MAYBE

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

Strict Trs:
  { active(zeros()) -> mark(cons(0(), zeros()))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(U11(X)) -> U11(active(X))
  , active(U11(tt())) -> mark(tt())
  , active(U21(X)) -> U21(active(X))
  , active(U21(tt())) -> mark(tt())
  , active(U31(X)) -> U31(active(X))
  , active(U31(tt())) -> mark(tt())
  , active(U41(X1, X2)) -> U41(active(X1), X2)
  , active(U41(tt(), V2)) -> mark(U42(isNatIList(V2)))
  , active(U42(X)) -> U42(active(X))
  , active(U42(tt())) -> mark(tt())
  , active(isNatIList(V)) -> mark(U31(isNatList(V)))
  , active(isNatIList(zeros())) -> mark(tt())
  , active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2))
  , active(U51(X1, X2)) -> U51(active(X1), X2)
  , active(U51(tt(), V2)) -> mark(U52(isNatList(V2)))
  , active(U52(X)) -> U52(active(X))
  , active(U52(tt())) -> mark(tt())
  , active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2))
  , active(isNatList(nil())) -> mark(tt())
  , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
  , active(U61(tt(), L, N)) -> mark(U62(isNat(N), L))
  , active(U62(X1, X2)) -> U62(active(X1), X2)
  , active(U62(tt(), L)) -> mark(s(length(L)))
  , active(isNat(0())) -> mark(tt())
  , active(isNat(s(V1))) -> mark(U21(isNat(V1)))
  , active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
  , active(s(X)) -> s(active(X))
  , active(length(X)) -> length(active(X))
  , active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N))
  , active(length(nil())) -> mark(0())
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , U11(mark(X)) -> mark(U11(X))
  , U11(ok(X)) -> ok(U11(X))
  , U21(mark(X)) -> mark(U21(X))
  , U21(ok(X)) -> ok(U21(X))
  , U31(mark(X)) -> mark(U31(X))
  , U31(ok(X)) -> ok(U31(X))
  , U41(mark(X1), X2) -> mark(U41(X1, X2))
  , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2))
  , U42(mark(X)) -> mark(U42(X))
  , U42(ok(X)) -> ok(U42(X))
  , isNatIList(ok(X)) -> ok(isNatIList(X))
  , U51(mark(X1), X2) -> mark(U51(X1, X2))
  , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
  , U52(mark(X)) -> mark(U52(X))
  , U52(ok(X)) -> ok(U52(X))
  , isNatList(ok(X)) -> ok(isNatList(X))
  , U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3))
  , U61(ok(X1), ok(X2), ok(X3)) -> ok(U61(X1, X2, X3))
  , U62(mark(X1), X2) -> mark(U62(X1, X2))
  , U62(ok(X1), ok(X2)) -> ok(U62(X1, X2))
  , isNat(ok(X)) -> ok(isNat(X))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , length(mark(X)) -> mark(length(X))
  , length(ok(X)) -> ok(length(X))
  , proper(zeros()) -> ok(zeros())
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(U11(X)) -> U11(proper(X))
  , proper(tt()) -> ok(tt())
  , proper(U21(X)) -> U21(proper(X))
  , proper(U31(X)) -> U31(proper(X))
  , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2))
  , proper(U42(X)) -> U42(proper(X))
  , proper(isNatIList(X)) -> isNatIList(proper(X))
  , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
  , proper(U52(X)) -> U52(proper(X))
  , proper(isNatList(X)) -> isNatList(proper(X))
  , proper(U61(X1, X2, X3)) ->
    U61(proper(X1), proper(X2), proper(X3))
  , proper(U62(X1, X2)) -> U62(proper(X1), proper(X2))
  , proper(isNat(X)) -> isNat(proper(X))
  , proper(s(X)) -> s(proper(X))
  , proper(length(X)) -> length(proper(X))
  , proper(nil()) -> ok(nil())
  , top(mark(X)) -> top(proper(X))
  , top(ok(X)) -> top(active(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:
     { active^#(zeros()) -> c_1(cons^#(0(), zeros()))
     , active^#(cons(X1, X2)) -> c_2(cons^#(active(X1), X2))
     , active^#(U11(X)) -> c_3(U11^#(active(X)))
     , active^#(U11(tt())) -> c_4()
     , active^#(U21(X)) -> c_5(U21^#(active(X)))
     , active^#(U21(tt())) -> c_6()
     , active^#(U31(X)) -> c_7(U31^#(active(X)))
     , active^#(U31(tt())) -> c_8()
     , active^#(U41(X1, X2)) -> c_9(U41^#(active(X1), X2))
     , active^#(U41(tt(), V2)) -> c_10(U42^#(isNatIList(V2)))
     , active^#(U42(X)) -> c_11(U42^#(active(X)))
     , active^#(U42(tt())) -> c_12()
     , active^#(isNatIList(V)) -> c_13(U31^#(isNatList(V)))
     , active^#(isNatIList(zeros())) -> c_14()
     , active^#(isNatIList(cons(V1, V2))) -> c_15(U41^#(isNat(V1), V2))
     , active^#(U51(X1, X2)) -> c_16(U51^#(active(X1), X2))
     , active^#(U51(tt(), V2)) -> c_17(U52^#(isNatList(V2)))
     , active^#(U52(X)) -> c_18(U52^#(active(X)))
     , active^#(U52(tt())) -> c_19()
     , active^#(isNatList(cons(V1, V2))) -> c_20(U51^#(isNat(V1), V2))
     , active^#(isNatList(nil())) -> c_21()
     , active^#(U61(X1, X2, X3)) -> c_22(U61^#(active(X1), X2, X3))
     , active^#(U61(tt(), L, N)) -> c_23(U62^#(isNat(N), L))
     , active^#(U62(X1, X2)) -> c_24(U62^#(active(X1), X2))
     , active^#(U62(tt(), L)) -> c_25(s^#(length(L)))
     , active^#(isNat(0())) -> c_26()
     , active^#(isNat(s(V1))) -> c_27(U21^#(isNat(V1)))
     , active^#(isNat(length(V1))) -> c_28(U11^#(isNatList(V1)))
     , active^#(s(X)) -> c_29(s^#(active(X)))
     , active^#(length(X)) -> c_30(length^#(active(X)))
     , active^#(length(cons(N, L))) -> c_31(U61^#(isNatList(L), L, N))
     , active^#(length(nil())) -> c_32()
     , cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2))
     , U11^#(mark(X)) -> c_35(U11^#(X))
     , U11^#(ok(X)) -> c_36(U11^#(X))
     , U21^#(mark(X)) -> c_37(U21^#(X))
     , U21^#(ok(X)) -> c_38(U21^#(X))
     , U31^#(mark(X)) -> c_39(U31^#(X))
     , U31^#(ok(X)) -> c_40(U31^#(X))
     , U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2))
     , U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2))
     , U42^#(mark(X)) -> c_43(U42^#(X))
     , U42^#(ok(X)) -> c_44(U42^#(X))
     , U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2))
     , U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2))
     , U52^#(mark(X)) -> c_48(U52^#(X))
     , U52^#(ok(X)) -> c_49(U52^#(X))
     , U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3))
     , U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3))
     , U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2))
     , U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2))
     , s^#(mark(X)) -> c_56(s^#(X))
     , s^#(ok(X)) -> c_57(s^#(X))
     , length^#(mark(X)) -> c_58(length^#(X))
     , length^#(ok(X)) -> c_59(length^#(X))
     , isNatIList^#(ok(X)) -> c_45(isNatIList^#(X))
     , isNatList^#(ok(X)) -> c_50(isNatList^#(X))
     , isNat^#(ok(X)) -> c_55(isNat^#(X))
     , proper^#(zeros()) -> c_60()
     , proper^#(cons(X1, X2)) -> c_61(cons^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_62()
     , proper^#(U11(X)) -> c_63(U11^#(proper(X)))
     , proper^#(tt()) -> c_64()
     , proper^#(U21(X)) -> c_65(U21^#(proper(X)))
     , proper^#(U31(X)) -> c_66(U31^#(proper(X)))
     , proper^#(U41(X1, X2)) -> c_67(U41^#(proper(X1), proper(X2)))
     , proper^#(U42(X)) -> c_68(U42^#(proper(X)))
     , proper^#(isNatIList(X)) -> c_69(isNatIList^#(proper(X)))
     , proper^#(U51(X1, X2)) -> c_70(U51^#(proper(X1), proper(X2)))
     , proper^#(U52(X)) -> c_71(U52^#(proper(X)))
     , proper^#(isNatList(X)) -> c_72(isNatList^#(proper(X)))
     , proper^#(U61(X1, X2, X3)) ->
       c_73(U61^#(proper(X1), proper(X2), proper(X3)))
     , proper^#(U62(X1, X2)) -> c_74(U62^#(proper(X1), proper(X2)))
     , proper^#(isNat(X)) -> c_75(isNat^#(proper(X)))
     , proper^#(s(X)) -> c_76(s^#(proper(X)))
     , proper^#(length(X)) -> c_77(length^#(proper(X)))
     , proper^#(nil()) -> c_78()
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { active^#(zeros()) -> c_1(cons^#(0(), zeros()))
     , active^#(cons(X1, X2)) -> c_2(cons^#(active(X1), X2))
     , active^#(U11(X)) -> c_3(U11^#(active(X)))
     , active^#(U11(tt())) -> c_4()
     , active^#(U21(X)) -> c_5(U21^#(active(X)))
     , active^#(U21(tt())) -> c_6()
     , active^#(U31(X)) -> c_7(U31^#(active(X)))
     , active^#(U31(tt())) -> c_8()
     , active^#(U41(X1, X2)) -> c_9(U41^#(active(X1), X2))
     , active^#(U41(tt(), V2)) -> c_10(U42^#(isNatIList(V2)))
     , active^#(U42(X)) -> c_11(U42^#(active(X)))
     , active^#(U42(tt())) -> c_12()
     , active^#(isNatIList(V)) -> c_13(U31^#(isNatList(V)))
     , active^#(isNatIList(zeros())) -> c_14()
     , active^#(isNatIList(cons(V1, V2))) -> c_15(U41^#(isNat(V1), V2))
     , active^#(U51(X1, X2)) -> c_16(U51^#(active(X1), X2))
     , active^#(U51(tt(), V2)) -> c_17(U52^#(isNatList(V2)))
     , active^#(U52(X)) -> c_18(U52^#(active(X)))
     , active^#(U52(tt())) -> c_19()
     , active^#(isNatList(cons(V1, V2))) -> c_20(U51^#(isNat(V1), V2))
     , active^#(isNatList(nil())) -> c_21()
     , active^#(U61(X1, X2, X3)) -> c_22(U61^#(active(X1), X2, X3))
     , active^#(U61(tt(), L, N)) -> c_23(U62^#(isNat(N), L))
     , active^#(U62(X1, X2)) -> c_24(U62^#(active(X1), X2))
     , active^#(U62(tt(), L)) -> c_25(s^#(length(L)))
     , active^#(isNat(0())) -> c_26()
     , active^#(isNat(s(V1))) -> c_27(U21^#(isNat(V1)))
     , active^#(isNat(length(V1))) -> c_28(U11^#(isNatList(V1)))
     , active^#(s(X)) -> c_29(s^#(active(X)))
     , active^#(length(X)) -> c_30(length^#(active(X)))
     , active^#(length(cons(N, L))) -> c_31(U61^#(isNatList(L), L, N))
     , active^#(length(nil())) -> c_32()
     , cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2))
     , U11^#(mark(X)) -> c_35(U11^#(X))
     , U11^#(ok(X)) -> c_36(U11^#(X))
     , U21^#(mark(X)) -> c_37(U21^#(X))
     , U21^#(ok(X)) -> c_38(U21^#(X))
     , U31^#(mark(X)) -> c_39(U31^#(X))
     , U31^#(ok(X)) -> c_40(U31^#(X))
     , U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2))
     , U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2))
     , U42^#(mark(X)) -> c_43(U42^#(X))
     , U42^#(ok(X)) -> c_44(U42^#(X))
     , U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2))
     , U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2))
     , U52^#(mark(X)) -> c_48(U52^#(X))
     , U52^#(ok(X)) -> c_49(U52^#(X))
     , U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3))
     , U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3))
     , U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2))
     , U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2))
     , s^#(mark(X)) -> c_56(s^#(X))
     , s^#(ok(X)) -> c_57(s^#(X))
     , length^#(mark(X)) -> c_58(length^#(X))
     , length^#(ok(X)) -> c_59(length^#(X))
     , isNatIList^#(ok(X)) -> c_45(isNatIList^#(X))
     , isNatList^#(ok(X)) -> c_50(isNatList^#(X))
     , isNat^#(ok(X)) -> c_55(isNat^#(X))
     , proper^#(zeros()) -> c_60()
     , proper^#(cons(X1, X2)) -> c_61(cons^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_62()
     , proper^#(U11(X)) -> c_63(U11^#(proper(X)))
     , proper^#(tt()) -> c_64()
     , proper^#(U21(X)) -> c_65(U21^#(proper(X)))
     , proper^#(U31(X)) -> c_66(U31^#(proper(X)))
     , proper^#(U41(X1, X2)) -> c_67(U41^#(proper(X1), proper(X2)))
     , proper^#(U42(X)) -> c_68(U42^#(proper(X)))
     , proper^#(isNatIList(X)) -> c_69(isNatIList^#(proper(X)))
     , proper^#(U51(X1, X2)) -> c_70(U51^#(proper(X1), proper(X2)))
     , proper^#(U52(X)) -> c_71(U52^#(proper(X)))
     , proper^#(isNatList(X)) -> c_72(isNatList^#(proper(X)))
     , proper^#(U61(X1, X2, X3)) ->
       c_73(U61^#(proper(X1), proper(X2), proper(X3)))
     , proper^#(U62(X1, X2)) -> c_74(U62^#(proper(X1), proper(X2)))
     , proper^#(isNat(X)) -> c_75(isNat^#(proper(X)))
     , proper^#(s(X)) -> c_76(s^#(proper(X)))
     , proper^#(length(X)) -> c_77(length^#(proper(X)))
     , proper^#(nil()) -> c_78()
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   Strict Trs:
     { active(zeros()) -> mark(cons(0(), zeros()))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X)) -> U11(active(X))
     , active(U11(tt())) -> mark(tt())
     , active(U21(X)) -> U21(active(X))
     , active(U21(tt())) -> mark(tt())
     , active(U31(X)) -> U31(active(X))
     , active(U31(tt())) -> mark(tt())
     , active(U41(X1, X2)) -> U41(active(X1), X2)
     , active(U41(tt(), V2)) -> mark(U42(isNatIList(V2)))
     , active(U42(X)) -> U42(active(X))
     , active(U42(tt())) -> mark(tt())
     , active(isNatIList(V)) -> mark(U31(isNatList(V)))
     , active(isNatIList(zeros())) -> mark(tt())
     , active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2))
     , active(U51(X1, X2)) -> U51(active(X1), X2)
     , active(U51(tt(), V2)) -> mark(U52(isNatList(V2)))
     , active(U52(X)) -> U52(active(X))
     , active(U52(tt())) -> mark(tt())
     , active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2))
     , active(isNatList(nil())) -> mark(tt())
     , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
     , active(U61(tt(), L, N)) -> mark(U62(isNat(N), L))
     , active(U62(X1, X2)) -> U62(active(X1), X2)
     , active(U62(tt(), L)) -> mark(s(length(L)))
     , active(isNat(0())) -> mark(tt())
     , active(isNat(s(V1))) -> mark(U21(isNat(V1)))
     , active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N))
     , active(length(nil())) -> mark(0())
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(mark(X)) -> mark(U11(X))
     , U11(ok(X)) -> ok(U11(X))
     , U21(mark(X)) -> mark(U21(X))
     , U21(ok(X)) -> ok(U21(X))
     , U31(mark(X)) -> mark(U31(X))
     , U31(ok(X)) -> ok(U31(X))
     , U41(mark(X1), X2) -> mark(U41(X1, X2))
     , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2))
     , U42(mark(X)) -> mark(U42(X))
     , U42(ok(X)) -> ok(U42(X))
     , isNatIList(ok(X)) -> ok(isNatIList(X))
     , U51(mark(X1), X2) -> mark(U51(X1, X2))
     , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
     , U52(mark(X)) -> mark(U52(X))
     , U52(ok(X)) -> ok(U52(X))
     , isNatList(ok(X)) -> ok(isNatList(X))
     , U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3))
     , U61(ok(X1), ok(X2), ok(X3)) -> ok(U61(X1, X2, X3))
     , U62(mark(X1), X2) -> mark(U62(X1, X2))
     , U62(ok(X1), ok(X2)) -> ok(U62(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , length(mark(X)) -> mark(length(X))
     , length(ok(X)) -> ok(length(X))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X)) -> U11(proper(X))
     , proper(tt()) -> ok(tt())
     , proper(U21(X)) -> U21(proper(X))
     , proper(U31(X)) -> U31(proper(X))
     , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2))
     , proper(U42(X)) -> U42(proper(X))
     , proper(isNatIList(X)) -> isNatIList(proper(X))
     , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
     , proper(U52(X)) -> U52(proper(X))
     , proper(isNatList(X)) -> isNatList(proper(X))
     , proper(U61(X1, X2, X3)) ->
       U61(proper(X1), proper(X2), proper(X3))
     , proper(U62(X1, X2)) -> U62(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Consider the dependency graph:
   
     1: active^#(zeros()) -> c_1(cons^#(0(), zeros()))
     
     2: active^#(cons(X1, X2)) -> c_2(cons^#(active(X1), X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2)) :34
        -->_1 cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2)) :33
     
     3: active^#(U11(X)) -> c_3(U11^#(active(X)))
        -->_1 U11^#(ok(X)) -> c_36(U11^#(X)) :36
        -->_1 U11^#(mark(X)) -> c_35(U11^#(X)) :35
     
     4: active^#(U11(tt())) -> c_4()
     
     5: active^#(U21(X)) -> c_5(U21^#(active(X)))
        -->_1 U21^#(ok(X)) -> c_38(U21^#(X)) :38
        -->_1 U21^#(mark(X)) -> c_37(U21^#(X)) :37
     
     6: active^#(U21(tt())) -> c_6()
     
     7: active^#(U31(X)) -> c_7(U31^#(active(X)))
        -->_1 U31^#(ok(X)) -> c_40(U31^#(X)) :40
        -->_1 U31^#(mark(X)) -> c_39(U31^#(X)) :39
     
     8: active^#(U31(tt())) -> c_8()
     
     9: active^#(U41(X1, X2)) -> c_9(U41^#(active(X1), X2))
        -->_1 U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2)) :42
        -->_1 U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2)) :41
     
     10: active^#(U41(tt(), V2)) -> c_10(U42^#(isNatIList(V2)))
        -->_1 U42^#(ok(X)) -> c_44(U42^#(X)) :44
        -->_1 U42^#(mark(X)) -> c_43(U42^#(X)) :43
     
     11: active^#(U42(X)) -> c_11(U42^#(active(X)))
        -->_1 U42^#(ok(X)) -> c_44(U42^#(X)) :44
        -->_1 U42^#(mark(X)) -> c_43(U42^#(X)) :43
     
     12: active^#(U42(tt())) -> c_12()
     
     13: active^#(isNatIList(V)) -> c_13(U31^#(isNatList(V)))
        -->_1 U31^#(ok(X)) -> c_40(U31^#(X)) :40
        -->_1 U31^#(mark(X)) -> c_39(U31^#(X)) :39
     
     14: active^#(isNatIList(zeros())) -> c_14()
     
     15: active^#(isNatIList(cons(V1, V2))) ->
         c_15(U41^#(isNat(V1), V2))
        -->_1 U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2)) :42
        -->_1 U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2)) :41
     
     16: active^#(U51(X1, X2)) -> c_16(U51^#(active(X1), X2))
        -->_1 U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2)) :46
        -->_1 U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2)) :45
     
     17: active^#(U51(tt(), V2)) -> c_17(U52^#(isNatList(V2)))
        -->_1 U52^#(ok(X)) -> c_49(U52^#(X)) :48
        -->_1 U52^#(mark(X)) -> c_48(U52^#(X)) :47
     
     18: active^#(U52(X)) -> c_18(U52^#(active(X)))
        -->_1 U52^#(ok(X)) -> c_49(U52^#(X)) :48
        -->_1 U52^#(mark(X)) -> c_48(U52^#(X)) :47
     
     19: active^#(U52(tt())) -> c_19()
     
     20: active^#(isNatList(cons(V1, V2))) -> c_20(U51^#(isNat(V1), V2))
        -->_1 U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2)) :46
        -->_1 U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2)) :45
     
     21: active^#(isNatList(nil())) -> c_21()
     
     22: active^#(U61(X1, X2, X3)) -> c_22(U61^#(active(X1), X2, X3))
        -->_1 U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3)) :50
        -->_1 U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3)) :49
     
     23: active^#(U61(tt(), L, N)) -> c_23(U62^#(isNat(N), L))
        -->_1 U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2)) :52
        -->_1 U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2)) :51
     
     24: active^#(U62(X1, X2)) -> c_24(U62^#(active(X1), X2))
        -->_1 U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2)) :52
        -->_1 U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2)) :51
     
     25: active^#(U62(tt(), L)) -> c_25(s^#(length(L)))
        -->_1 s^#(ok(X)) -> c_57(s^#(X)) :54
        -->_1 s^#(mark(X)) -> c_56(s^#(X)) :53
     
     26: active^#(isNat(0())) -> c_26()
     
     27: active^#(isNat(s(V1))) -> c_27(U21^#(isNat(V1)))
        -->_1 U21^#(ok(X)) -> c_38(U21^#(X)) :38
        -->_1 U21^#(mark(X)) -> c_37(U21^#(X)) :37
     
     28: active^#(isNat(length(V1))) -> c_28(U11^#(isNatList(V1)))
        -->_1 U11^#(ok(X)) -> c_36(U11^#(X)) :36
        -->_1 U11^#(mark(X)) -> c_35(U11^#(X)) :35
     
     29: active^#(s(X)) -> c_29(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_57(s^#(X)) :54
        -->_1 s^#(mark(X)) -> c_56(s^#(X)) :53
     
     30: active^#(length(X)) -> c_30(length^#(active(X)))
        -->_1 length^#(ok(X)) -> c_59(length^#(X)) :56
        -->_1 length^#(mark(X)) -> c_58(length^#(X)) :55
     
     31: active^#(length(cons(N, L))) -> c_31(U61^#(isNatList(L), L, N))
        -->_1 U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3)) :50
        -->_1 U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3)) :49
     
     32: active^#(length(nil())) -> c_32()
     
     33: cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2)) :34
        -->_1 cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2)) :33
     
     34: cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2)) :34
        -->_1 cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2)) :33
     
     35: U11^#(mark(X)) -> c_35(U11^#(X))
        -->_1 U11^#(ok(X)) -> c_36(U11^#(X)) :36
        -->_1 U11^#(mark(X)) -> c_35(U11^#(X)) :35
     
     36: U11^#(ok(X)) -> c_36(U11^#(X))
        -->_1 U11^#(ok(X)) -> c_36(U11^#(X)) :36
        -->_1 U11^#(mark(X)) -> c_35(U11^#(X)) :35
     
     37: U21^#(mark(X)) -> c_37(U21^#(X))
        -->_1 U21^#(ok(X)) -> c_38(U21^#(X)) :38
        -->_1 U21^#(mark(X)) -> c_37(U21^#(X)) :37
     
     38: U21^#(ok(X)) -> c_38(U21^#(X))
        -->_1 U21^#(ok(X)) -> c_38(U21^#(X)) :38
        -->_1 U21^#(mark(X)) -> c_37(U21^#(X)) :37
     
     39: U31^#(mark(X)) -> c_39(U31^#(X))
        -->_1 U31^#(ok(X)) -> c_40(U31^#(X)) :40
        -->_1 U31^#(mark(X)) -> c_39(U31^#(X)) :39
     
     40: U31^#(ok(X)) -> c_40(U31^#(X))
        -->_1 U31^#(ok(X)) -> c_40(U31^#(X)) :40
        -->_1 U31^#(mark(X)) -> c_39(U31^#(X)) :39
     
     41: U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2))
        -->_1 U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2)) :42
        -->_1 U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2)) :41
     
     42: U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2))
        -->_1 U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2)) :42
        -->_1 U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2)) :41
     
     43: U42^#(mark(X)) -> c_43(U42^#(X))
        -->_1 U42^#(ok(X)) -> c_44(U42^#(X)) :44
        -->_1 U42^#(mark(X)) -> c_43(U42^#(X)) :43
     
     44: U42^#(ok(X)) -> c_44(U42^#(X))
        -->_1 U42^#(ok(X)) -> c_44(U42^#(X)) :44
        -->_1 U42^#(mark(X)) -> c_43(U42^#(X)) :43
     
     45: U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2))
        -->_1 U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2)) :46
        -->_1 U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2)) :45
     
     46: U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2))
        -->_1 U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2)) :46
        -->_1 U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2)) :45
     
     47: U52^#(mark(X)) -> c_48(U52^#(X))
        -->_1 U52^#(ok(X)) -> c_49(U52^#(X)) :48
        -->_1 U52^#(mark(X)) -> c_48(U52^#(X)) :47
     
     48: U52^#(ok(X)) -> c_49(U52^#(X))
        -->_1 U52^#(ok(X)) -> c_49(U52^#(X)) :48
        -->_1 U52^#(mark(X)) -> c_48(U52^#(X)) :47
     
     49: U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3))
        -->_1 U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3)) :50
        -->_1 U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3)) :49
     
     50: U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3))
        -->_1 U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3)) :50
        -->_1 U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3)) :49
     
     51: U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2))
        -->_1 U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2)) :52
        -->_1 U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2)) :51
     
     52: U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2))
        -->_1 U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2)) :52
        -->_1 U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2)) :51
     
     53: s^#(mark(X)) -> c_56(s^#(X))
        -->_1 s^#(ok(X)) -> c_57(s^#(X)) :54
        -->_1 s^#(mark(X)) -> c_56(s^#(X)) :53
     
     54: s^#(ok(X)) -> c_57(s^#(X))
        -->_1 s^#(ok(X)) -> c_57(s^#(X)) :54
        -->_1 s^#(mark(X)) -> c_56(s^#(X)) :53
     
     55: length^#(mark(X)) -> c_58(length^#(X))
        -->_1 length^#(ok(X)) -> c_59(length^#(X)) :56
        -->_1 length^#(mark(X)) -> c_58(length^#(X)) :55
     
     56: length^#(ok(X)) -> c_59(length^#(X))
        -->_1 length^#(ok(X)) -> c_59(length^#(X)) :56
        -->_1 length^#(mark(X)) -> c_58(length^#(X)) :55
     
     57: isNatIList^#(ok(X)) -> c_45(isNatIList^#(X))
        -->_1 isNatIList^#(ok(X)) -> c_45(isNatIList^#(X)) :57
     
     58: isNatList^#(ok(X)) -> c_50(isNatList^#(X))
        -->_1 isNatList^#(ok(X)) -> c_50(isNatList^#(X)) :58
     
     59: isNat^#(ok(X)) -> c_55(isNat^#(X))
        -->_1 isNat^#(ok(X)) -> c_55(isNat^#(X)) :59
     
     60: proper^#(zeros()) -> c_60()
     
     61: proper^#(cons(X1, X2)) -> c_61(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2)) :34
        -->_1 cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2)) :33
     
     62: proper^#(0()) -> c_62()
     
     63: proper^#(U11(X)) -> c_63(U11^#(proper(X)))
        -->_1 U11^#(ok(X)) -> c_36(U11^#(X)) :36
        -->_1 U11^#(mark(X)) -> c_35(U11^#(X)) :35
     
     64: proper^#(tt()) -> c_64()
     
     65: proper^#(U21(X)) -> c_65(U21^#(proper(X)))
        -->_1 U21^#(ok(X)) -> c_38(U21^#(X)) :38
        -->_1 U21^#(mark(X)) -> c_37(U21^#(X)) :37
     
     66: proper^#(U31(X)) -> c_66(U31^#(proper(X)))
        -->_1 U31^#(ok(X)) -> c_40(U31^#(X)) :40
        -->_1 U31^#(mark(X)) -> c_39(U31^#(X)) :39
     
     67: proper^#(U41(X1, X2)) -> c_67(U41^#(proper(X1), proper(X2)))
        -->_1 U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2)) :42
        -->_1 U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2)) :41
     
     68: proper^#(U42(X)) -> c_68(U42^#(proper(X)))
        -->_1 U42^#(ok(X)) -> c_44(U42^#(X)) :44
        -->_1 U42^#(mark(X)) -> c_43(U42^#(X)) :43
     
     69: proper^#(isNatIList(X)) -> c_69(isNatIList^#(proper(X)))
        -->_1 isNatIList^#(ok(X)) -> c_45(isNatIList^#(X)) :57
     
     70: proper^#(U51(X1, X2)) -> c_70(U51^#(proper(X1), proper(X2)))
        -->_1 U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2)) :46
        -->_1 U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2)) :45
     
     71: proper^#(U52(X)) -> c_71(U52^#(proper(X)))
        -->_1 U52^#(ok(X)) -> c_49(U52^#(X)) :48
        -->_1 U52^#(mark(X)) -> c_48(U52^#(X)) :47
     
     72: proper^#(isNatList(X)) -> c_72(isNatList^#(proper(X)))
        -->_1 isNatList^#(ok(X)) -> c_50(isNatList^#(X)) :58
     
     73: proper^#(U61(X1, X2, X3)) ->
         c_73(U61^#(proper(X1), proper(X2), proper(X3)))
        -->_1 U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3)) :50
        -->_1 U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3)) :49
     
     74: proper^#(U62(X1, X2)) -> c_74(U62^#(proper(X1), proper(X2)))
        -->_1 U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2)) :52
        -->_1 U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2)) :51
     
     75: proper^#(isNat(X)) -> c_75(isNat^#(proper(X)))
        -->_1 isNat^#(ok(X)) -> c_55(isNat^#(X)) :59
     
     76: proper^#(s(X)) -> c_76(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_57(s^#(X)) :54
        -->_1 s^#(mark(X)) -> c_56(s^#(X)) :53
     
     77: proper^#(length(X)) -> c_77(length^#(proper(X)))
        -->_1 length^#(ok(X)) -> c_59(length^#(X)) :56
        -->_1 length^#(mark(X)) -> c_58(length^#(X)) :55
     
     78: proper^#(nil()) -> c_78()
     
     79: top^#(mark(X)) -> c_79(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_80(top^#(active(X))) :80
        -->_1 top^#(mark(X)) -> c_79(top^#(proper(X))) :79
     
     80: top^#(ok(X)) -> c_80(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_80(top^#(active(X))) :80
        -->_1 top^#(mark(X)) -> c_79(top^#(proper(X))) :79
     
   
   Only the nodes
   {1,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62,64,78,79,80}
   are reachable from nodes
   {1,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62,64,78,79,80}
   that start derivation from marked basic terms. The nodes not
   reachable are removed from the problem.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { active^#(zeros()) -> c_1(cons^#(0(), zeros()))
     , cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2))
     , U11^#(mark(X)) -> c_35(U11^#(X))
     , U11^#(ok(X)) -> c_36(U11^#(X))
     , U21^#(mark(X)) -> c_37(U21^#(X))
     , U21^#(ok(X)) -> c_38(U21^#(X))
     , U31^#(mark(X)) -> c_39(U31^#(X))
     , U31^#(ok(X)) -> c_40(U31^#(X))
     , U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2))
     , U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2))
     , U42^#(mark(X)) -> c_43(U42^#(X))
     , U42^#(ok(X)) -> c_44(U42^#(X))
     , U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2))
     , U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2))
     , U52^#(mark(X)) -> c_48(U52^#(X))
     , U52^#(ok(X)) -> c_49(U52^#(X))
     , U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3))
     , U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3))
     , U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2))
     , U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2))
     , s^#(mark(X)) -> c_56(s^#(X))
     , s^#(ok(X)) -> c_57(s^#(X))
     , length^#(mark(X)) -> c_58(length^#(X))
     , length^#(ok(X)) -> c_59(length^#(X))
     , isNatIList^#(ok(X)) -> c_45(isNatIList^#(X))
     , isNatList^#(ok(X)) -> c_50(isNatList^#(X))
     , isNat^#(ok(X)) -> c_55(isNat^#(X))
     , proper^#(zeros()) -> c_60()
     , proper^#(0()) -> c_62()
     , proper^#(tt()) -> c_64()
     , proper^#(nil()) -> c_78()
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   Strict Trs:
     { active(zeros()) -> mark(cons(0(), zeros()))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X)) -> U11(active(X))
     , active(U11(tt())) -> mark(tt())
     , active(U21(X)) -> U21(active(X))
     , active(U21(tt())) -> mark(tt())
     , active(U31(X)) -> U31(active(X))
     , active(U31(tt())) -> mark(tt())
     , active(U41(X1, X2)) -> U41(active(X1), X2)
     , active(U41(tt(), V2)) -> mark(U42(isNatIList(V2)))
     , active(U42(X)) -> U42(active(X))
     , active(U42(tt())) -> mark(tt())
     , active(isNatIList(V)) -> mark(U31(isNatList(V)))
     , active(isNatIList(zeros())) -> mark(tt())
     , active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2))
     , active(U51(X1, X2)) -> U51(active(X1), X2)
     , active(U51(tt(), V2)) -> mark(U52(isNatList(V2)))
     , active(U52(X)) -> U52(active(X))
     , active(U52(tt())) -> mark(tt())
     , active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2))
     , active(isNatList(nil())) -> mark(tt())
     , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
     , active(U61(tt(), L, N)) -> mark(U62(isNat(N), L))
     , active(U62(X1, X2)) -> U62(active(X1), X2)
     , active(U62(tt(), L)) -> mark(s(length(L)))
     , active(isNat(0())) -> mark(tt())
     , active(isNat(s(V1))) -> mark(U21(isNat(V1)))
     , active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N))
     , active(length(nil())) -> mark(0())
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(mark(X)) -> mark(U11(X))
     , U11(ok(X)) -> ok(U11(X))
     , U21(mark(X)) -> mark(U21(X))
     , U21(ok(X)) -> ok(U21(X))
     , U31(mark(X)) -> mark(U31(X))
     , U31(ok(X)) -> ok(U31(X))
     , U41(mark(X1), X2) -> mark(U41(X1, X2))
     , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2))
     , U42(mark(X)) -> mark(U42(X))
     , U42(ok(X)) -> ok(U42(X))
     , isNatIList(ok(X)) -> ok(isNatIList(X))
     , U51(mark(X1), X2) -> mark(U51(X1, X2))
     , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
     , U52(mark(X)) -> mark(U52(X))
     , U52(ok(X)) -> ok(U52(X))
     , isNatList(ok(X)) -> ok(isNatList(X))
     , U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3))
     , U61(ok(X1), ok(X2), ok(X3)) -> ok(U61(X1, X2, X3))
     , U62(mark(X1), X2) -> mark(U62(X1, X2))
     , U62(ok(X1), ok(X2)) -> ok(U62(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , length(mark(X)) -> mark(length(X))
     , length(ok(X)) -> ok(length(X))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X)) -> U11(proper(X))
     , proper(tt()) -> ok(tt())
     , proper(U21(X)) -> U21(proper(X))
     , proper(U31(X)) -> U31(proper(X))
     , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2))
     , proper(U42(X)) -> U42(proper(X))
     , proper(isNatIList(X)) -> isNatIList(proper(X))
     , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
     , proper(U52(X)) -> U52(proper(X))
     , proper(isNatList(X)) -> isNatList(proper(X))
     , proper(U61(X1, X2, X3)) ->
       U61(proper(X1), proper(X2), proper(X3))
     , proper(U62(X1, X2)) -> U62(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,29,30,31,32} by
   applications of Pre({1,29,30,31,32}) = {}. Here rules are labeled
   as follows:
   
     DPs:
       { 1: active^#(zeros()) -> c_1(cons^#(0(), zeros()))
       , 2: cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2))
       , 3: cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2))
       , 4: U11^#(mark(X)) -> c_35(U11^#(X))
       , 5: U11^#(ok(X)) -> c_36(U11^#(X))
       , 6: U21^#(mark(X)) -> c_37(U21^#(X))
       , 7: U21^#(ok(X)) -> c_38(U21^#(X))
       , 8: U31^#(mark(X)) -> c_39(U31^#(X))
       , 9: U31^#(ok(X)) -> c_40(U31^#(X))
       , 10: U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2))
       , 11: U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2))
       , 12: U42^#(mark(X)) -> c_43(U42^#(X))
       , 13: U42^#(ok(X)) -> c_44(U42^#(X))
       , 14: U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2))
       , 15: U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2))
       , 16: U52^#(mark(X)) -> c_48(U52^#(X))
       , 17: U52^#(ok(X)) -> c_49(U52^#(X))
       , 18: U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3))
       , 19: U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3))
       , 20: U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2))
       , 21: U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2))
       , 22: s^#(mark(X)) -> c_56(s^#(X))
       , 23: s^#(ok(X)) -> c_57(s^#(X))
       , 24: length^#(mark(X)) -> c_58(length^#(X))
       , 25: length^#(ok(X)) -> c_59(length^#(X))
       , 26: isNatIList^#(ok(X)) -> c_45(isNatIList^#(X))
       , 27: isNatList^#(ok(X)) -> c_50(isNatList^#(X))
       , 28: isNat^#(ok(X)) -> c_55(isNat^#(X))
       , 29: proper^#(zeros()) -> c_60()
       , 30: proper^#(0()) -> c_62()
       , 31: proper^#(tt()) -> c_64()
       , 32: proper^#(nil()) -> c_78()
       , 33: top^#(mark(X)) -> c_79(top^#(proper(X)))
       , 34: top^#(ok(X)) -> c_80(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cons^#(mark(X1), X2) -> c_33(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_34(cons^#(X1, X2))
     , U11^#(mark(X)) -> c_35(U11^#(X))
     , U11^#(ok(X)) -> c_36(U11^#(X))
     , U21^#(mark(X)) -> c_37(U21^#(X))
     , U21^#(ok(X)) -> c_38(U21^#(X))
     , U31^#(mark(X)) -> c_39(U31^#(X))
     , U31^#(ok(X)) -> c_40(U31^#(X))
     , U41^#(mark(X1), X2) -> c_41(U41^#(X1, X2))
     , U41^#(ok(X1), ok(X2)) -> c_42(U41^#(X1, X2))
     , U42^#(mark(X)) -> c_43(U42^#(X))
     , U42^#(ok(X)) -> c_44(U42^#(X))
     , U51^#(mark(X1), X2) -> c_46(U51^#(X1, X2))
     , U51^#(ok(X1), ok(X2)) -> c_47(U51^#(X1, X2))
     , U52^#(mark(X)) -> c_48(U52^#(X))
     , U52^#(ok(X)) -> c_49(U52^#(X))
     , U61^#(mark(X1), X2, X3) -> c_51(U61^#(X1, X2, X3))
     , U61^#(ok(X1), ok(X2), ok(X3)) -> c_52(U61^#(X1, X2, X3))
     , U62^#(mark(X1), X2) -> c_53(U62^#(X1, X2))
     , U62^#(ok(X1), ok(X2)) -> c_54(U62^#(X1, X2))
     , s^#(mark(X)) -> c_56(s^#(X))
     , s^#(ok(X)) -> c_57(s^#(X))
     , length^#(mark(X)) -> c_58(length^#(X))
     , length^#(ok(X)) -> c_59(length^#(X))
     , isNatIList^#(ok(X)) -> c_45(isNatIList^#(X))
     , isNatList^#(ok(X)) -> c_50(isNatList^#(X))
     , isNat^#(ok(X)) -> c_55(isNat^#(X))
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   Strict Trs:
     { active(zeros()) -> mark(cons(0(), zeros()))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X)) -> U11(active(X))
     , active(U11(tt())) -> mark(tt())
     , active(U21(X)) -> U21(active(X))
     , active(U21(tt())) -> mark(tt())
     , active(U31(X)) -> U31(active(X))
     , active(U31(tt())) -> mark(tt())
     , active(U41(X1, X2)) -> U41(active(X1), X2)
     , active(U41(tt(), V2)) -> mark(U42(isNatIList(V2)))
     , active(U42(X)) -> U42(active(X))
     , active(U42(tt())) -> mark(tt())
     , active(isNatIList(V)) -> mark(U31(isNatList(V)))
     , active(isNatIList(zeros())) -> mark(tt())
     , active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2))
     , active(U51(X1, X2)) -> U51(active(X1), X2)
     , active(U51(tt(), V2)) -> mark(U52(isNatList(V2)))
     , active(U52(X)) -> U52(active(X))
     , active(U52(tt())) -> mark(tt())
     , active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2))
     , active(isNatList(nil())) -> mark(tt())
     , active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
     , active(U61(tt(), L, N)) -> mark(U62(isNat(N), L))
     , active(U62(X1, X2)) -> U62(active(X1), X2)
     , active(U62(tt(), L)) -> mark(s(length(L)))
     , active(isNat(0())) -> mark(tt())
     , active(isNat(s(V1))) -> mark(U21(isNat(V1)))
     , active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N))
     , active(length(nil())) -> mark(0())
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(mark(X)) -> mark(U11(X))
     , U11(ok(X)) -> ok(U11(X))
     , U21(mark(X)) -> mark(U21(X))
     , U21(ok(X)) -> ok(U21(X))
     , U31(mark(X)) -> mark(U31(X))
     , U31(ok(X)) -> ok(U31(X))
     , U41(mark(X1), X2) -> mark(U41(X1, X2))
     , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2))
     , U42(mark(X)) -> mark(U42(X))
     , U42(ok(X)) -> ok(U42(X))
     , isNatIList(ok(X)) -> ok(isNatIList(X))
     , U51(mark(X1), X2) -> mark(U51(X1, X2))
     , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
     , U52(mark(X)) -> mark(U52(X))
     , U52(ok(X)) -> ok(U52(X))
     , isNatList(ok(X)) -> ok(isNatList(X))
     , U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3))
     , U61(ok(X1), ok(X2), ok(X3)) -> ok(U61(X1, X2, X3))
     , U62(mark(X1), X2) -> mark(U62(X1, X2))
     , U62(ok(X1), ok(X2)) -> ok(U62(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , length(mark(X)) -> mark(length(X))
     , length(ok(X)) -> ok(length(X))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X)) -> U11(proper(X))
     , proper(tt()) -> ok(tt())
     , proper(U21(X)) -> U21(proper(X))
     , proper(U31(X)) -> U31(proper(X))
     , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2))
     , proper(U42(X)) -> U42(proper(X))
     , proper(isNatIList(X)) -> isNatIList(proper(X))
     , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
     , proper(U52(X)) -> U52(proper(X))
     , proper(isNatList(X)) -> isNatList(proper(X))
     , proper(U61(X1, X2, X3)) ->
       U61(proper(X1), proper(X2), proper(X3))
     , proper(U62(X1, X2)) -> U62(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { active^#(zeros()) -> c_1(cons^#(0(), zeros()))
     , proper^#(zeros()) -> c_60()
     , proper^#(0()) -> c_62()
     , proper^#(tt()) -> c_64()
     , proper^#(nil()) -> c_78() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..