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__U61(X1, X2, X3) -> U61(X1, X2, X3)
  , a__U61(tt(), L, N) -> a__U62(a__isNat(N), L)
  , a__U62(X1, X2) -> U62(X1, X2)
  , a__U62(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__U61(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(length(X)) -> a__length(mark(X))
  , mark(nil()) -> nil()
  , 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, X3)) -> a__U61(mark(X1), X2, X3)
  , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
  , mark(isNat(X)) -> a__isNat(X) }
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) '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.
      
   

3) '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__U61^#(X1, X2, X3) -> c_24(X1, X2, X3)
     , a__U61^#(tt(), L, N) -> c_25(a__U62^#(a__isNat(N), L))
     , a__U62^#(X1, X2) -> c_26(X1, X2)
     , a__U62^#(tt(), L) -> c_27(a__length^#(mark(L)))
     , a__length^#(X) -> c_32(X)
     , a__length^#(cons(N, L)) -> c_33(a__U61^#(a__isNatList(L), L, N))
     , a__length^#(nil()) -> c_34()
     , a__isNat^#(X) -> c_28(X)
     , a__isNat^#(0()) -> c_29()
     , a__isNat^#(s(V1)) -> c_30(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_31(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_35(mark^#(X1), X2)
     , mark^#(0()) -> c_36()
     , mark^#(zeros()) -> c_37(a__zeros^#())
     , mark^#(tt()) -> c_38()
     , mark^#(s(X)) -> c_39(mark^#(X))
     , mark^#(length(X)) -> c_40(a__length^#(mark(X)))
     , mark^#(nil()) -> c_41()
     , mark^#(U11(X)) -> c_42(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_43(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_44(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_45(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_46(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_47(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_48(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_49(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_50(a__isNatList^#(X))
     , mark^#(U61(X1, X2, X3)) -> c_51(a__U61^#(mark(X1), X2, X3))
     , mark^#(U62(X1, X2)) -> c_52(a__U62^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_53(a__isNat^#(X)) }
   
   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__U61^#(X1, X2, X3) -> c_24(X1, X2, X3)
     , a__U61^#(tt(), L, N) -> c_25(a__U62^#(a__isNat(N), L))
     , a__U62^#(X1, X2) -> c_26(X1, X2)
     , a__U62^#(tt(), L) -> c_27(a__length^#(mark(L)))
     , a__length^#(X) -> c_32(X)
     , a__length^#(cons(N, L)) -> c_33(a__U61^#(a__isNatList(L), L, N))
     , a__length^#(nil()) -> c_34()
     , a__isNat^#(X) -> c_28(X)
     , a__isNat^#(0()) -> c_29()
     , a__isNat^#(s(V1)) -> c_30(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_31(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_35(mark^#(X1), X2)
     , mark^#(0()) -> c_36()
     , mark^#(zeros()) -> c_37(a__zeros^#())
     , mark^#(tt()) -> c_38()
     , mark^#(s(X)) -> c_39(mark^#(X))
     , mark^#(length(X)) -> c_40(a__length^#(mark(X)))
     , mark^#(nil()) -> c_41()
     , mark^#(U11(X)) -> c_42(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_43(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_44(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_45(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_46(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_47(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_48(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_49(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_50(a__isNatList^#(X))
     , mark^#(U61(X1, X2, X3)) -> c_51(a__U61^#(mark(X1), X2, X3))
     , mark^#(U62(X1, X2)) -> c_52(a__U62^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_53(a__isNat^#(X)) }
   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__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U61(tt(), L, N) -> a__U62(a__isNat(N), L)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__U62(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__U61(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(length(X)) -> a__length(mark(X))
     , mark(nil()) -> nil()
     , 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, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of
   {1,2,4,6,8,12,16,20,23,30,32,36,38,41} by applications of
   Pre({1,2,4,6,8,12,16,20,23,30,32,36,38,41}) =
   {3,5,7,9,10,11,13,14,17,18,19,21,24,26,27,28,31,33,34,35,37,39,40,42,43,44,46,47,49,50,53}.
   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__U61^#(X1, X2, X3) -> c_24(X1, X2, X3)
       , 25: a__U61^#(tt(), L, N) -> c_25(a__U62^#(a__isNat(N), L))
       , 26: a__U62^#(X1, X2) -> c_26(X1, X2)
       , 27: a__U62^#(tt(), L) -> c_27(a__length^#(mark(L)))
       , 28: a__length^#(X) -> c_32(X)
       , 29: a__length^#(cons(N, L)) ->
             c_33(a__U61^#(a__isNatList(L), L, N))
       , 30: a__length^#(nil()) -> c_34()
       , 31: a__isNat^#(X) -> c_28(X)
       , 32: a__isNat^#(0()) -> c_29()
       , 33: a__isNat^#(s(V1)) -> c_30(a__U21^#(a__isNat(V1)))
       , 34: a__isNat^#(length(V1)) -> c_31(a__U11^#(a__isNatList(V1)))
       , 35: mark^#(cons(X1, X2)) -> c_35(mark^#(X1), X2)
       , 36: mark^#(0()) -> c_36()
       , 37: mark^#(zeros()) -> c_37(a__zeros^#())
       , 38: mark^#(tt()) -> c_38()
       , 39: mark^#(s(X)) -> c_39(mark^#(X))
       , 40: mark^#(length(X)) -> c_40(a__length^#(mark(X)))
       , 41: mark^#(nil()) -> c_41()
       , 42: mark^#(U11(X)) -> c_42(a__U11^#(mark(X)))
       , 43: mark^#(U21(X)) -> c_43(a__U21^#(mark(X)))
       , 44: mark^#(U31(X)) -> c_44(a__U31^#(mark(X)))
       , 45: mark^#(U41(X1, X2)) -> c_45(a__U41^#(mark(X1), X2))
       , 46: mark^#(U42(X)) -> c_46(a__U42^#(mark(X)))
       , 47: mark^#(isNatIList(X)) -> c_47(a__isNatIList^#(X))
       , 48: mark^#(U51(X1, X2)) -> c_48(a__U51^#(mark(X1), X2))
       , 49: mark^#(U52(X)) -> c_49(a__U52^#(mark(X)))
       , 50: mark^#(isNatList(X)) -> c_50(a__isNatList^#(X))
       , 51: mark^#(U61(X1, X2, X3)) -> c_51(a__U61^#(mark(X1), X2, X3))
       , 52: mark^#(U62(X1, X2)) -> c_52(a__U62^#(mark(X1), X2))
       , 53: mark^#(isNat(X)) -> c_53(a__isNat^#(X)) }
   
   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__U61^#(X1, X2, X3) -> c_24(X1, X2, X3)
     , a__U61^#(tt(), L, N) -> c_25(a__U62^#(a__isNat(N), L))
     , a__U62^#(X1, X2) -> c_26(X1, X2)
     , a__U62^#(tt(), L) -> c_27(a__length^#(mark(L)))
     , a__length^#(X) -> c_32(X)
     , a__length^#(cons(N, L)) -> c_33(a__U61^#(a__isNatList(L), L, N))
     , a__isNat^#(X) -> c_28(X)
     , a__isNat^#(s(V1)) -> c_30(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_31(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_35(mark^#(X1), X2)
     , mark^#(zeros()) -> c_37(a__zeros^#())
     , mark^#(s(X)) -> c_39(mark^#(X))
     , mark^#(length(X)) -> c_40(a__length^#(mark(X)))
     , mark^#(U11(X)) -> c_42(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_43(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_44(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_45(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_46(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_47(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_48(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_49(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_50(a__isNatList^#(X))
     , mark^#(U61(X1, X2, X3)) -> c_51(a__U61^#(mark(X1), X2, X3))
     , mark^#(U62(X1, X2)) -> c_52(a__U62^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_53(a__isNat^#(X)) }
   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__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U61(tt(), L, N) -> a__U62(a__isNat(N), L)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__U62(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__U61(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(length(X)) -> a__length(mark(X))
     , mark(nil()) -> nil()
     , 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, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X) }
   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__length^#(nil()) -> c_34()
     , a__isNat^#(0()) -> c_29()
     , mark^#(0()) -> c_36()
     , mark^#(tt()) -> c_38()
     , mark^#(nil()) -> c_41() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {25} by applications of
   Pre({25}) = {1,2,3,4,6,8,10,12,13,15,17,19,21,24,26}. 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__U61^#(X1, X2, X3) -> c_24(X1, X2, X3)
       , 16: a__U61^#(tt(), L, N) -> c_25(a__U62^#(a__isNat(N), L))
       , 17: a__U62^#(X1, X2) -> c_26(X1, X2)
       , 18: a__U62^#(tt(), L) -> c_27(a__length^#(mark(L)))
       , 19: a__length^#(X) -> c_32(X)
       , 20: a__length^#(cons(N, L)) ->
             c_33(a__U61^#(a__isNatList(L), L, N))
       , 21: a__isNat^#(X) -> c_28(X)
       , 22: a__isNat^#(s(V1)) -> c_30(a__U21^#(a__isNat(V1)))
       , 23: a__isNat^#(length(V1)) -> c_31(a__U11^#(a__isNatList(V1)))
       , 24: mark^#(cons(X1, X2)) -> c_35(mark^#(X1), X2)
       , 25: mark^#(zeros()) -> c_37(a__zeros^#())
       , 26: mark^#(s(X)) -> c_39(mark^#(X))
       , 27: mark^#(length(X)) -> c_40(a__length^#(mark(X)))
       , 28: mark^#(U11(X)) -> c_42(a__U11^#(mark(X)))
       , 29: mark^#(U21(X)) -> c_43(a__U21^#(mark(X)))
       , 30: mark^#(U31(X)) -> c_44(a__U31^#(mark(X)))
       , 31: mark^#(U41(X1, X2)) -> c_45(a__U41^#(mark(X1), X2))
       , 32: mark^#(U42(X)) -> c_46(a__U42^#(mark(X)))
       , 33: mark^#(isNatIList(X)) -> c_47(a__isNatIList^#(X))
       , 34: mark^#(U51(X1, X2)) -> c_48(a__U51^#(mark(X1), X2))
       , 35: mark^#(U52(X)) -> c_49(a__U52^#(mark(X)))
       , 36: mark^#(isNatList(X)) -> c_50(a__isNatList^#(X))
       , 37: mark^#(U61(X1, X2, X3)) -> c_51(a__U61^#(mark(X1), X2, X3))
       , 38: mark^#(U62(X1, X2)) -> c_52(a__U62^#(mark(X1), X2))
       , 39: mark^#(isNat(X)) -> c_53(a__isNat^#(X))
       , 40: a__zeros^#() -> c_1()
       , 41: a__zeros^#() -> c_2()
       , 42: a__U11^#(tt()) -> c_4()
       , 43: a__U21^#(tt()) -> c_6()
       , 44: a__U31^#(tt()) -> c_8()
       , 45: a__U42^#(tt()) -> c_12()
       , 46: a__isNatIList^#(zeros()) -> c_16()
       , 47: a__U52^#(tt()) -> c_20()
       , 48: a__isNatList^#(nil()) -> c_23()
       , 49: a__length^#(nil()) -> c_34()
       , 50: a__isNat^#(0()) -> c_29()
       , 51: mark^#(0()) -> c_36()
       , 52: mark^#(tt()) -> c_38()
       , 53: mark^#(nil()) -> c_41() }
   
   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__U61^#(X1, X2, X3) -> c_24(X1, X2, X3)
     , a__U61^#(tt(), L, N) -> c_25(a__U62^#(a__isNat(N), L))
     , a__U62^#(X1, X2) -> c_26(X1, X2)
     , a__U62^#(tt(), L) -> c_27(a__length^#(mark(L)))
     , a__length^#(X) -> c_32(X)
     , a__length^#(cons(N, L)) -> c_33(a__U61^#(a__isNatList(L), L, N))
     , a__isNat^#(X) -> c_28(X)
     , a__isNat^#(s(V1)) -> c_30(a__U21^#(a__isNat(V1)))
     , a__isNat^#(length(V1)) -> c_31(a__U11^#(a__isNatList(V1)))
     , mark^#(cons(X1, X2)) -> c_35(mark^#(X1), X2)
     , mark^#(s(X)) -> c_39(mark^#(X))
     , mark^#(length(X)) -> c_40(a__length^#(mark(X)))
     , mark^#(U11(X)) -> c_42(a__U11^#(mark(X)))
     , mark^#(U21(X)) -> c_43(a__U21^#(mark(X)))
     , mark^#(U31(X)) -> c_44(a__U31^#(mark(X)))
     , mark^#(U41(X1, X2)) -> c_45(a__U41^#(mark(X1), X2))
     , mark^#(U42(X)) -> c_46(a__U42^#(mark(X)))
     , mark^#(isNatIList(X)) -> c_47(a__isNatIList^#(X))
     , mark^#(U51(X1, X2)) -> c_48(a__U51^#(mark(X1), X2))
     , mark^#(U52(X)) -> c_49(a__U52^#(mark(X)))
     , mark^#(isNatList(X)) -> c_50(a__isNatList^#(X))
     , mark^#(U61(X1, X2, X3)) -> c_51(a__U61^#(mark(X1), X2, X3))
     , mark^#(U62(X1, X2)) -> c_52(a__U62^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_53(a__isNat^#(X)) }
   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__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U61(tt(), L, N) -> a__U62(a__isNat(N), L)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__U62(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__U61(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(length(X)) -> a__length(mark(X))
     , mark(nil()) -> nil()
     , 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, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X) }
   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__length^#(nil()) -> c_34()
     , a__isNat^#(0()) -> c_29()
     , mark^#(0()) -> c_36()
     , mark^#(zeros()) -> c_37(a__zeros^#())
     , mark^#(tt()) -> c_38()
     , mark^#(nil()) -> c_41() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..