MAYBE

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

Strict Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , cons(X1, X2) -> n__cons(X1, X2)
  , 0() -> n__0()
  , U11(tt()) -> tt()
  , U21(tt()) -> tt()
  , U31(tt()) -> tt()
  , U41(tt(), V2) -> U42(isNatIList(activate(V2)))
  , U42(tt()) -> tt()
  , isNatIList(V) -> U31(isNatList(activate(V)))
  , isNatIList(n__zeros()) -> tt()
  , isNatIList(n__cons(V1, V2)) ->
    U41(isNat(activate(V1)), activate(V2))
  , activate(X) -> X
  , activate(n__zeros()) -> zeros()
  , activate(n__0()) -> 0()
  , activate(n__length(X)) -> length(activate(X))
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
  , activate(n__nil()) -> nil()
  , U51(tt(), V2) -> U52(isNatList(activate(V2)))
  , U52(tt()) -> tt()
  , isNatList(n__cons(V1, V2)) ->
    U51(isNat(activate(V1)), activate(V2))
  , isNatList(n__nil()) -> tt()
  , U61(tt(), L, N) -> U62(isNat(activate(N)), activate(L))
  , U62(tt(), L) -> s(length(activate(L)))
  , isNat(n__0()) -> tt()
  , isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
  , isNat(n__s(V1)) -> U21(isNat(activate(V1)))
  , s(X) -> n__s(X)
  , length(X) -> n__length(X)
  , length(cons(N, L)) -> U61(isNatList(activate(L)), activate(L), N)
  , length(nil()) -> 0()
  , nil() -> n__nil() }
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) '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) '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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   
   3) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { zeros^#() -> c_1(cons^#(0(), n__zeros()))
     , zeros^#() -> c_2()
     , cons^#(X1, X2) -> c_3(X1, X2)
     , 0^#() -> c_4()
     , U11^#(tt()) -> c_5()
     , U21^#(tt()) -> c_6()
     , U31^#(tt()) -> c_7()
     , U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
     , U42^#(tt()) -> c_9()
     , isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
     , isNatIList^#(n__zeros()) -> c_11()
     , isNatIList^#(n__cons(V1, V2)) ->
       c_12(U41^#(isNat(activate(V1)), activate(V2)))
     , activate^#(X) -> c_13(X)
     , activate^#(n__zeros()) -> c_14(zeros^#())
     , activate^#(n__0()) -> c_15(0^#())
     , activate^#(n__length(X)) -> c_16(length^#(activate(X)))
     , activate^#(n__s(X)) -> c_17(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
     , activate^#(n__nil()) -> c_19(nil^#())
     , length^#(X) -> c_30(X)
     , length^#(cons(N, L)) ->
       c_31(U61^#(isNatList(activate(L)), activate(L), N))
     , length^#(nil()) -> c_32(0^#())
     , s^#(X) -> c_29(X)
     , nil^#() -> c_33()
     , U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
     , U52^#(tt()) -> c_21()
     , isNatList^#(n__cons(V1, V2)) ->
       c_22(U51^#(isNat(activate(V1)), activate(V2)))
     , isNatList^#(n__nil()) -> c_23()
     , U61^#(tt(), L, N) -> c_24(U62^#(isNat(activate(N)), activate(L)))
     , U62^#(tt(), L) -> c_25(s^#(length(activate(L))))
     , isNat^#(n__0()) -> c_26()
     , isNat^#(n__length(V1)) -> c_27(U11^#(isNatList(activate(V1))))
     , isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { zeros^#() -> c_1(cons^#(0(), n__zeros()))
     , zeros^#() -> c_2()
     , cons^#(X1, X2) -> c_3(X1, X2)
     , 0^#() -> c_4()
     , U11^#(tt()) -> c_5()
     , U21^#(tt()) -> c_6()
     , U31^#(tt()) -> c_7()
     , U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
     , U42^#(tt()) -> c_9()
     , isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
     , isNatIList^#(n__zeros()) -> c_11()
     , isNatIList^#(n__cons(V1, V2)) ->
       c_12(U41^#(isNat(activate(V1)), activate(V2)))
     , activate^#(X) -> c_13(X)
     , activate^#(n__zeros()) -> c_14(zeros^#())
     , activate^#(n__0()) -> c_15(0^#())
     , activate^#(n__length(X)) -> c_16(length^#(activate(X)))
     , activate^#(n__s(X)) -> c_17(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
     , activate^#(n__nil()) -> c_19(nil^#())
     , length^#(X) -> c_30(X)
     , length^#(cons(N, L)) ->
       c_31(U61^#(isNatList(activate(L)), activate(L), N))
     , length^#(nil()) -> c_32(0^#())
     , s^#(X) -> c_29(X)
     , nil^#() -> c_33()
     , U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
     , U52^#(tt()) -> c_21()
     , isNatList^#(n__cons(V1, V2)) ->
       c_22(U51^#(isNat(activate(V1)), activate(V2)))
     , isNatList^#(n__nil()) -> c_23()
     , U61^#(tt(), L, N) -> c_24(U62^#(isNat(activate(N)), activate(L)))
     , U62^#(tt(), L) -> c_25(s^#(length(activate(L))))
     , isNat^#(n__0()) -> c_26()
     , isNat^#(n__length(V1)) -> c_27(U11^#(isNatList(activate(V1))))
     , isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   Strict Trs:
     { zeros() -> cons(0(), n__zeros())
     , zeros() -> n__zeros()
     , cons(X1, X2) -> n__cons(X1, X2)
     , 0() -> n__0()
     , U11(tt()) -> tt()
     , U21(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNatIList(activate(V2)))
     , U42(tt()) -> tt()
     , isNatIList(V) -> U31(isNatList(activate(V)))
     , isNatIList(n__zeros()) -> tt()
     , isNatIList(n__cons(V1, V2)) ->
       U41(isNat(activate(V1)), activate(V2))
     , activate(X) -> X
     , activate(n__zeros()) -> zeros()
     , activate(n__0()) -> 0()
     , activate(n__length(X)) -> length(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , activate(n__nil()) -> nil()
     , U51(tt(), V2) -> U52(isNatList(activate(V2)))
     , U52(tt()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U51(isNat(activate(V1)), activate(V2))
     , isNatList(n__nil()) -> tt()
     , U61(tt(), L, N) -> U62(isNat(activate(N)), activate(L))
     , U62(tt(), L) -> s(length(activate(L)))
     , isNat(n__0()) -> tt()
     , isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
     , isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     , s(X) -> n__s(X)
     , length(X) -> n__length(X)
     , length(cons(N, L)) -> U61(isNatList(activate(L)), activate(L), N)
     , length(nil()) -> 0()
     , nil() -> n__nil() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of
   {2,4,5,6,7,9,11,24,26,28,31} by applications of
   Pre({2,4,5,6,7,9,11,24,26,28,31}) =
   {3,8,10,13,14,15,19,20,22,23,25,32,33}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: zeros^#() -> c_1(cons^#(0(), n__zeros()))
       , 2: zeros^#() -> c_2()
       , 3: cons^#(X1, X2) -> c_3(X1, X2)
       , 4: 0^#() -> c_4()
       , 5: U11^#(tt()) -> c_5()
       , 6: U21^#(tt()) -> c_6()
       , 7: U31^#(tt()) -> c_7()
       , 8: U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
       , 9: U42^#(tt()) -> c_9()
       , 10: isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
       , 11: isNatIList^#(n__zeros()) -> c_11()
       , 12: isNatIList^#(n__cons(V1, V2)) ->
             c_12(U41^#(isNat(activate(V1)), activate(V2)))
       , 13: activate^#(X) -> c_13(X)
       , 14: activate^#(n__zeros()) -> c_14(zeros^#())
       , 15: activate^#(n__0()) -> c_15(0^#())
       , 16: activate^#(n__length(X)) -> c_16(length^#(activate(X)))
       , 17: activate^#(n__s(X)) -> c_17(s^#(activate(X)))
       , 18: activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
       , 19: activate^#(n__nil()) -> c_19(nil^#())
       , 20: length^#(X) -> c_30(X)
       , 21: length^#(cons(N, L)) ->
             c_31(U61^#(isNatList(activate(L)), activate(L), N))
       , 22: length^#(nil()) -> c_32(0^#())
       , 23: s^#(X) -> c_29(X)
       , 24: nil^#() -> c_33()
       , 25: U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
       , 26: U52^#(tt()) -> c_21()
       , 27: isNatList^#(n__cons(V1, V2)) ->
             c_22(U51^#(isNat(activate(V1)), activate(V2)))
       , 28: isNatList^#(n__nil()) -> c_23()
       , 29: U61^#(tt(), L, N) ->
             c_24(U62^#(isNat(activate(N)), activate(L)))
       , 30: U62^#(tt(), L) -> c_25(s^#(length(activate(L))))
       , 31: isNat^#(n__0()) -> c_26()
       , 32: isNat^#(n__length(V1)) ->
             c_27(U11^#(isNatList(activate(V1))))
       , 33: isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { zeros^#() -> c_1(cons^#(0(), n__zeros()))
     , cons^#(X1, X2) -> c_3(X1, X2)
     , U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
     , isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
     , isNatIList^#(n__cons(V1, V2)) ->
       c_12(U41^#(isNat(activate(V1)), activate(V2)))
     , activate^#(X) -> c_13(X)
     , activate^#(n__zeros()) -> c_14(zeros^#())
     , activate^#(n__0()) -> c_15(0^#())
     , activate^#(n__length(X)) -> c_16(length^#(activate(X)))
     , activate^#(n__s(X)) -> c_17(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
     , activate^#(n__nil()) -> c_19(nil^#())
     , length^#(X) -> c_30(X)
     , length^#(cons(N, L)) ->
       c_31(U61^#(isNatList(activate(L)), activate(L), N))
     , length^#(nil()) -> c_32(0^#())
     , s^#(X) -> c_29(X)
     , U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
     , isNatList^#(n__cons(V1, V2)) ->
       c_22(U51^#(isNat(activate(V1)), activate(V2)))
     , U61^#(tt(), L, N) -> c_24(U62^#(isNat(activate(N)), activate(L)))
     , U62^#(tt(), L) -> c_25(s^#(length(activate(L))))
     , isNat^#(n__length(V1)) -> c_27(U11^#(isNatList(activate(V1))))
     , isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   Strict Trs:
     { zeros() -> cons(0(), n__zeros())
     , zeros() -> n__zeros()
     , cons(X1, X2) -> n__cons(X1, X2)
     , 0() -> n__0()
     , U11(tt()) -> tt()
     , U21(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNatIList(activate(V2)))
     , U42(tt()) -> tt()
     , isNatIList(V) -> U31(isNatList(activate(V)))
     , isNatIList(n__zeros()) -> tt()
     , isNatIList(n__cons(V1, V2)) ->
       U41(isNat(activate(V1)), activate(V2))
     , activate(X) -> X
     , activate(n__zeros()) -> zeros()
     , activate(n__0()) -> 0()
     , activate(n__length(X)) -> length(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , activate(n__nil()) -> nil()
     , U51(tt(), V2) -> U52(isNatList(activate(V2)))
     , U52(tt()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U51(isNat(activate(V1)), activate(V2))
     , isNatList(n__nil()) -> tt()
     , U61(tt(), L, N) -> U62(isNat(activate(N)), activate(L))
     , U62(tt(), L) -> s(length(activate(L)))
     , isNat(n__0()) -> tt()
     , isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
     , isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     , s(X) -> n__s(X)
     , length(X) -> n__length(X)
     , length(cons(N, L)) -> U61(isNatList(activate(L)), activate(L), N)
     , length(nil()) -> 0()
     , nil() -> n__nil() }
   Weak DPs:
     { zeros^#() -> c_2()
     , 0^#() -> c_4()
     , U11^#(tt()) -> c_5()
     , U21^#(tt()) -> c_6()
     , U31^#(tt()) -> c_7()
     , U42^#(tt()) -> c_9()
     , isNatIList^#(n__zeros()) -> c_11()
     , nil^#() -> c_33()
     , U52^#(tt()) -> c_21()
     , isNatList^#(n__nil()) -> c_23()
     , isNat^#(n__0()) -> c_26() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,4,8,12,15,17,21,22} by
   applications of Pre({3,4,8,12,15,17,21,22}) = {2,5,6,9,13,16,18}.
   Here rules are labeled as follows:
   
     DPs:
       { 1: zeros^#() -> c_1(cons^#(0(), n__zeros()))
       , 2: cons^#(X1, X2) -> c_3(X1, X2)
       , 3: U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
       , 4: isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
       , 5: isNatIList^#(n__cons(V1, V2)) ->
            c_12(U41^#(isNat(activate(V1)), activate(V2)))
       , 6: activate^#(X) -> c_13(X)
       , 7: activate^#(n__zeros()) -> c_14(zeros^#())
       , 8: activate^#(n__0()) -> c_15(0^#())
       , 9: activate^#(n__length(X)) -> c_16(length^#(activate(X)))
       , 10: activate^#(n__s(X)) -> c_17(s^#(activate(X)))
       , 11: activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
       , 12: activate^#(n__nil()) -> c_19(nil^#())
       , 13: length^#(X) -> c_30(X)
       , 14: length^#(cons(N, L)) ->
             c_31(U61^#(isNatList(activate(L)), activate(L), N))
       , 15: length^#(nil()) -> c_32(0^#())
       , 16: s^#(X) -> c_29(X)
       , 17: U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
       , 18: isNatList^#(n__cons(V1, V2)) ->
             c_22(U51^#(isNat(activate(V1)), activate(V2)))
       , 19: U61^#(tt(), L, N) ->
             c_24(U62^#(isNat(activate(N)), activate(L)))
       , 20: U62^#(tt(), L) -> c_25(s^#(length(activate(L))))
       , 21: isNat^#(n__length(V1)) ->
             c_27(U11^#(isNatList(activate(V1))))
       , 22: isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1))))
       , 23: zeros^#() -> c_2()
       , 24: 0^#() -> c_4()
       , 25: U11^#(tt()) -> c_5()
       , 26: U21^#(tt()) -> c_6()
       , 27: U31^#(tt()) -> c_7()
       , 28: U42^#(tt()) -> c_9()
       , 29: isNatIList^#(n__zeros()) -> c_11()
       , 30: nil^#() -> c_33()
       , 31: U52^#(tt()) -> c_21()
       , 32: isNatList^#(n__nil()) -> c_23()
       , 33: isNat^#(n__0()) -> c_26() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { zeros^#() -> c_1(cons^#(0(), n__zeros()))
     , cons^#(X1, X2) -> c_3(X1, X2)
     , isNatIList^#(n__cons(V1, V2)) ->
       c_12(U41^#(isNat(activate(V1)), activate(V2)))
     , activate^#(X) -> c_13(X)
     , activate^#(n__zeros()) -> c_14(zeros^#())
     , activate^#(n__length(X)) -> c_16(length^#(activate(X)))
     , activate^#(n__s(X)) -> c_17(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
     , length^#(X) -> c_30(X)
     , length^#(cons(N, L)) ->
       c_31(U61^#(isNatList(activate(L)), activate(L), N))
     , s^#(X) -> c_29(X)
     , isNatList^#(n__cons(V1, V2)) ->
       c_22(U51^#(isNat(activate(V1)), activate(V2)))
     , U61^#(tt(), L, N) -> c_24(U62^#(isNat(activate(N)), activate(L)))
     , U62^#(tt(), L) -> c_25(s^#(length(activate(L)))) }
   Strict Trs:
     { zeros() -> cons(0(), n__zeros())
     , zeros() -> n__zeros()
     , cons(X1, X2) -> n__cons(X1, X2)
     , 0() -> n__0()
     , U11(tt()) -> tt()
     , U21(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNatIList(activate(V2)))
     , U42(tt()) -> tt()
     , isNatIList(V) -> U31(isNatList(activate(V)))
     , isNatIList(n__zeros()) -> tt()
     , isNatIList(n__cons(V1, V2)) ->
       U41(isNat(activate(V1)), activate(V2))
     , activate(X) -> X
     , activate(n__zeros()) -> zeros()
     , activate(n__0()) -> 0()
     , activate(n__length(X)) -> length(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , activate(n__nil()) -> nil()
     , U51(tt(), V2) -> U52(isNatList(activate(V2)))
     , U52(tt()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U51(isNat(activate(V1)), activate(V2))
     , isNatList(n__nil()) -> tt()
     , U61(tt(), L, N) -> U62(isNat(activate(N)), activate(L))
     , U62(tt(), L) -> s(length(activate(L)))
     , isNat(n__0()) -> tt()
     , isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
     , isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     , s(X) -> n__s(X)
     , length(X) -> n__length(X)
     , length(cons(N, L)) -> U61(isNatList(activate(L)), activate(L), N)
     , length(nil()) -> 0()
     , nil() -> n__nil() }
   Weak DPs:
     { zeros^#() -> c_2()
     , 0^#() -> c_4()
     , U11^#(tt()) -> c_5()
     , U21^#(tt()) -> c_6()
     , U31^#(tt()) -> c_7()
     , U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
     , U42^#(tt()) -> c_9()
     , isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
     , isNatIList^#(n__zeros()) -> c_11()
     , activate^#(n__0()) -> c_15(0^#())
     , activate^#(n__nil()) -> c_19(nil^#())
     , length^#(nil()) -> c_32(0^#())
     , nil^#() -> c_33()
     , U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
     , U52^#(tt()) -> c_21()
     , isNatList^#(n__nil()) -> c_23()
     , isNat^#(n__0()) -> c_26()
     , isNat^#(n__length(V1)) -> c_27(U11^#(isNatList(activate(V1))))
     , isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,12} by applications of
   Pre({3,12}) = {2,4,9,11}. Here rules are labeled as follows:
   
     DPs:
       { 1: zeros^#() -> c_1(cons^#(0(), n__zeros()))
       , 2: cons^#(X1, X2) -> c_3(X1, X2)
       , 3: isNatIList^#(n__cons(V1, V2)) ->
            c_12(U41^#(isNat(activate(V1)), activate(V2)))
       , 4: activate^#(X) -> c_13(X)
       , 5: activate^#(n__zeros()) -> c_14(zeros^#())
       , 6: activate^#(n__length(X)) -> c_16(length^#(activate(X)))
       , 7: activate^#(n__s(X)) -> c_17(s^#(activate(X)))
       , 8: activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
       , 9: length^#(X) -> c_30(X)
       , 10: length^#(cons(N, L)) ->
             c_31(U61^#(isNatList(activate(L)), activate(L), N))
       , 11: s^#(X) -> c_29(X)
       , 12: isNatList^#(n__cons(V1, V2)) ->
             c_22(U51^#(isNat(activate(V1)), activate(V2)))
       , 13: U61^#(tt(), L, N) ->
             c_24(U62^#(isNat(activate(N)), activate(L)))
       , 14: U62^#(tt(), L) -> c_25(s^#(length(activate(L))))
       , 15: zeros^#() -> c_2()
       , 16: 0^#() -> c_4()
       , 17: U11^#(tt()) -> c_5()
       , 18: U21^#(tt()) -> c_6()
       , 19: U31^#(tt()) -> c_7()
       , 20: U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
       , 21: U42^#(tt()) -> c_9()
       , 22: isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
       , 23: isNatIList^#(n__zeros()) -> c_11()
       , 24: activate^#(n__0()) -> c_15(0^#())
       , 25: activate^#(n__nil()) -> c_19(nil^#())
       , 26: length^#(nil()) -> c_32(0^#())
       , 27: nil^#() -> c_33()
       , 28: U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
       , 29: U52^#(tt()) -> c_21()
       , 30: isNatList^#(n__nil()) -> c_23()
       , 31: isNat^#(n__0()) -> c_26()
       , 32: isNat^#(n__length(V1)) ->
             c_27(U11^#(isNatList(activate(V1))))
       , 33: isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { zeros^#() -> c_1(cons^#(0(), n__zeros()))
     , cons^#(X1, X2) -> c_3(X1, X2)
     , activate^#(X) -> c_13(X)
     , activate^#(n__zeros()) -> c_14(zeros^#())
     , activate^#(n__length(X)) -> c_16(length^#(activate(X)))
     , activate^#(n__s(X)) -> c_17(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_18(cons^#(activate(X1), X2))
     , length^#(X) -> c_30(X)
     , length^#(cons(N, L)) ->
       c_31(U61^#(isNatList(activate(L)), activate(L), N))
     , s^#(X) -> c_29(X)
     , U61^#(tt(), L, N) -> c_24(U62^#(isNat(activate(N)), activate(L)))
     , U62^#(tt(), L) -> c_25(s^#(length(activate(L)))) }
   Strict Trs:
     { zeros() -> cons(0(), n__zeros())
     , zeros() -> n__zeros()
     , cons(X1, X2) -> n__cons(X1, X2)
     , 0() -> n__0()
     , U11(tt()) -> tt()
     , U21(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNatIList(activate(V2)))
     , U42(tt()) -> tt()
     , isNatIList(V) -> U31(isNatList(activate(V)))
     , isNatIList(n__zeros()) -> tt()
     , isNatIList(n__cons(V1, V2)) ->
       U41(isNat(activate(V1)), activate(V2))
     , activate(X) -> X
     , activate(n__zeros()) -> zeros()
     , activate(n__0()) -> 0()
     , activate(n__length(X)) -> length(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , activate(n__nil()) -> nil()
     , U51(tt(), V2) -> U52(isNatList(activate(V2)))
     , U52(tt()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U51(isNat(activate(V1)), activate(V2))
     , isNatList(n__nil()) -> tt()
     , U61(tt(), L, N) -> U62(isNat(activate(N)), activate(L))
     , U62(tt(), L) -> s(length(activate(L)))
     , isNat(n__0()) -> tt()
     , isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
     , isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     , s(X) -> n__s(X)
     , length(X) -> n__length(X)
     , length(cons(N, L)) -> U61(isNatList(activate(L)), activate(L), N)
     , length(nil()) -> 0()
     , nil() -> n__nil() }
   Weak DPs:
     { zeros^#() -> c_2()
     , 0^#() -> c_4()
     , U11^#(tt()) -> c_5()
     , U21^#(tt()) -> c_6()
     , U31^#(tt()) -> c_7()
     , U41^#(tt(), V2) -> c_8(U42^#(isNatIList(activate(V2))))
     , U42^#(tt()) -> c_9()
     , isNatIList^#(V) -> c_10(U31^#(isNatList(activate(V))))
     , isNatIList^#(n__zeros()) -> c_11()
     , isNatIList^#(n__cons(V1, V2)) ->
       c_12(U41^#(isNat(activate(V1)), activate(V2)))
     , activate^#(n__0()) -> c_15(0^#())
     , activate^#(n__nil()) -> c_19(nil^#())
     , length^#(nil()) -> c_32(0^#())
     , nil^#() -> c_33()
     , U51^#(tt(), V2) -> c_20(U52^#(isNatList(activate(V2))))
     , U52^#(tt()) -> c_21()
     , isNatList^#(n__cons(V1, V2)) ->
       c_22(U51^#(isNat(activate(V1)), activate(V2)))
     , isNatList^#(n__nil()) -> c_23()
     , isNat^#(n__0()) -> c_26()
     , isNat^#(n__length(V1)) -> c_27(U11^#(isNatList(activate(V1))))
     , isNat^#(n__s(V1)) -> c_28(U21^#(isNat(activate(V1)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..