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(isList(X)) -> a__isList(X)
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isList(V) -> a__isNeList(V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
  , a__isList(nil()) -> tt()
  , a__isNeList(V) -> a__isQid(V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
  , a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
  , 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__isQid(V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
  , a__isPal(V) -> a__isNePal(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^#(isList(X)) -> c_8(a__isList^#(X))
  , mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
  , 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^#(and(X1, X2)) -> c_16(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isQid(X)) -> c_17(a__isQid^#(X))
  , mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
  , a__isList^#(V) -> c_21(a__isNeList^#(V))
  , a__isList^#(X) -> c_22()
  , a__isList^#(__(V1, V2)) ->
    c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
  , a__isList^#(nil()) -> c_24()
  , a__isNeList^#(V) -> c_25(a__isQid^#(V))
  , a__isNeList^#(X) -> c_26()
  , a__isNeList^#(__(V1, V2)) ->
    c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
  , a__isPal^#(V) -> c_38(a__isNePal^#(V))
  , a__isPal^#(X) -> c_39()
  , a__isPal^#(nil()) -> c_40()
  , a__and^#(X1, X2) -> c_19()
  , a__and^#(tt(), X) -> c_20(mark^#(X))
  , a__isQid^#(X) -> c_29()
  , a__isQid^#(a()) -> c_30()
  , a__isQid^#(e()) -> c_31()
  , a__isQid^#(i()) -> c_32()
  , a__isQid^#(o()) -> c_33()
  , a__isQid^#(u()) -> c_34()
  , a__isNePal^#(V) -> c_35(a__isQid^#(V))
  , a__isNePal^#(X) -> c_36()
  , a__isNePal^#(__(I, __(P, I))) ->
    c_37(a__and^#(a__isQid(I), isPal(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^#(isList(X)) -> c_8(a__isList^#(X))
  , mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
  , 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^#(and(X1, X2)) -> c_16(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isQid(X)) -> c_17(a__isQid^#(X))
  , mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
  , a__isList^#(V) -> c_21(a__isNeList^#(V))
  , a__isList^#(X) -> c_22()
  , a__isList^#(__(V1, V2)) ->
    c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
  , a__isList^#(nil()) -> c_24()
  , a__isNeList^#(V) -> c_25(a__isQid^#(V))
  , a__isNeList^#(X) -> c_26()
  , a__isNeList^#(__(V1, V2)) ->
    c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
  , a__isPal^#(V) -> c_38(a__isNePal^#(V))
  , a__isPal^#(X) -> c_39()
  , a__isPal^#(nil()) -> c_40()
  , a__and^#(X1, X2) -> c_19()
  , a__and^#(tt(), X) -> c_20(mark^#(X))
  , a__isQid^#(X) -> c_29()
  , a__isQid^#(a()) -> c_30()
  , a__isQid^#(e()) -> c_31()
  , a__isQid^#(i()) -> c_32()
  , a__isQid^#(o()) -> c_33()
  , a__isQid^#(u()) -> c_34()
  , a__isNePal^#(V) -> c_35(a__isQid^#(V))
  , a__isNePal^#(X) -> c_36()
  , a__isNePal^#(__(I, __(P, I))) ->
    c_37(a__and^#(a__isQid(I), isPal(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(isList(X)) -> a__isList(X)
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isList(V) -> a__isNeList(V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
  , a__isList(nil()) -> tt()
  , a__isNeList(V) -> a__isQid(V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
  , a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
  , 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__isQid(V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
  , a__isPal(V) -> a__isNePal(V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of
{1,6,7,11,12,13,14,15,20,22,24,28,29,30,32,33,34,35,36,37,39} by
applications of
Pre({1,6,7,11,12,13,14,15,20,22,24,28,29,30,32,33,34,35,36,37,39})
= {2,3,4,5,8,9,10,16,17,18,19,21,23,25,26,27,31,38,40}. 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^#(isList(X)) -> c_8(a__isList^#(X))
    , 9: mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
    , 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^#(and(X1, X2)) ->
          c_16(a__and^#(mark(X1), X2), mark^#(X1))
    , 17: mark^#(isQid(X)) -> c_17(a__isQid^#(X))
    , 18: mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
    , 19: a__isList^#(V) -> c_21(a__isNeList^#(V))
    , 20: a__isList^#(X) -> c_22()
    , 21: a__isList^#(__(V1, V2)) ->
          c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
    , 22: a__isList^#(nil()) -> c_24()
    , 23: a__isNeList^#(V) -> c_25(a__isQid^#(V))
    , 24: a__isNeList^#(X) -> c_26()
    , 25: a__isNeList^#(__(V1, V2)) ->
          c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
    , 26: a__isNeList^#(__(V1, V2)) ->
          c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
    , 27: a__isPal^#(V) -> c_38(a__isNePal^#(V))
    , 28: a__isPal^#(X) -> c_39()
    , 29: a__isPal^#(nil()) -> c_40()
    , 30: a__and^#(X1, X2) -> c_19()
    , 31: a__and^#(tt(), X) -> c_20(mark^#(X))
    , 32: a__isQid^#(X) -> c_29()
    , 33: a__isQid^#(a()) -> c_30()
    , 34: a__isQid^#(e()) -> c_31()
    , 35: a__isQid^#(i()) -> c_32()
    , 36: a__isQid^#(o()) -> c_33()
    , 37: a__isQid^#(u()) -> c_34()
    , 38: a__isNePal^#(V) -> c_35(a__isQid^#(V))
    , 39: a__isNePal^#(X) -> c_36()
    , 40: a__isNePal^#(__(I, __(P, I))) ->
          c_37(a__and^#(a__isQid(I), isPal(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^#(isList(X)) -> c_8(a__isList^#(X))
  , mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(and(X1, X2)) -> c_16(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isQid(X)) -> c_17(a__isQid^#(X))
  , mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
  , a__isList^#(V) -> c_21(a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
  , a__isNeList^#(V) -> c_25(a__isQid^#(V))
  , a__isNeList^#(__(V1, V2)) ->
    c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
  , a__isPal^#(V) -> c_38(a__isNePal^#(V))
  , a__and^#(tt(), X) -> c_20(mark^#(X))
  , a__isNePal^#(V) -> c_35(a__isQid^#(V))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_37(a__and^#(a__isQid(I), isPal(P)), 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__isList^#(X) -> c_22()
  , a__isList^#(nil()) -> c_24()
  , a__isNeList^#(X) -> c_26()
  , a__isPal^#(X) -> c_39()
  , a__isPal^#(nil()) -> c_40()
  , a__and^#(X1, X2) -> c_19()
  , a__isQid^#(X) -> c_29()
  , a__isQid^#(a()) -> c_30()
  , a__isQid^#(e()) -> c_31()
  , a__isQid^#(i()) -> c_32()
  , a__isQid^#(o()) -> c_33()
  , a__isQid^#(u()) -> c_34()
  , a__isNePal^#(X) -> c_36() }
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(isList(X)) -> a__isList(X)
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isList(V) -> a__isNeList(V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
  , a__isList(nil()) -> tt()
  , a__isNeList(V) -> a__isQid(V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
  , a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
  , 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__isQid(V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
  , a__isPal(V) -> a__isNePal(V)
  , a__isPal(X) -> isPal(X)
  , a__isPal(nil()) -> tt() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {9,13,18} by applications
of Pre({9,13,18}) = {1,2,3,4,6,8,10,11,15,16,17}. 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^#(isList(X)) -> c_8(a__isList^#(X))
    , 6: mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
    , 7: mark^#(isPal(X)) -> c_10(a__isPal^#(X))
    , 8: mark^#(and(X1, X2)) ->
         c_16(a__and^#(mark(X1), X2), mark^#(X1))
    , 9: mark^#(isQid(X)) -> c_17(a__isQid^#(X))
    , 10: mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
    , 11: a__isList^#(V) -> c_21(a__isNeList^#(V))
    , 12: a__isList^#(__(V1, V2)) ->
          c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
    , 13: a__isNeList^#(V) -> c_25(a__isQid^#(V))
    , 14: a__isNeList^#(__(V1, V2)) ->
          c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
    , 15: a__isNeList^#(__(V1, V2)) ->
          c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
    , 16: a__isPal^#(V) -> c_38(a__isNePal^#(V))
    , 17: a__and^#(tt(), X) -> c_20(mark^#(X))
    , 18: a__isNePal^#(V) -> c_35(a__isQid^#(V))
    , 19: a__isNePal^#(__(I, __(P, I))) ->
          c_37(a__and^#(a__isQid(I), isPal(P)), a__isQid^#(I))
    , 20: a____^#(X1, X2) -> c_1()
    , 21: mark^#(nil()) -> c_6()
    , 22: mark^#(tt()) -> c_7()
    , 23: mark^#(a()) -> c_11()
    , 24: mark^#(e()) -> c_12()
    , 25: mark^#(i()) -> c_13()
    , 26: mark^#(o()) -> c_14()
    , 27: mark^#(u()) -> c_15()
    , 28: a__isList^#(X) -> c_22()
    , 29: a__isList^#(nil()) -> c_24()
    , 30: a__isNeList^#(X) -> c_26()
    , 31: a__isPal^#(X) -> c_39()
    , 32: a__isPal^#(nil()) -> c_40()
    , 33: a__and^#(X1, X2) -> c_19()
    , 34: a__isQid^#(X) -> c_29()
    , 35: a__isQid^#(a()) -> c_30()
    , 36: a__isQid^#(e()) -> c_31()
    , 37: a__isQid^#(i()) -> c_32()
    , 38: a__isQid^#(o()) -> c_33()
    , 39: a__isQid^#(u()) -> c_34()
    , 40: a__isNePal^#(X) -> c_36() }

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^#(isList(X)) -> c_8(a__isList^#(X))
  , mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(and(X1, X2)) -> c_16(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
  , a__isList^#(V) -> c_21(a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
  , a__isPal^#(V) -> c_38(a__isNePal^#(V))
  , a__and^#(tt(), X) -> c_20(mark^#(X))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_37(a__and^#(a__isQid(I), isPal(P)), 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_17(a__isQid^#(X))
  , a__isList^#(X) -> c_22()
  , a__isList^#(nil()) -> c_24()
  , a__isNeList^#(V) -> c_25(a__isQid^#(V))
  , a__isNeList^#(X) -> c_26()
  , a__isPal^#(X) -> c_39()
  , a__isPal^#(nil()) -> c_40()
  , a__and^#(X1, X2) -> c_19()
  , a__isQid^#(X) -> c_29()
  , a__isQid^#(a()) -> c_30()
  , a__isQid^#(e()) -> c_31()
  , a__isQid^#(i()) -> c_32()
  , a__isQid^#(o()) -> c_33()
  , a__isQid^#(u()) -> c_34()
  , a__isNePal^#(V) -> c_35(a__isQid^#(V))
  , a__isNePal^#(X) -> c_36() }
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(isList(X)) -> a__isList(X)
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isList(V) -> a__isNeList(V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
  , a__isList(nil()) -> tt()
  , a__isNeList(V) -> a__isQid(V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
  , a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
  , 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__isQid(V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
  , a__isPal(V) -> a__isNePal(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_17(a__isQid^#(X))
, a__isList^#(X) -> c_22()
, a__isList^#(nil()) -> c_24()
, a__isNeList^#(V) -> c_25(a__isQid^#(V))
, a__isNeList^#(X) -> c_26()
, a__isPal^#(X) -> c_39()
, a__isPal^#(nil()) -> c_40()
, a__and^#(X1, X2) -> c_19()
, a__isQid^#(X) -> c_29()
, a__isQid^#(a()) -> c_30()
, a__isQid^#(e()) -> c_31()
, a__isQid^#(i()) -> c_32()
, a__isQid^#(o()) -> c_33()
, a__isQid^#(u()) -> c_34()
, a__isNePal^#(V) -> c_35(a__isQid^#(V))
, a__isNePal^#(X) -> c_36() }

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^#(isList(X)) -> c_8(a__isList^#(X))
  , mark^#(isNeList(X)) -> c_9(a__isNeList^#(X))
  , mark^#(isPal(X)) -> c_10(a__isPal^#(X))
  , mark^#(and(X1, X2)) -> c_16(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isNePal(X)) -> c_18(a__isNePal^#(X))
  , a__isList^#(V) -> c_21(a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_23(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_27(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_28(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
  , a__isPal^#(V) -> c_38(a__isNePal^#(V))
  , a__and^#(tt(), X) -> c_20(mark^#(X))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_37(a__and^#(a__isQid(I), isPal(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(isList(X)) -> a__isList(X)
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isList(V) -> a__isNeList(V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
  , a__isList(nil()) -> tt()
  , a__isNeList(V) -> a__isQid(V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
  , a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
  , 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__isQid(V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
  , a__isPal(V) -> a__isNePal(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:

  { a__isNePal^#(__(I, __(P, I))) ->
    c_37(a__and^#(a__isQid(I), isPal(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^#(isList(X)) -> c_5(a__isList^#(X))
  , mark^#(isNeList(X)) -> c_6(a__isNeList^#(X))
  , mark^#(isPal(X)) -> c_7(a__isPal^#(X))
  , mark^#(and(X1, X2)) -> c_8(a__and^#(mark(X1), X2), mark^#(X1))
  , mark^#(isNePal(X)) -> c_9(a__isNePal^#(X))
  , a__isList^#(V) -> c_10(a__isNeList^#(V))
  , a__isList^#(__(V1, V2)) ->
    c_11(a__and^#(a__isList(V1), isList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_12(a__and^#(a__isList(V1), isNeList(V2)), a__isList^#(V1))
  , a__isNeList^#(__(V1, V2)) ->
    c_13(a__and^#(a__isNeList(V1), isList(V2)), a__isNeList^#(V1))
  , a__isPal^#(V) -> c_14(a__isNePal^#(V))
  , a__and^#(tt(), X) -> c_15(mark^#(X))
  , a__isNePal^#(__(I, __(P, I))) ->
    c_16(a__and^#(a__isQid(I), isPal(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(isList(X)) -> a__isList(X)
  , mark(isNeList(X)) -> a__isNeList(X)
  , mark(isPal(X)) -> a__isPal(X)
  , mark(a()) -> a()
  , mark(e()) -> e()
  , mark(i()) -> i()
  , mark(o()) -> o()
  , mark(u()) -> u()
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isQid(X)) -> a__isQid(X)
  , mark(isNePal(X)) -> a__isNePal(X)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isList(V) -> a__isNeList(V)
  , a__isList(X) -> isList(X)
  , a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
  , a__isList(nil()) -> tt()
  , a__isNeList(V) -> a__isQid(V)
  , a__isNeList(X) -> isNeList(X)
  , a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
  , a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
  , 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__isQid(V)
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
  , a__isPal(V) -> a__isNePal(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:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   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..