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(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(isList(X)) -> a__isList(X)
  , mark(U31(X)) -> a__U31(mark(X))
  , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
  , mark(U42(X)) -> a__U42(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(U61(X)) -> a__U61(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isPal(X)) -> a__isPal(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V2) -> a__U22(a__isList(V2))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__isList(V) -> a__U11(a__isNeList(V))
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2)
  , a__isList(nil()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNeList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isQid(V))
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2)
  , a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2)
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__U61(X) -> U61(X)
  , a__U61(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), P) -> a__U72(a__isPal(P))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isPal(V) -> a__U81(a__isNePal(V))
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt()
  , a__U81(X) -> U81(X)
  , a__U81(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__isNePal(V) -> a__U61(a__isQid(V))
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) }
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^#(a()) -> c_8()
  , mark^#(e()) -> c_9()
  , mark^#(i()) -> c_10()
  , mark^#(o()) -> c_11()
  , mark^#(u()) -> c_12()
  , mark^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U21(X1, X2)) -> c_14(a__U21^#(mark(X1), X2), mark^#(X1))
  , mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
  , mark^#(isList(X)) -> c_16(a__isList^#(X))
  , mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2)) -> c_18(a__U41^#(mark(X1), X2), mark^#(X1))
  , mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
  , mark^#(U51(X1, X2)) -> c_21(a__U51^#(mark(X1), X2), mark^#(X1))
  , mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
  , mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_24(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isPal(X)) -> c_26(a__isPal^#(X))
  , mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
  , mark^#(isQid(X)) -> c_28(a__isQid^#(X))
  , mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
  , a__U11^#(X) -> c_30()
  , a__U11^#(tt()) -> c_31()
  , a__U21^#(X1, X2) -> c_32()
  , a__U21^#(tt(), V2) ->
    c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
  , a__U22^#(X) -> c_34()
  , a__U22^#(tt()) -> c_35()
  , a__isList^#(V) ->
    c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isList^#(X) -> c_37()
  , a__isList^#(__(V1, V2)) ->
    c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isList^#(nil()) -> c_39()
  , a__U31^#(X) -> c_40()
  , a__U31^#(tt()) -> c_41()
  , a__U41^#(X1, X2) -> c_42()
  , a__U41^#(tt(), V2) ->
    c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U42^#(X) -> c_44()
  , a__U42^#(tt()) -> c_45()
  , a__isNeList^#(V) -> c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
  , a__isNeList^#(X) -> c_47()
  , a__isNeList^#(__(V1, V2)) ->
    c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U51^#(X1, X2) -> c_50()
  , a__U51^#(tt(), V2) ->
    c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
  , a__U52^#(X) -> c_52()
  , a__U52^#(tt()) -> c_53()
  , a__U61^#(X) -> c_54()
  , a__U61^#(tt()) -> c_55()
  , a__U71^#(X1, X2) -> c_56()
  , a__U71^#(tt(), P) -> c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
  , a__U72^#(X) -> c_58()
  , a__U72^#(tt()) -> c_59()
  , a__isPal^#(V) -> c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isPal^#(X) -> c_61()
  , a__isPal^#(nil()) -> c_62()
  , a__U81^#(X) -> c_63()
  , a__U81^#(tt()) -> c_64()
  , a__isQid^#(X) -> c_65()
  , a__isQid^#(a()) -> c_66()
  , a__isQid^#(e()) -> c_67()
  , a__isQid^#(i()) -> c_68()
  , a__isQid^#(o()) -> c_69()
  , a__isQid^#(u()) -> c_70()
  , a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
  , a__isNePal^#(X) -> c_72()
  , a__isNePal^#(__(I, __(P, I))) ->
    c_73(a__U71^#(a__isQid(I), P), 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^#(a()) -> c_8()
  , mark^#(e()) -> c_9()
  , mark^#(i()) -> c_10()
  , mark^#(o()) -> c_11()
  , mark^#(u()) -> c_12()
  , mark^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U21(X1, X2)) -> c_14(a__U21^#(mark(X1), X2), mark^#(X1))
  , mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
  , mark^#(isList(X)) -> c_16(a__isList^#(X))
  , mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2)) -> c_18(a__U41^#(mark(X1), X2), mark^#(X1))
  , mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
  , mark^#(U51(X1, X2)) -> c_21(a__U51^#(mark(X1), X2), mark^#(X1))
  , mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
  , mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_24(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isPal(X)) -> c_26(a__isPal^#(X))
  , mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
  , mark^#(isQid(X)) -> c_28(a__isQid^#(X))
  , mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
  , a__U11^#(X) -> c_30()
  , a__U11^#(tt()) -> c_31()
  , a__U21^#(X1, X2) -> c_32()
  , a__U21^#(tt(), V2) ->
    c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
  , a__U22^#(X) -> c_34()
  , a__U22^#(tt()) -> c_35()
  , a__isList^#(V) ->
    c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isList^#(X) -> c_37()
  , a__isList^#(__(V1, V2)) ->
    c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isList^#(nil()) -> c_39()
  , a__U31^#(X) -> c_40()
  , a__U31^#(tt()) -> c_41()
  , a__U41^#(X1, X2) -> c_42()
  , a__U41^#(tt(), V2) ->
    c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U42^#(X) -> c_44()
  , a__U42^#(tt()) -> c_45()
  , a__isNeList^#(V) -> c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
  , a__isNeList^#(X) -> c_47()
  , a__isNeList^#(__(V1, V2)) ->
    c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U51^#(X1, X2) -> c_50()
  , a__U51^#(tt(), V2) ->
    c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
  , a__U52^#(X) -> c_52()
  , a__U52^#(tt()) -> c_53()
  , a__U61^#(X) -> c_54()
  , a__U61^#(tt()) -> c_55()
  , a__U71^#(X1, X2) -> c_56()
  , a__U71^#(tt(), P) -> c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
  , a__U72^#(X) -> c_58()
  , a__U72^#(tt()) -> c_59()
  , a__isPal^#(V) -> c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isPal^#(X) -> c_61()
  , a__isPal^#(nil()) -> c_62()
  , a__U81^#(X) -> c_63()
  , a__U81^#(tt()) -> c_64()
  , a__isQid^#(X) -> c_65()
  , a__isQid^#(a()) -> c_66()
  , a__isQid^#(e()) -> c_67()
  , a__isQid^#(i()) -> c_68()
  , a__isQid^#(o()) -> c_69()
  , a__isQid^#(u()) -> c_70()
  , a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
  , a__isNePal^#(X) -> c_72()
  , a__isNePal^#(__(I, __(P, I))) ->
    c_73(a__U71^#(a__isQid(I), P), 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(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(isList(X)) -> a__isList(X)
  , mark(U31(X)) -> a__U31(mark(X))
  , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
  , mark(U42(X)) -> a__U42(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(U61(X)) -> a__U61(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isPal(X)) -> a__isPal(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V2) -> a__U22(a__isList(V2))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__isList(V) -> a__U11(a__isNeList(V))
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2)
  , a__isList(nil()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNeList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isQid(V))
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2)
  , a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2)
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__U61(X) -> U61(X)
  , a__U61(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), P) -> a__U72(a__isPal(P))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isPal(V) -> a__U81(a__isNePal(V))
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt()
  , a__U81(X) -> U81(X)
  , a__U81(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__isNePal(V) -> a__U61(a__isQid(V))
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of
{1,6,7,8,9,10,11,12,30,31,32,34,35,37,39,40,41,42,44,45,47,50,52,53,54,55,56,58,59,61,62,63,64,65,66,67,68,69,70,72}
by applications of
Pre({1,6,7,8,9,10,11,12,30,31,32,34,35,37,39,40,41,42,44,45,47,50,52,53,54,55,56,58,59,61,62,63,64,65,66,67,68,69,70,72})
=
{2,3,4,5,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,33,36,38,43,46,48,49,51,57,60,71,73}.
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^#(a()) -> c_8()
    , 9: mark^#(e()) -> c_9()
    , 10: mark^#(i()) -> c_10()
    , 11: mark^#(o()) -> c_11()
    , 12: mark^#(u()) -> c_12()
    , 13: mark^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
    , 14: mark^#(U21(X1, X2)) ->
          c_14(a__U21^#(mark(X1), X2), mark^#(X1))
    , 15: mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
    , 16: mark^#(isList(X)) -> c_16(a__isList^#(X))
    , 17: mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
    , 18: mark^#(U41(X1, X2)) ->
          c_18(a__U41^#(mark(X1), X2), mark^#(X1))
    , 19: mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
    , 20: mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
    , 21: mark^#(U51(X1, X2)) ->
          c_21(a__U51^#(mark(X1), X2), mark^#(X1))
    , 22: mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
    , 23: mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
    , 24: mark^#(U71(X1, X2)) ->
          c_24(a__U71^#(mark(X1), X2), mark^#(X1))
    , 25: mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
    , 26: mark^#(isPal(X)) -> c_26(a__isPal^#(X))
    , 27: mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
    , 28: mark^#(isQid(X)) -> c_28(a__isQid^#(X))
    , 29: mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
    , 30: a__U11^#(X) -> c_30()
    , 31: a__U11^#(tt()) -> c_31()
    , 32: a__U21^#(X1, X2) -> c_32()
    , 33: a__U21^#(tt(), V2) ->
          c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
    , 34: a__U22^#(X) -> c_34()
    , 35: a__U22^#(tt()) -> c_35()
    , 36: a__isList^#(V) ->
          c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
    , 37: a__isList^#(X) -> c_37()
    , 38: a__isList^#(__(V1, V2)) ->
          c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
    , 39: a__isList^#(nil()) -> c_39()
    , 40: a__U31^#(X) -> c_40()
    , 41: a__U31^#(tt()) -> c_41()
    , 42: a__U41^#(X1, X2) -> c_42()
    , 43: a__U41^#(tt(), V2) ->
          c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
    , 44: a__U42^#(X) -> c_44()
    , 45: a__U42^#(tt()) -> c_45()
    , 46: a__isNeList^#(V) ->
          c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
    , 47: a__isNeList^#(X) -> c_47()
    , 48: a__isNeList^#(__(V1, V2)) ->
          c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
    , 49: a__isNeList^#(__(V1, V2)) ->
          c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
    , 50: a__U51^#(X1, X2) -> c_50()
    , 51: a__U51^#(tt(), V2) ->
          c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
    , 52: a__U52^#(X) -> c_52()
    , 53: a__U52^#(tt()) -> c_53()
    , 54: a__U61^#(X) -> c_54()
    , 55: a__U61^#(tt()) -> c_55()
    , 56: a__U71^#(X1, X2) -> c_56()
    , 57: a__U71^#(tt(), P) ->
          c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
    , 58: a__U72^#(X) -> c_58()
    , 59: a__U72^#(tt()) -> c_59()
    , 60: a__isPal^#(V) ->
          c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
    , 61: a__isPal^#(X) -> c_61()
    , 62: a__isPal^#(nil()) -> c_62()
    , 63: a__U81^#(X) -> c_63()
    , 64: a__U81^#(tt()) -> c_64()
    , 65: a__isQid^#(X) -> c_65()
    , 66: a__isQid^#(a()) -> c_66()
    , 67: a__isQid^#(e()) -> c_67()
    , 68: a__isQid^#(i()) -> c_68()
    , 69: a__isQid^#(o()) -> c_69()
    , 70: a__isQid^#(u()) -> c_70()
    , 71: a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
    , 72: a__isNePal^#(X) -> c_72()
    , 73: a__isNePal^#(__(I, __(P, I))) ->
          c_73(a__U71^#(a__isQid(I), P), 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^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U21(X1, X2)) -> c_14(a__U21^#(mark(X1), X2), mark^#(X1))
  , mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
  , mark^#(isList(X)) -> c_16(a__isList^#(X))
  , mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2)) -> c_18(a__U41^#(mark(X1), X2), mark^#(X1))
  , mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
  , mark^#(U51(X1, X2)) -> c_21(a__U51^#(mark(X1), X2), mark^#(X1))
  , mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
  , mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_24(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isPal(X)) -> c_26(a__isPal^#(X))
  , mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
  , mark^#(isQid(X)) -> c_28(a__isQid^#(X))
  , mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
  , a__U21^#(tt(), V2) ->
    c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U41^#(tt(), V2) ->
    c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__isNeList^#(V) -> c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
  , a__isNeList^#(__(V1, V2)) ->
    c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U51^#(tt(), V2) ->
    c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), P) -> c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
  , a__isPal^#(V) -> c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_73(a__U71^#(a__isQid(I), P), a__isQid^#(I)) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(a()) -> c_8()
  , mark^#(e()) -> c_9()
  , mark^#(i()) -> c_10()
  , mark^#(o()) -> c_11()
  , mark^#(u()) -> c_12()
  , a__U11^#(X) -> c_30()
  , a__U11^#(tt()) -> c_31()
  , a__U21^#(X1, X2) -> c_32()
  , a__U22^#(X) -> c_34()
  , a__U22^#(tt()) -> c_35()
  , a__isList^#(X) -> c_37()
  , a__isList^#(nil()) -> c_39()
  , a__U31^#(X) -> c_40()
  , a__U31^#(tt()) -> c_41()
  , a__U41^#(X1, X2) -> c_42()
  , a__U42^#(X) -> c_44()
  , a__U42^#(tt()) -> c_45()
  , a__isNeList^#(X) -> c_47()
  , a__U51^#(X1, X2) -> c_50()
  , a__U52^#(X) -> c_52()
  , a__U52^#(tt()) -> c_53()
  , a__U61^#(X) -> c_54()
  , a__U61^#(tt()) -> c_55()
  , a__U71^#(X1, X2) -> c_56()
  , a__U72^#(X) -> c_58()
  , a__U72^#(tt()) -> c_59()
  , a__isPal^#(X) -> c_61()
  , a__isPal^#(nil()) -> c_62()
  , a__U81^#(X) -> c_63()
  , a__U81^#(tt()) -> c_64()
  , a__isQid^#(X) -> c_65()
  , a__isQid^#(a()) -> c_66()
  , a__isQid^#(e()) -> c_67()
  , a__isQid^#(i()) -> c_68()
  , a__isQid^#(o()) -> c_69()
  , a__isQid^#(u()) -> c_70()
  , a__isNePal^#(X) -> c_72() }
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(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(isList(X)) -> a__isList(X)
  , mark(U31(X)) -> a__U31(mark(X))
  , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
  , mark(U42(X)) -> a__U42(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(U61(X)) -> a__U61(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isPal(X)) -> a__isPal(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V2) -> a__U22(a__isList(V2))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__isList(V) -> a__U11(a__isNeList(V))
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2)
  , a__isList(nil()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNeList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isQid(V))
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2)
  , a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2)
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__U61(X) -> U61(X)
  , a__U61(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), P) -> a__U72(a__isPal(P))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isPal(V) -> a__U81(a__isNePal(V))
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt()
  , a__U81(X) -> U81(X)
  , a__U81(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__isNePal(V) -> a__U61(a__isQid(V))
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {20,26,32} by applications
of Pre({20,26,32}) =
{1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,19,21,23,25,28,31}. 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^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
    , 6: mark^#(U21(X1, X2)) ->
         c_14(a__U21^#(mark(X1), X2), mark^#(X1))
    , 7: mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
    , 8: mark^#(isList(X)) -> c_16(a__isList^#(X))
    , 9: mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
    , 10: mark^#(U41(X1, X2)) ->
          c_18(a__U41^#(mark(X1), X2), mark^#(X1))
    , 11: mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
    , 12: mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
    , 13: mark^#(U51(X1, X2)) ->
          c_21(a__U51^#(mark(X1), X2), mark^#(X1))
    , 14: mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
    , 15: mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
    , 16: mark^#(U71(X1, X2)) ->
          c_24(a__U71^#(mark(X1), X2), mark^#(X1))
    , 17: mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
    , 18: mark^#(isPal(X)) -> c_26(a__isPal^#(X))
    , 19: mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
    , 20: mark^#(isQid(X)) -> c_28(a__isQid^#(X))
    , 21: mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
    , 22: a__U21^#(tt(), V2) ->
          c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
    , 23: a__isList^#(V) ->
          c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
    , 24: a__isList^#(__(V1, V2)) ->
          c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
    , 25: a__U41^#(tt(), V2) ->
          c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
    , 26: a__isNeList^#(V) ->
          c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
    , 27: a__isNeList^#(__(V1, V2)) ->
          c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
    , 28: a__isNeList^#(__(V1, V2)) ->
          c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
    , 29: a__U51^#(tt(), V2) ->
          c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
    , 30: a__U71^#(tt(), P) ->
          c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
    , 31: a__isPal^#(V) ->
          c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
    , 32: a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
    , 33: a__isNePal^#(__(I, __(P, I))) ->
          c_73(a__U71^#(a__isQid(I), P), a__isQid^#(I))
    , 34: a____^#(X1, X2) -> c_1()
    , 35: mark^#(nil()) -> c_6()
    , 36: mark^#(tt()) -> c_7()
    , 37: mark^#(a()) -> c_8()
    , 38: mark^#(e()) -> c_9()
    , 39: mark^#(i()) -> c_10()
    , 40: mark^#(o()) -> c_11()
    , 41: mark^#(u()) -> c_12()
    , 42: a__U11^#(X) -> c_30()
    , 43: a__U11^#(tt()) -> c_31()
    , 44: a__U21^#(X1, X2) -> c_32()
    , 45: a__U22^#(X) -> c_34()
    , 46: a__U22^#(tt()) -> c_35()
    , 47: a__isList^#(X) -> c_37()
    , 48: a__isList^#(nil()) -> c_39()
    , 49: a__U31^#(X) -> c_40()
    , 50: a__U31^#(tt()) -> c_41()
    , 51: a__U41^#(X1, X2) -> c_42()
    , 52: a__U42^#(X) -> c_44()
    , 53: a__U42^#(tt()) -> c_45()
    , 54: a__isNeList^#(X) -> c_47()
    , 55: a__U51^#(X1, X2) -> c_50()
    , 56: a__U52^#(X) -> c_52()
    , 57: a__U52^#(tt()) -> c_53()
    , 58: a__U61^#(X) -> c_54()
    , 59: a__U61^#(tt()) -> c_55()
    , 60: a__U71^#(X1, X2) -> c_56()
    , 61: a__U72^#(X) -> c_58()
    , 62: a__U72^#(tt()) -> c_59()
    , 63: a__isPal^#(X) -> c_61()
    , 64: a__isPal^#(nil()) -> c_62()
    , 65: a__U81^#(X) -> c_63()
    , 66: a__U81^#(tt()) -> c_64()
    , 67: a__isQid^#(X) -> c_65()
    , 68: a__isQid^#(a()) -> c_66()
    , 69: a__isQid^#(e()) -> c_67()
    , 70: a__isQid^#(i()) -> c_68()
    , 71: a__isQid^#(o()) -> c_69()
    , 72: a__isQid^#(u()) -> c_70()
    , 73: a__isNePal^#(X) -> c_72() }

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^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U21(X1, X2)) -> c_14(a__U21^#(mark(X1), X2), mark^#(X1))
  , mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
  , mark^#(isList(X)) -> c_16(a__isList^#(X))
  , mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2)) -> c_18(a__U41^#(mark(X1), X2), mark^#(X1))
  , mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
  , mark^#(U51(X1, X2)) -> c_21(a__U51^#(mark(X1), X2), mark^#(X1))
  , mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
  , mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_24(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isPal(X)) -> c_26(a__isPal^#(X))
  , mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
  , a__U21^#(tt(), V2) ->
    c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U41^#(tt(), V2) ->
    c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__isNeList^#(__(V1, V2)) ->
    c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U51^#(tt(), V2) ->
    c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), P) -> c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
  , a__isPal^#(V) -> c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_73(a__U71^#(a__isQid(I), P), a__isQid^#(I)) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(a()) -> c_8()
  , mark^#(e()) -> c_9()
  , mark^#(i()) -> c_10()
  , mark^#(o()) -> c_11()
  , mark^#(u()) -> c_12()
  , mark^#(isQid(X)) -> c_28(a__isQid^#(X))
  , a__U11^#(X) -> c_30()
  , a__U11^#(tt()) -> c_31()
  , a__U21^#(X1, X2) -> c_32()
  , a__U22^#(X) -> c_34()
  , a__U22^#(tt()) -> c_35()
  , a__isList^#(X) -> c_37()
  , a__isList^#(nil()) -> c_39()
  , a__U31^#(X) -> c_40()
  , a__U31^#(tt()) -> c_41()
  , a__U41^#(X1, X2) -> c_42()
  , a__U42^#(X) -> c_44()
  , a__U42^#(tt()) -> c_45()
  , a__isNeList^#(V) -> c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
  , a__isNeList^#(X) -> c_47()
  , a__U51^#(X1, X2) -> c_50()
  , a__U52^#(X) -> c_52()
  , a__U52^#(tt()) -> c_53()
  , a__U61^#(X) -> c_54()
  , a__U61^#(tt()) -> c_55()
  , a__U71^#(X1, X2) -> c_56()
  , a__U72^#(X) -> c_58()
  , a__U72^#(tt()) -> c_59()
  , a__isPal^#(X) -> c_61()
  , a__isPal^#(nil()) -> c_62()
  , a__U81^#(X) -> c_63()
  , a__U81^#(tt()) -> c_64()
  , a__isQid^#(X) -> c_65()
  , a__isQid^#(a()) -> c_66()
  , a__isQid^#(e()) -> c_67()
  , a__isQid^#(i()) -> c_68()
  , a__isQid^#(o()) -> c_69()
  , a__isQid^#(u()) -> c_70()
  , a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
  , a__isNePal^#(X) -> c_72() }
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(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(isList(X)) -> a__isList(X)
  , mark(U31(X)) -> a__U31(mark(X))
  , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
  , mark(U42(X)) -> a__U42(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(U61(X)) -> a__U61(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isPal(X)) -> a__isPal(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V2) -> a__U22(a__isList(V2))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__isList(V) -> a__U11(a__isNeList(V))
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2)
  , a__isList(nil()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNeList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isQid(V))
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2)
  , a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2)
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__U61(X) -> U61(X)
  , a__U61(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), P) -> a__U72(a__isPal(P))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isPal(V) -> a__U81(a__isNePal(V))
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt()
  , a__U81(X) -> U81(X)
  , a__U81(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__isNePal(V) -> a__U61(a__isQid(V))
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) }
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_8()
, mark^#(e()) -> c_9()
, mark^#(i()) -> c_10()
, mark^#(o()) -> c_11()
, mark^#(u()) -> c_12()
, mark^#(isQid(X)) -> c_28(a__isQid^#(X))
, a__U11^#(X) -> c_30()
, a__U11^#(tt()) -> c_31()
, a__U21^#(X1, X2) -> c_32()
, a__U22^#(X) -> c_34()
, a__U22^#(tt()) -> c_35()
, a__isList^#(X) -> c_37()
, a__isList^#(nil()) -> c_39()
, a__U31^#(X) -> c_40()
, a__U31^#(tt()) -> c_41()
, a__U41^#(X1, X2) -> c_42()
, a__U42^#(X) -> c_44()
, a__U42^#(tt()) -> c_45()
, a__isNeList^#(V) -> c_46(a__U31^#(a__isQid(V)), a__isQid^#(V))
, a__isNeList^#(X) -> c_47()
, a__U51^#(X1, X2) -> c_50()
, a__U52^#(X) -> c_52()
, a__U52^#(tt()) -> c_53()
, a__U61^#(X) -> c_54()
, a__U61^#(tt()) -> c_55()
, a__U71^#(X1, X2) -> c_56()
, a__U72^#(X) -> c_58()
, a__U72^#(tt()) -> c_59()
, a__isPal^#(X) -> c_61()
, a__isPal^#(nil()) -> c_62()
, a__U81^#(X) -> c_63()
, a__U81^#(tt()) -> c_64()
, a__isQid^#(X) -> c_65()
, a__isQid^#(a()) -> c_66()
, a__isQid^#(e()) -> c_67()
, a__isQid^#(i()) -> c_68()
, a__isQid^#(o()) -> c_69()
, a__isQid^#(u()) -> c_70()
, a__isNePal^#(V) -> c_71(a__U61^#(a__isQid(V)), a__isQid^#(V))
, a__isNePal^#(X) -> c_72() }

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^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U21(X1, X2)) -> c_14(a__U21^#(mark(X1), X2), mark^#(X1))
  , mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
  , mark^#(isList(X)) -> c_16(a__isList^#(X))
  , mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
  , mark^#(U41(X1, X2)) -> c_18(a__U41^#(mark(X1), X2), mark^#(X1))
  , mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
  , mark^#(isNeList(X)) -> c_20(a__isNeList^#(X))
  , mark^#(U51(X1, X2)) -> c_21(a__U51^#(mark(X1), X2), mark^#(X1))
  , mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
  , mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
  , mark^#(U71(X1, X2)) -> c_24(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
  , mark^#(isPal(X)) -> c_26(a__isPal^#(X))
  , mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_29(a__isNePal^#(X))
  , a__U21^#(tt(), V2) ->
    c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_38(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U41^#(tt(), V2) ->
    c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__isNeList^#(__(V1, V2)) ->
    c_48(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_49(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U51^#(tt(), V2) ->
    c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), P) -> c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
  , a__isPal^#(V) -> c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_73(a__U71^#(a__isQid(I), P), 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(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(isList(X)) -> a__isList(X)
  , mark(U31(X)) -> a__U31(mark(X))
  , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
  , mark(U42(X)) -> a__U42(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(U61(X)) -> a__U61(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isPal(X)) -> a__isPal(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V2) -> a__U22(a__isList(V2))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__isList(V) -> a__U11(a__isNeList(V))
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2)
  , a__isList(nil()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNeList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isQid(V))
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2)
  , a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2)
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__U61(X) -> U61(X)
  , a__U61(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), P) -> a__U72(a__isPal(P))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isPal(V) -> a__U81(a__isNePal(V))
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt()
  , a__U81(X) -> U81(X)
  , a__U81(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__isNePal(V) -> a__U61(a__isQid(V))
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) }
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^#(U11(X)) -> c_13(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U22(X)) -> c_15(a__U22^#(mark(X)), mark^#(X))
  , mark^#(U31(X)) -> c_17(a__U31^#(mark(X)), mark^#(X))
  , mark^#(U42(X)) -> c_19(a__U42^#(mark(X)), mark^#(X))
  , mark^#(U52(X)) -> c_22(a__U52^#(mark(X)), mark^#(X))
  , mark^#(U61(X)) -> c_23(a__U61^#(mark(X)), mark^#(X))
  , mark^#(U72(X)) -> c_25(a__U72^#(mark(X)), mark^#(X))
  , mark^#(U81(X)) -> c_27(a__U81^#(mark(X)), mark^#(X))
  , a__U21^#(tt(), V2) ->
    c_33(a__U22^#(a__isList(V2)), a__isList^#(V2))
  , a__isList^#(V) ->
    c_36(a__U11^#(a__isNeList(V)), a__isNeList^#(V))
  , a__U41^#(tt(), V2) ->
    c_43(a__U42^#(a__isNeList(V2)), a__isNeList^#(V2))
  , a__U51^#(tt(), V2) ->
    c_51(a__U52^#(a__isList(V2)), a__isList^#(V2))
  , a__U71^#(tt(), P) -> c_57(a__U72^#(a__isPal(P)), a__isPal^#(P))
  , a__isPal^#(V) -> c_60(a__U81^#(a__isNePal(V)), a__isNePal^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_73(a__U71^#(a__isQid(I), P), 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^#(U11(X)) -> c_5(mark^#(X))
  , mark^#(U21(X1, X2)) -> c_6(a__U21^#(mark(X1), X2), mark^#(X1))
  , mark^#(U22(X)) -> c_7(mark^#(X))
  , mark^#(isList(X)) -> c_8(a__isList^#(X))
  , mark^#(U31(X)) -> c_9(mark^#(X))
  , mark^#(U41(X1, X2)) -> c_10(a__U41^#(mark(X1), X2), mark^#(X1))
  , mark^#(U42(X)) -> c_11(mark^#(X))
  , mark^#(isNeList(X)) -> c_12(a__isNeList^#(X))
  , mark^#(U51(X1, X2)) -> c_13(a__U51^#(mark(X1), X2), mark^#(X1))
  , mark^#(U52(X)) -> c_14(mark^#(X))
  , mark^#(U61(X)) -> c_15(mark^#(X))
  , mark^#(U71(X1, X2)) -> c_16(a__U71^#(mark(X1), X2), mark^#(X1))
  , mark^#(U72(X)) -> c_17(mark^#(X))
  , mark^#(isPal(X)) -> c_18(a__isPal^#(X))
  , mark^#(U81(X)) -> c_19(mark^#(X))
  , mark^#(isNePal(X)) -> c_20(a__isNePal^#(X))
  , a__U21^#(tt(), V2) -> c_21(a__isList^#(V2))
  , a__isList^#(V) -> c_22(a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_23(a__U21^#(a__isList(V1), V2), a__isList^#(V1))
  , a__U41^#(tt(), V2) -> c_24(a__isNeList^#(V2))
  , a__isNeList^#(__(V1, V2)) ->
    c_25(a__U41^#(a__isList(V1), V2), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_26(a__U51^#(a__isNeList(V1), V2), a__isNeList^#(V1))
  , a__U51^#(tt(), V2) -> c_27(a__isList^#(V2))
  , a__U71^#(tt(), P) -> c_28(a__isPal^#(P))
  , a__isPal^#(V) -> c_29(a__isNePal^#(V))
  , a__isNePal^#(__(I, __(P, I))) -> c_30(a__U71^#(a__isQid(I), P)) }
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(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(isList(X)) -> a__isList(X)
  , mark(U31(X)) -> a__U31(mark(X))
  , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
  , mark(U42(X)) -> a__U42(mark(X))
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(U61(X)) -> a__U61(mark(X))
  , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
  , mark(U72(X)) -> a__U72(mark(X))
  , mark(isPal(X)) -> a__isPal(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V2) -> a__U22(a__isList(V2))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__isList(V) -> a__U11(a__isNeList(V))
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2)
  , a__isList(nil()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNeList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNeList(V) -> a__U31(a__isQid(V))
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2)
  , a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2)
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__U61(X) -> U61(X)
  , a__U61(tt()) -> tt()
  , a__U71(X1, X2) -> U71(X1, X2)
  , a__U71(tt(), P) -> a__U72(a__isPal(P))
  , a__U72(X) -> U72(X)
  , a__U72(tt()) -> tt()
  , a__isPal(V) -> a__U81(a__isNePal(V))
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt()
  , a__U81(X) -> U81(X)
  , a__U81(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__isNePal(V) -> a__U61(a__isQid(V))
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..