__U12(a__isNeList(V))
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) ->
    a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isNeList(__(V1, V2)) ->
    a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2)
  , a__U22(X1, X2) -> U22(X1, X2)
  , a__U22(tt(), V2) -> a__U23(a__isList(V2))
  , a__isList(V) -> a__U11(a__isPalListKind(V), V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) ->
    a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isList(nil()) -> tt()
  , a__U23(X) -> U23(X)
  , a__U23(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), V) -> a__U32(a__isQid(V))
  , a__U32(X) -> U32(X)
  , a__U32(tt()) -> tt()
  , a__isQid(X) -> isQid(X)
  , a__isQid(a()) -> tt()
  , a__isQid(e()) -> tt()
  , a__isQid(i()) -> tt()
  , a__isQid(o()) -> tt()
  , a__isQid(u()) -> tt()
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2)
  , a__U42(X1, X2) -> U42(X1, X2)
  , a__U42(tt(), V2) -> a__U43(a__isNeList(V2))
  , a__U43(X) -> U43(X)
  , a__U43(tt()) -> tt()
  , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2)
  , a__U52(X1, X2) -> U52(X1, X2)
  , a__U52(tt(), V2) -> a__U53(a__isList(V2))
  , a__U53(X) -> U53(X)
  , a__U53(tt()) -> tt()
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V) -> a__U62(a__isQid(V))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), V) -> a__U72(a__isNePal(V))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) ->
    a__and(a__and(a__isQid(I), isPalListKind(I)),
           and(isPal(P), isPalListKind(P)))
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isPalListKind(X) -> isPalListKind(X)
  , a__isPalListKind(__(V1, V2)) ->
    a__and(a__isPalListKind(V1), isPalListKind(V2))
  , a__isPalListKind(nil()) -> tt()
  , a__isPalListKind(a()) -> tt()
  , a__isPalListKind(e()) -> tt()
  , a__isPalListKind(i()) -> tt()
  , a__isPalListKind(o()) -> tt()
  , a__isPalListKind(u()) -> tt()
  , a__isPal(V) -> a__U71(a__isPalListKind(V), V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { mark^#(U12(X)) -> c_17(a__U12^#(mark(X)), mark^#(X))
  , mark^#(U23(X)) -> c_22(a__U23^#(mark(X)), mark^#(X))
  , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2), mark^#(X1))
  , mark^#(U32(X)) -> c_24(a__U32^#(mark(X)), mark^#(X))
  , mark^#(U43(X)) -> c_28(a__U43^#(mark(X)), mark^#(X))
  , mark^#(U53(X)) -> c_31(a__U53^#(mark(X)), mark^#(X))
  , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2), mark^#(X1))
  , mark^#(U62(X)) -> c_33(a__U62^#(mark(X)), mark^#(X))
  , mark^#(U72(X)) -> c_35(a__U72^#(mark(X)), mark^#(X))
  , a__U11^#(tt(), V) ->
    c_38(a__U12^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isNeList^#(V) ->
    c_41(a__U31^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__U22^#(tt(), V2) ->
    c_48(a__U23^#(a__isList(V2)), a__isList^#(V2))
  , a__U42^#(tt(), V2) ->
    c_68(a__U43^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U52^#(tt(), V2) ->
    c_74(a__U53^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), V) ->
    c_82(a__U72^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(V) ->
    c_85(a__U61^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I)),
         a__isQid^#(I)) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a____^#(X, nil()) -> c_1(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_2(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_3(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_4(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(isPalListKind(X)) -> c_5(a__isPalListKind^#(X))
  , mark^#(and(X1, X2)) -> c_6(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isPal(X)) -> c_7(a__isPal^#(X))
  , mark^#(U11(X1, X2)) -> c_8(a__U11^#(mark(X1), X2), mark^#(X1))
  , mark^#(U12(X)) -> c_9(mark^#(X))
  , mark^#(isNeList(X)) -> c_10(a__isNeList^#(X))
  , mark^#(U21(X1, X2, X3)) ->
    c_11(a__U21^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U22(X1, X2)) -> c_12(a__U22^#(mark(X1), X2), mark^#(X1))
  , mark^#(isList(X)) -> c_13(a__isList^#(X))
  , mark^#(U23(X)) -> c_14(mark^#(X))
  , mark^#(U31(X1, X2)) -> c_15(mark^#(X1))
  , mark^#(U32(X)) -> c_16(mark^#(X))
  , mark^#(U41(X1, X2, X3)) ->
    c_17(a__U41^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U42(X1, X2)) -> c_18(a__U42^#(mark(X1), X2), mark^#(X1))
  , mark^#(U43(X)) -> c_19(mark^#(X))
  , mark^#(U51(X1, X2, X3)) ->
    c_20(a__U51^#(mark(X1), X2, X3), mark^#(X1))
  , mark^#(U52(X1, X2)) -> c_21(a__U52^#(mark(X1), X2), mark^#(X1))
  , mark^#(U53(X)) -> c_22(mark^#(X))
  , mark^#(U61(X1, X2)) -> c_23(mark^#(X1))
  , mark^#(U62(X)) -> c_24(mark^#(X))
  , mark^#(U71(X1, X2)) -> c_25(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_26(mark^#(X))
  , mark^#(isNePal(X)) -> c_27(a__isNePal^#(X))
  , a__isPalListKind^#(__(V1, V2)) ->
    c_28(a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__and^#(tt(), X) -> c_29(mark^#(X))
  , a__isPal^#(V) ->
    c_30(a__U71^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__U11^#(tt(), V) -> c_31(a__isNeList^#(V))
  , a__isNeList^#(V) -> c_32(a__isPalListKind^#(V))
  , a__isNeList^#(__(V1, V2)) ->
    c_33(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_34(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U21^#(tt(), V1, V2) ->
    c_35(a__U22^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U22^#(tt(), V2) -> c_36(a__isList^#(V2))
  , a__isList^#(V) ->
    c_37(a__U11^#(a__isPalListKind(V), V), a__isPalListKind^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_38(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)),
                  V1,
                  V2),
         a__and^#(a__isPalListKind(V1), isPalListKind(V2)),
         a__isPalListKind^#(V1))
  , a__U41^#(tt(), V1, V2) ->
    c_39(a__U42^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U42^#(tt(), V2) -> c_40(a__isNeList^#(V2))
  , a__U51^#(tt(), V1, V2) ->
    c_41(a__U52^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U52^#(tt(), V2) -> c_42(a__isList^#(V2))
  , a__U71^#(tt(), V) -> c_43(a__isNePal^#(V))
  , a__isNePal^#(V) -> c_44(a__isPalListKind^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_45(a__and^#(a__and(a__isQid(I), isPalListKind(I)),
                  and(isPal(P), isPalListKind(P))),
         a__and^#(a__isQid(I), isPalListKind(I))) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(isPalListKind(X)) -> a__isPalListKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  , mark(isList(X)) -> a__isList(X)
  , mark(U23(X)) -> a__U23(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U32(X)) -> a__U32(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
  , mark(U43(X)) -> a__U43(mark(X))
  , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  , mark(U53(X)) -> a__U53(mark(X))
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X1, X2) -> U11(X1, X2)
  , a__U11(tt(), V) -> a__U12(a__isNeList(V))
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) ->
    a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isNeList(__(V1, V2)) ->
    a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2)
  , a__U22(X1, X2) -> U22(X1, X2)
  , a__U22(tt(), V2) -> a__U23(a__isList(V2))
  , a__isList(V) -> a__U11(a__isPalListKind(V), V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) ->
    a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)
  , a__isList(nil()) -> tt()
  , a__U23(X) -> U23(X)
  , a__U23(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), V) -> a__U32(a__isQid(V))
  , a__U32(X) -> U32(X)
  , a__U32(tt()) -> tt()
  , a__isQid(X) -> isQid(X)
  , a__isQid(a()) -> tt()
  , a__isQid(e()) -> tt()
  , a__isQid(i()) -> tt()
  , a__isQid(o()) -> tt()
  , a__isQid(u()) -> tt()
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2)
  , a__U42(X1, X2) -> U42(X1, X2)
  , a__U42(tt(), V2) -> a__U43(a__isNeList(V2))
  , a__U43(X) -> U43(X)
  , a__U43(tt()) -> tt()
  , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2)
  , a__U52(X1, X2) -> U52(X1, X2)
  , a__U52(tt(), V2) -> a__U53(a__isList(V2))
  , a__U53(X) -> U53(X)
  , a__U53(tt()) -> tt()
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V) -> a__U62(a__isQid(V))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), V) -> a__U72(a__isNePal(V))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) ->
    a__and(a__and(a__isQid(I), isPalListKind(I)),
           and(isPal(P), isPalListKind(P)))
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isPalListKind(X) -> isPalListKind(X)
  , a__isPalListKind(__(V1, V2)) ->
    a__and(a__isPalListKind(V1), isPalListKind(V2))
  , a__isPalListKind(nil()) -> tt()
  , a__isPalListKind(a()) -> tt()
  , a__isPalListKind(e()) -> tt()
  , a__isPalListKind(i()) -> tt()
  , a__isPalListKind(o()) -> tt()
  , a__isPalListKind(u()) -> tt()
  , a__isPal(V) -> a__U71(a__isPalListKind(V), V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..