MAYBE

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

Strict Trs:
  { a__zeros() -> cons(0(), zeros())
  , a__zeros() -> zeros()
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> tt()
  , a__U21(X) -> U21(X)
  , a__U21(tt()) -> tt()
  , a__U31(X) -> U31(X)
  , a__U31(tt()) -> tt()
  , a__U41(X1, X2) -> U41(X1, X2)
  , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2))
  , a__U42(X) -> U42(X)
  , a__U42(tt()) -> tt()
  , a__isNatIList(V) -> a__U31(a__isNatList(V))
  , a__isNatIList(X) -> isNatIList(X)
  , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2)
  , a__isNatIList(zeros()) -> tt()
  , a__U51(X1, X2) -> U51(X1, X2)
  , a__U51(tt(), V2) -> a__U52(a__isNatList(V2))
  , a__U52(X) -> U52(X)
  , a__U52(tt()) -> tt()
  , a__isNatList(X) -> isNatList(X)
  , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2)
  , a__isNatList(nil()) -> tt()
  , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2)
  , a__U61(X1, X2) -> U61(X1, X2)
  , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2))
  , a__U62(X) -> U62(X)
  , a__U62(tt()) -> tt()
  , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
  , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L)
  , a__U72(X1, X2) -> U72(X1, X2)
  , a__U72(tt(), L) -> s(a__length(mark(L)))
  , a__isNat(X) -> isNat(X)
  , a__isNat(0()) -> tt()
  , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
  , a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
  , a__length(X) -> length(X)
  , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N)
  , a__length(nil()) -> 0()
  , mark(cons(X1, X2)) -> cons(mark(X1), X2)
  , mark(0()) -> 0()
  , mark(zeros()) -> a__zeros()
  , mark(tt()) -> tt()
  , mark(s(X)) -> s(mark(X))
  , mark(nil()) -> nil()
  , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
  , mark(length(X)) -> a__length(mark(X))
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U21(X)) -> a__U21(mark(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(isNatIList(X)) -> a__isNatIList(X)
  , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  , mark(U52(X)) -> a__U52(mark(X))
  , mark(isNatList(X)) -> a__isNatList(X)
  , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  , mark(U62(X)) -> a__U62(mark(X))
  , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
  , mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
  , mark(isNat(X)) -> a__isNat(X)
  , mark(U81(X)) -> a__U81(mark(X))
  , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
  , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4)
  , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4)
  , a__U81(X) -> U81(X)
  , a__U81(tt()) -> nil()
  , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
  , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N)
  , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4)
  , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N)
  , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4)
  , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
  , a__take(X1, X2) -> take(X1, X2)
  , a__take(0(), IL) -> a__U81(a__isNatIList(IL))
  , a__take(s(M), cons(N, IL)) ->
    a__U91(a__isNatIList(IL), IL, M, N) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { a__zeros^#() -> c_1()
     , a__zeros^#() -> c_2()
     , a__U11^#(X) -> c_3(X)
     , a__U11^#(tt()) -> c_4()
     , a__U21^#(X) -> c_5(X)
     , a__U21^#(tt()) -> c_6()
     , a__U31^#(X) -> c_7(X)
     , a__U31^#(tt()) -> c_8()
     , a__U41^#(X1, X2) -> c_9(X1, X2)
     , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2)))
     , a__U42^#(X) -> c_11(X)
     , a__U42^#(tt()) -> c_12()
     , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V)))
     , a__isNatIList^#(X) -> c_14(X)
     , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2))
     , a__isNatIList^#(zeros()) -> c_16()
     , a__U51^#(X1, X2) -> c_17(X1, X2)
     , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2)))
     , a__U52^#(X) -> c_19(X)
     , a__U52^#(tt()) -> c_20()
     , a__isNatList^#(X) -> c_21(X)
     , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2))
     , a__isNatList^#(nil()) -> c_23()
     , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2))
     , a__U61^#(X1, X2) -> c_25(X1, X2)
     , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2)))
     , a__U62^#(X) -> c_27(X)
     , a__U62^#(tt()) -> c_28()
     , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3)
     , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L))
     , a__U72^#(X1, X2) -> c_31(X1, X2)
     , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L)))
     , a__length^#(X) -> c_37(X)
     , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N))
     , a__length^#(nil()) -> c_39()
     , a__isNat^#(X) -> c_33(X)
     , a__isNat^#(0()) -> c_34()
     , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2)
     , mark^#(0()) -> c_41()
     , mark^#(zeros()) -> c_42(a__zeros^#())
     , mark^#(tt()) -> c_43()
     , mark^#(s(X)) -> c_44(mark^#(X))
     , mark^#(nil()) -> c_45()
     , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2)))
     , mark^#(length(X)) -> c_47(a__length^#(mark(X)))
     , mark^#(U11(X)) -> c_48(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_49(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_50(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_52(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_55(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X))
     , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2))
     , mark^#(U62(X)) -> c_58(a__U62^#(mark(X)))
     , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3))
     , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_61(a__isNat^#(X))
     , mark^#(U81(X)) -> c_62(a__U81^#(mark(X)))
     , mark^#(U91(X1, X2, X3, X4)) ->
       c_63(a__U91^#(mark(X1), X2, X3, X4))
     , mark^#(U92(X1, X2, X3, X4)) ->
       c_64(a__U92^#(mark(X1), X2, X3, X4))
     , mark^#(U93(X1, X2, X3, X4)) ->
       c_65(a__U93^#(mark(X1), X2, X3, X4))
     , a__take^#(X1, X2) -> c_74(X1, X2)
     , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL)))
     , a__take^#(s(M), cons(N, IL)) ->
       c_76(a__U91^#(a__isNatIList(IL), IL, M, N))
     , a__U81^#(X) -> c_66(X)
     , a__U81^#(tt()) -> c_67()
     , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4)
     , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N))
     , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4)
     , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N))
     , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4)
     , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__zeros^#() -> c_1()
     , a__zeros^#() -> c_2()
     , a__U11^#(X) -> c_3(X)
     , a__U11^#(tt()) -> c_4()
     , a__U21^#(X) -> c_5(X)
     , a__U21^#(tt()) -> c_6()
     , a__U31^#(X) -> c_7(X)
     , a__U31^#(tt()) -> c_8()
     , a__U41^#(X1, X2) -> c_9(X1, X2)
     , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2)))
     , a__U42^#(X) -> c_11(X)
     , a__U42^#(tt()) -> c_12()
     , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V)))
     , a__isNatIList^#(X) -> c_14(X)
     , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2))
     , a__isNatIList^#(zeros()) -> c_16()
     , a__U51^#(X1, X2) -> c_17(X1, X2)
     , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2)))
     , a__U52^#(X) -> c_19(X)
     , a__U52^#(tt()) -> c_20()
     , a__isNatList^#(X) -> c_21(X)
     , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2))
     , a__isNatList^#(nil()) -> c_23()
     , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2))
     , a__U61^#(X1, X2) -> c_25(X1, X2)
     , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2)))
     , a__U62^#(X) -> c_27(X)
     , a__U62^#(tt()) -> c_28()
     , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3)
     , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L))
     , a__U72^#(X1, X2) -> c_31(X1, X2)
     , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L)))
     , a__length^#(X) -> c_37(X)
     , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N))
     , a__length^#(nil()) -> c_39()
     , a__isNat^#(X) -> c_33(X)
     , a__isNat^#(0()) -> c_34()
     , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2)
     , mark^#(0()) -> c_41()
     , mark^#(zeros()) -> c_42(a__zeros^#())
     , mark^#(tt()) -> c_43()
     , mark^#(s(X)) -> c_44(mark^#(X))
     , mark^#(nil()) -> c_45()
     , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2)))
     , mark^#(length(X)) -> c_47(a__length^#(mark(X)))
     , mark^#(U11(X)) -> c_48(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_49(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_50(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_52(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_55(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X))
     , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2))
     , mark^#(U62(X)) -> c_58(a__U62^#(mark(X)))
     , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3))
     , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_61(a__isNat^#(X))
     , mark^#(U81(X)) -> c_62(a__U81^#(mark(X)))
     , mark^#(U91(X1, X2, X3, X4)) ->
       c_63(a__U91^#(mark(X1), X2, X3, X4))
     , mark^#(U92(X1, X2, X3, X4)) ->
       c_64(a__U92^#(mark(X1), X2, X3, X4))
     , mark^#(U93(X1, X2, X3, X4)) ->
       c_65(a__U93^#(mark(X1), X2, X3, X4))
     , a__take^#(X1, X2) -> c_74(X1, X2)
     , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL)))
     , a__take^#(s(M), cons(N, IL)) ->
       c_76(a__U91^#(a__isNatIList(IL), IL, M, N))
     , a__U81^#(X) -> c_66(X)
     , a__U81^#(tt()) -> c_67()
     , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4)
     , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N))
     , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4)
     , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N))
     , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4)
     , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) }
   Strict Trs:
     { a__zeros() -> cons(0(), zeros())
     , a__zeros() -> zeros()
     , a__U11(X) -> U11(X)
     , a__U11(tt()) -> tt()
     , a__U21(X) -> U21(X)
     , a__U21(tt()) -> tt()
     , a__U31(X) -> U31(X)
     , a__U31(tt()) -> tt()
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2))
     , a__U42(X) -> U42(X)
     , a__U42(tt()) -> tt()
     , a__isNatIList(V) -> a__U31(a__isNatList(V))
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2)
     , a__isNatIList(zeros()) -> tt()
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U51(tt(), V2) -> a__U52(a__isNatList(V2))
     , a__U52(X) -> U52(X)
     , a__U52(tt()) -> tt()
     , a__isNatList(X) -> isNatList(X)
     , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2)
     , a__U61(X1, X2) -> U61(X1, X2)
     , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2))
     , a__U62(X) -> U62(X)
     , a__U62(tt()) -> tt()
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L)
     , a__U72(X1, X2) -> U72(X1, X2)
     , a__U72(tt(), L) -> s(a__length(mark(L)))
     , a__isNat(X) -> isNat(X)
     , a__isNat(0()) -> tt()
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
     , a__length(X) -> length(X)
     , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N)
     , a__length(nil()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(zeros()) -> a__zeros()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(length(X)) -> a__length(mark(X))
     , mark(U11(X)) -> a__U11(mark(X))
     , mark(U21(X)) -> a__U21(mark(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(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X)) -> a__U52(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
     , mark(U62(X)) -> a__U62(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U81(X)) -> a__U81(mark(X))
     , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
     , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4)
     , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4)
     , a__U81(X) -> U81(X)
     , a__U81(tt()) -> nil()
     , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
     , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N)
     , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4)
     , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N)
     , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4)
     , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__take(X1, X2) -> take(X1, X2)
     , a__take(0(), IL) -> a__U81(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U91(a__isNatIList(IL), IL, M, N) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of
   {1,2,4,6,8,12,16,20,23,28,35,37,41,43,45,70} by applications of
   Pre({1,2,4,6,8,12,16,20,23,28,35,37,41,43,45,70}) =
   {3,5,7,9,10,11,13,14,17,18,19,21,25,26,27,29,31,32,33,36,38,39,40,42,44,47,48,49,50,52,53,55,56,58,61,62,66,67,69,71,73,75,76}.
   Here rules are labeled as follows:
   
     DPs:
       { 1: a__zeros^#() -> c_1()
       , 2: a__zeros^#() -> c_2()
       , 3: a__U11^#(X) -> c_3(X)
       , 4: a__U11^#(tt()) -> c_4()
       , 5: a__U21^#(X) -> c_5(X)
       , 6: a__U21^#(tt()) -> c_6()
       , 7: a__U31^#(X) -> c_7(X)
       , 8: a__U31^#(tt()) -> c_8()
       , 9: a__U41^#(X1, X2) -> c_9(X1, X2)
       , 10: a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2)))
       , 11: a__U42^#(X) -> c_11(X)
       , 12: a__U42^#(tt()) -> c_12()
       , 13: a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V)))
       , 14: a__isNatIList^#(X) -> c_14(X)
       , 15: a__isNatIList^#(cons(V1, V2)) ->
             c_15(a__U41^#(a__isNat(V1), V2))
       , 16: a__isNatIList^#(zeros()) -> c_16()
       , 17: a__U51^#(X1, X2) -> c_17(X1, X2)
       , 18: a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2)))
       , 19: a__U52^#(X) -> c_19(X)
       , 20: a__U52^#(tt()) -> c_20()
       , 21: a__isNatList^#(X) -> c_21(X)
       , 22: a__isNatList^#(cons(V1, V2)) ->
             c_22(a__U51^#(a__isNat(V1), V2))
       , 23: a__isNatList^#(nil()) -> c_23()
       , 24: a__isNatList^#(take(V1, V2)) ->
             c_24(a__U61^#(a__isNat(V1), V2))
       , 25: a__U61^#(X1, X2) -> c_25(X1, X2)
       , 26: a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2)))
       , 27: a__U62^#(X) -> c_27(X)
       , 28: a__U62^#(tt()) -> c_28()
       , 29: a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3)
       , 30: a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L))
       , 31: a__U72^#(X1, X2) -> c_31(X1, X2)
       , 32: a__U72^#(tt(), L) -> c_32(a__length^#(mark(L)))
       , 33: a__length^#(X) -> c_37(X)
       , 34: a__length^#(cons(N, L)) ->
             c_38(a__U71^#(a__isNatList(L), L, N))
       , 35: a__length^#(nil()) -> c_39()
       , 36: a__isNat^#(X) -> c_33(X)
       , 37: a__isNat^#(0()) -> c_34()
       , 38: a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1)))
       , 39: a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1)))
       , 40: mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2)
       , 41: mark^#(0()) -> c_41()
       , 42: mark^#(zeros()) -> c_42(a__zeros^#())
       , 43: mark^#(tt()) -> c_43()
       , 44: mark^#(s(X)) -> c_44(mark^#(X))
       , 45: mark^#(nil()) -> c_45()
       , 46: mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2)))
       , 47: mark^#(length(X)) -> c_47(a__length^#(mark(X)))
       , 48: mark^#(U11(X)) -> c_48(a__U11^#(mark(X)))
       , 49: mark^#(U21(X)) -> c_49(a__U21^#(mark(X)))
       , 50: mark^#(U31(X)) -> c_50(a__U31^#(mark(X)))
       , 51: mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2))
       , 52: mark^#(U42(X)) -> c_52(a__U42^#(mark(X)))
       , 53: mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X))
       , 54: mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2))
       , 55: mark^#(U52(X)) -> c_55(a__U52^#(mark(X)))
       , 56: mark^#(isNatList(X)) -> c_56(a__isNatList^#(X))
       , 57: mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2))
       , 58: mark^#(U62(X)) -> c_58(a__U62^#(mark(X)))
       , 59: mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3))
       , 60: mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2))
       , 61: mark^#(isNat(X)) -> c_61(a__isNat^#(X))
       , 62: mark^#(U81(X)) -> c_62(a__U81^#(mark(X)))
       , 63: mark^#(U91(X1, X2, X3, X4)) ->
             c_63(a__U91^#(mark(X1), X2, X3, X4))
       , 64: mark^#(U92(X1, X2, X3, X4)) ->
             c_64(a__U92^#(mark(X1), X2, X3, X4))
       , 65: mark^#(U93(X1, X2, X3, X4)) ->
             c_65(a__U93^#(mark(X1), X2, X3, X4))
       , 66: a__take^#(X1, X2) -> c_74(X1, X2)
       , 67: a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL)))
       , 68: a__take^#(s(M), cons(N, IL)) ->
             c_76(a__U91^#(a__isNatIList(IL), IL, M, N))
       , 69: a__U81^#(X) -> c_66(X)
       , 70: a__U81^#(tt()) -> c_67()
       , 71: a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4)
       , 72: a__U91^#(tt(), IL, M, N) ->
             c_69(a__U92^#(a__isNat(M), IL, M, N))
       , 73: a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4)
       , 74: a__U92^#(tt(), IL, M, N) ->
             c_71(a__U93^#(a__isNat(N), IL, M, N))
       , 75: a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4)
       , 76: a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__U11^#(X) -> c_3(X)
     , a__U21^#(X) -> c_5(X)
     , a__U31^#(X) -> c_7(X)
     , a__U41^#(X1, X2) -> c_9(X1, X2)
     , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2)))
     , a__U42^#(X) -> c_11(X)
     , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V)))
     , a__isNatIList^#(X) -> c_14(X)
     , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2))
     , a__U51^#(X1, X2) -> c_17(X1, X2)
     , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2)))
     , a__U52^#(X) -> c_19(X)
     , a__isNatList^#(X) -> c_21(X)
     , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2))
     , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2))
     , a__U61^#(X1, X2) -> c_25(X1, X2)
     , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2)))
     , a__U62^#(X) -> c_27(X)
     , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3)
     , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L))
     , a__U72^#(X1, X2) -> c_31(X1, X2)
     , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L)))
     , a__length^#(X) -> c_37(X)
     , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N))
     , a__isNat^#(X) -> c_33(X)
     , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2)
     , mark^#(zeros()) -> c_42(a__zeros^#())
     , mark^#(s(X)) -> c_44(mark^#(X))
     , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2)))
     , mark^#(length(X)) -> c_47(a__length^#(mark(X)))
     , mark^#(U11(X)) -> c_48(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_49(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_50(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_52(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_55(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X))
     , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2))
     , mark^#(U62(X)) -> c_58(a__U62^#(mark(X)))
     , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3))
     , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_61(a__isNat^#(X))
     , mark^#(U81(X)) -> c_62(a__U81^#(mark(X)))
     , mark^#(U91(X1, X2, X3, X4)) ->
       c_63(a__U91^#(mark(X1), X2, X3, X4))
     , mark^#(U92(X1, X2, X3, X4)) ->
       c_64(a__U92^#(mark(X1), X2, X3, X4))
     , mark^#(U93(X1, X2, X3, X4)) ->
       c_65(a__U93^#(mark(X1), X2, X3, X4))
     , a__take^#(X1, X2) -> c_74(X1, X2)
     , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL)))
     , a__take^#(s(M), cons(N, IL)) ->
       c_76(a__U91^#(a__isNatIList(IL), IL, M, N))
     , a__U81^#(X) -> c_66(X)
     , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4)
     , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N))
     , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4)
     , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N))
     , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4)
     , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) }
   Strict Trs:
     { a__zeros() -> cons(0(), zeros())
     , a__zeros() -> zeros()
     , a__U11(X) -> U11(X)
     , a__U11(tt()) -> tt()
     , a__U21(X) -> U21(X)
     , a__U21(tt()) -> tt()
     , a__U31(X) -> U31(X)
     , a__U31(tt()) -> tt()
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2))
     , a__U42(X) -> U42(X)
     , a__U42(tt()) -> tt()
     , a__isNatIList(V) -> a__U31(a__isNatList(V))
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2)
     , a__isNatIList(zeros()) -> tt()
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U51(tt(), V2) -> a__U52(a__isNatList(V2))
     , a__U52(X) -> U52(X)
     , a__U52(tt()) -> tt()
     , a__isNatList(X) -> isNatList(X)
     , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2)
     , a__U61(X1, X2) -> U61(X1, X2)
     , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2))
     , a__U62(X) -> U62(X)
     , a__U62(tt()) -> tt()
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L)
     , a__U72(X1, X2) -> U72(X1, X2)
     , a__U72(tt(), L) -> s(a__length(mark(L)))
     , a__isNat(X) -> isNat(X)
     , a__isNat(0()) -> tt()
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
     , a__length(X) -> length(X)
     , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N)
     , a__length(nil()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(zeros()) -> a__zeros()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(length(X)) -> a__length(mark(X))
     , mark(U11(X)) -> a__U11(mark(X))
     , mark(U21(X)) -> a__U21(mark(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(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X)) -> a__U52(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
     , mark(U62(X)) -> a__U62(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U81(X)) -> a__U81(mark(X))
     , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
     , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4)
     , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4)
     , a__U81(X) -> U81(X)
     , a__U81(tt()) -> nil()
     , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
     , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N)
     , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4)
     , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N)
     , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4)
     , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__take(X1, X2) -> take(X1, X2)
     , a__take(0(), IL) -> a__U81(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U91(a__isNatIList(IL), IL, M, N) }
   Weak DPs:
     { a__zeros^#() -> c_1()
     , a__zeros^#() -> c_2()
     , a__U11^#(tt()) -> c_4()
     , a__U21^#(tt()) -> c_6()
     , a__U31^#(tt()) -> c_8()
     , a__U42^#(tt()) -> c_12()
     , a__isNatIList^#(zeros()) -> c_16()
     , a__U52^#(tt()) -> c_20()
     , a__isNatList^#(nil()) -> c_23()
     , a__U62^#(tt()) -> c_28()
     , a__length^#(nil()) -> c_39()
     , a__isNat^#(0()) -> c_34()
     , mark^#(0()) -> c_41()
     , mark^#(tt()) -> c_43()
     , mark^#(nil()) -> c_45()
     , a__U81^#(tt()) -> c_67() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {29} by applications of
   Pre({29}) =
   {1,2,3,4,6,8,10,12,13,16,18,19,21,23,25,28,30,51,54,55,57,59,60}.
   Here rules are labeled as follows:
   
     DPs:
       { 1: a__U11^#(X) -> c_3(X)
       , 2: a__U21^#(X) -> c_5(X)
       , 3: a__U31^#(X) -> c_7(X)
       , 4: a__U41^#(X1, X2) -> c_9(X1, X2)
       , 5: a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2)))
       , 6: a__U42^#(X) -> c_11(X)
       , 7: a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V)))
       , 8: a__isNatIList^#(X) -> c_14(X)
       , 9: a__isNatIList^#(cons(V1, V2)) ->
            c_15(a__U41^#(a__isNat(V1), V2))
       , 10: a__U51^#(X1, X2) -> c_17(X1, X2)
       , 11: a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2)))
       , 12: a__U52^#(X) -> c_19(X)
       , 13: a__isNatList^#(X) -> c_21(X)
       , 14: a__isNatList^#(cons(V1, V2)) ->
             c_22(a__U51^#(a__isNat(V1), V2))
       , 15: a__isNatList^#(take(V1, V2)) ->
             c_24(a__U61^#(a__isNat(V1), V2))
       , 16: a__U61^#(X1, X2) -> c_25(X1, X2)
       , 17: a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2)))
       , 18: a__U62^#(X) -> c_27(X)
       , 19: a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3)
       , 20: a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L))
       , 21: a__U72^#(X1, X2) -> c_31(X1, X2)
       , 22: a__U72^#(tt(), L) -> c_32(a__length^#(mark(L)))
       , 23: a__length^#(X) -> c_37(X)
       , 24: a__length^#(cons(N, L)) ->
             c_38(a__U71^#(a__isNatList(L), L, N))
       , 25: a__isNat^#(X) -> c_33(X)
       , 26: a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1)))
       , 27: a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1)))
       , 28: mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2)
       , 29: mark^#(zeros()) -> c_42(a__zeros^#())
       , 30: mark^#(s(X)) -> c_44(mark^#(X))
       , 31: mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2)))
       , 32: mark^#(length(X)) -> c_47(a__length^#(mark(X)))
       , 33: mark^#(U11(X)) -> c_48(a__U11^#(mark(X)))
       , 34: mark^#(U21(X)) -> c_49(a__U21^#(mark(X)))
       , 35: mark^#(U31(X)) -> c_50(a__U31^#(mark(X)))
       , 36: mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2))
       , 37: mark^#(U42(X)) -> c_52(a__U42^#(mark(X)))
       , 38: mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X))
       , 39: mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2))
       , 40: mark^#(U52(X)) -> c_55(a__U52^#(mark(X)))
       , 41: mark^#(isNatList(X)) -> c_56(a__isNatList^#(X))
       , 42: mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2))
       , 43: mark^#(U62(X)) -> c_58(a__U62^#(mark(X)))
       , 44: mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3))
       , 45: mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2))
       , 46: mark^#(isNat(X)) -> c_61(a__isNat^#(X))
       , 47: mark^#(U81(X)) -> c_62(a__U81^#(mark(X)))
       , 48: mark^#(U91(X1, X2, X3, X4)) ->
             c_63(a__U91^#(mark(X1), X2, X3, X4))
       , 49: mark^#(U92(X1, X2, X3, X4)) ->
             c_64(a__U92^#(mark(X1), X2, X3, X4))
       , 50: mark^#(U93(X1, X2, X3, X4)) ->
             c_65(a__U93^#(mark(X1), X2, X3, X4))
       , 51: a__take^#(X1, X2) -> c_74(X1, X2)
       , 52: a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL)))
       , 53: a__take^#(s(M), cons(N, IL)) ->
             c_76(a__U91^#(a__isNatIList(IL), IL, M, N))
       , 54: a__U81^#(X) -> c_66(X)
       , 55: a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4)
       , 56: a__U91^#(tt(), IL, M, N) ->
             c_69(a__U92^#(a__isNat(M), IL, M, N))
       , 57: a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4)
       , 58: a__U92^#(tt(), IL, M, N) ->
             c_71(a__U93^#(a__isNat(N), IL, M, N))
       , 59: a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4)
       , 60: a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL)
       , 61: a__zeros^#() -> c_1()
       , 62: a__zeros^#() -> c_2()
       , 63: a__U11^#(tt()) -> c_4()
       , 64: a__U21^#(tt()) -> c_6()
       , 65: a__U31^#(tt()) -> c_8()
       , 66: a__U42^#(tt()) -> c_12()
       , 67: a__isNatIList^#(zeros()) -> c_16()
       , 68: a__U52^#(tt()) -> c_20()
       , 69: a__isNatList^#(nil()) -> c_23()
       , 70: a__U62^#(tt()) -> c_28()
       , 71: a__length^#(nil()) -> c_39()
       , 72: a__isNat^#(0()) -> c_34()
       , 73: mark^#(0()) -> c_41()
       , 74: mark^#(tt()) -> c_43()
       , 75: mark^#(nil()) -> c_45()
       , 76: a__U81^#(tt()) -> c_67() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__U11^#(X) -> c_3(X)
     , a__U21^#(X) -> c_5(X)
     , a__U31^#(X) -> c_7(X)
     , a__U41^#(X1, X2) -> c_9(X1, X2)
     , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2)))
     , a__U42^#(X) -> c_11(X)
     , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V)))
     , a__isNatIList^#(X) -> c_14(X)
     , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2))
     , a__U51^#(X1, X2) -> c_17(X1, X2)
     , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2)))
     , a__U52^#(X) -> c_19(X)
     , a__isNatList^#(X) -> c_21(X)
     , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2))
     , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2))
     , a__U61^#(X1, X2) -> c_25(X1, X2)
     , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2)))
     , a__U62^#(X) -> c_27(X)
     , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3)
     , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L))
     , a__U72^#(X1, X2) -> c_31(X1, X2)
     , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L)))
     , a__length^#(X) -> c_37(X)
     , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N))
     , a__isNat^#(X) -> c_33(X)
     , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2)
     , mark^#(s(X)) -> c_44(mark^#(X))
     , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2)))
     , mark^#(length(X)) -> c_47(a__length^#(mark(X)))
     , mark^#(U11(X)) -> c_48(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_49(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_50(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_52(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_55(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X))
     , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2))
     , mark^#(U62(X)) -> c_58(a__U62^#(mark(X)))
     , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3))
     , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_61(a__isNat^#(X))
     , mark^#(U81(X)) -> c_62(a__U81^#(mark(X)))
     , mark^#(U91(X1, X2, X3, X4)) ->
       c_63(a__U91^#(mark(X1), X2, X3, X4))
     , mark^#(U92(X1, X2, X3, X4)) ->
       c_64(a__U92^#(mark(X1), X2, X3, X4))
     , mark^#(U93(X1, X2, X3, X4)) ->
       c_65(a__U93^#(mark(X1), X2, X3, X4))
     , a__take^#(X1, X2) -> c_74(X1, X2)
     , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL)))
     , a__take^#(s(M), cons(N, IL)) ->
       c_76(a__U91^#(a__isNatIList(IL), IL, M, N))
     , a__U81^#(X) -> c_66(X)
     , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4)
     , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N))
     , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4)
     , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N))
     , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4)
     , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) }
   Strict Trs:
     { a__zeros() -> cons(0(), zeros())
     , a__zeros() -> zeros()
     , a__U11(X) -> U11(X)
     , a__U11(tt()) -> tt()
     , a__U21(X) -> U21(X)
     , a__U21(tt()) -> tt()
     , a__U31(X) -> U31(X)
     , a__U31(tt()) -> tt()
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2))
     , a__U42(X) -> U42(X)
     , a__U42(tt()) -> tt()
     , a__isNatIList(V) -> a__U31(a__isNatList(V))
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2)
     , a__isNatIList(zeros()) -> tt()
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U51(tt(), V2) -> a__U52(a__isNatList(V2))
     , a__U52(X) -> U52(X)
     , a__U52(tt()) -> tt()
     , a__isNatList(X) -> isNatList(X)
     , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2)
     , a__U61(X1, X2) -> U61(X1, X2)
     , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2))
     , a__U62(X) -> U62(X)
     , a__U62(tt()) -> tt()
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L)
     , a__U72(X1, X2) -> U72(X1, X2)
     , a__U72(tt(), L) -> s(a__length(mark(L)))
     , a__isNat(X) -> isNat(X)
     , a__isNat(0()) -> tt()
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
     , a__length(X) -> length(X)
     , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N)
     , a__length(nil()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(zeros()) -> a__zeros()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(length(X)) -> a__length(mark(X))
     , mark(U11(X)) -> a__U11(mark(X))
     , mark(U21(X)) -> a__U21(mark(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(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X)) -> a__U52(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
     , mark(U62(X)) -> a__U62(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U81(X)) -> a__U81(mark(X))
     , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
     , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4)
     , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4)
     , a__U81(X) -> U81(X)
     , a__U81(tt()) -> nil()
     , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
     , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N)
     , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4)
     , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N)
     , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4)
     , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__take(X1, X2) -> take(X1, X2)
     , a__take(0(), IL) -> a__U81(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U91(a__isNatIList(IL), IL, M, N) }
   Weak DPs:
     { a__zeros^#() -> c_1()
     , a__zeros^#() -> c_2()
     , a__U11^#(tt()) -> c_4()
     , a__U21^#(tt()) -> c_6()
     , a__U31^#(tt()) -> c_8()
     , a__U42^#(tt()) -> c_12()
     , a__isNatIList^#(zeros()) -> c_16()
     , a__U52^#(tt()) -> c_20()
     , a__isNatList^#(nil()) -> c_23()
     , a__U62^#(tt()) -> c_28()
     , a__length^#(nil()) -> c_39()
     , a__isNat^#(0()) -> c_34()
     , mark^#(0()) -> c_41()
     , mark^#(zeros()) -> c_42(a__zeros^#())
     , mark^#(tt()) -> c_43()
     , mark^#(nil()) -> c_45()
     , a__U81^#(tt()) -> c_67() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.

3) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   


Arrrr..