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(X1, X2)) -> U11(active(X1), X2)
  , active(U11(tt(), L)) -> mark(U12(tt(), L))
  , active(U12(X1, X2)) -> U12(active(X1), X2)
  , active(U12(tt(), L)) -> mark(s(length(L)))
  , active(s(X)) -> s(active(X))
  , active(length(X)) -> length(active(X))
  , active(length(cons(N, L))) -> mark(U11(tt(), L))
  , active(length(nil())) -> mark(0())
  , active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
  , active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N))
  , active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
  , active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N))
  , active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
  , active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
  , active(take(X1, X2)) -> take(X1, active(X2))
  , active(take(X1, X2)) -> take(active(X1), X2)
  , active(take(0(), IL)) -> mark(nil())
  , active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N))
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , U11(mark(X1), X2) -> mark(U11(X1, X2))
  , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
  , U12(mark(X1), X2) -> mark(U12(X1, X2))
  , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , length(mark(X)) -> mark(length(X))
  , length(ok(X)) -> ok(length(X))
  , U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
  , U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
  , U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
  , U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
  , U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
  , U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
  , take(X1, mark(X2)) -> mark(take(X1, X2))
  , take(mark(X1), X2) -> mark(take(X1, X2))
  , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
  , proper(zeros()) -> ok(zeros())
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
  , proper(tt()) -> ok(tt())
  , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(length(X)) -> length(proper(X))
  , proper(U21(X1, X2, X3, X4)) ->
    U21(proper(X1), proper(X2), proper(X3), proper(X4))
  , proper(U22(X1, X2, X3, X4)) ->
    U22(proper(X1), proper(X2), proper(X3), proper(X4))
  , proper(U23(X1, X2, X3, X4)) ->
    U23(proper(X1), proper(X2), proper(X3), proper(X4))
  , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
  , 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) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      Computation stopped due to timeout after 5.0 seconds.
   
   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:
     { active^#(zeros()) -> c_1(cons^#(0(), zeros()))
     , active^#(cons(X1, X2)) -> c_2(cons^#(active(X1), X2))
     , active^#(U11(X1, X2)) -> c_3(U11^#(active(X1), X2))
     , active^#(U11(tt(), L)) -> c_4(U12^#(tt(), L))
     , active^#(U12(X1, X2)) -> c_5(U12^#(active(X1), X2))
     , active^#(U12(tt(), L)) -> c_6(s^#(length(L)))
     , active^#(s(X)) -> c_7(s^#(active(X)))
     , active^#(length(X)) -> c_8(length^#(active(X)))
     , active^#(length(cons(N, L))) -> c_9(U11^#(tt(), L))
     , active^#(length(nil())) -> c_10()
     , active^#(U21(X1, X2, X3, X4)) ->
       c_11(U21^#(active(X1), X2, X3, X4))
     , active^#(U21(tt(), IL, M, N)) -> c_12(U22^#(tt(), IL, M, N))
     , active^#(U22(X1, X2, X3, X4)) ->
       c_13(U22^#(active(X1), X2, X3, X4))
     , active^#(U22(tt(), IL, M, N)) -> c_14(U23^#(tt(), IL, M, N))
     , active^#(U23(X1, X2, X3, X4)) ->
       c_15(U23^#(active(X1), X2, X3, X4))
     , active^#(U23(tt(), IL, M, N)) -> c_16(cons^#(N, take(M, IL)))
     , active^#(take(X1, X2)) -> c_17(take^#(X1, active(X2)))
     , active^#(take(X1, X2)) -> c_18(take^#(active(X1), X2))
     , active^#(take(0(), IL)) -> c_19()
     , active^#(take(s(M), cons(N, IL))) -> c_20(U21^#(tt(), IL, M, N))
     , cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2))
     , U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2))
     , U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2))
     , U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2))
     , U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2))
     , s^#(mark(X)) -> c_27(s^#(X))
     , s^#(ok(X)) -> c_28(s^#(X))
     , length^#(mark(X)) -> c_29(length^#(X))
     , length^#(ok(X)) -> c_30(length^#(X))
     , U21^#(mark(X1), X2, X3, X4) -> c_31(U21^#(X1, X2, X3, X4))
     , U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_32(U21^#(X1, X2, X3, X4))
     , U22^#(mark(X1), X2, X3, X4) -> c_33(U22^#(X1, X2, X3, X4))
     , U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_34(U22^#(X1, X2, X3, X4))
     , U23^#(mark(X1), X2, X3, X4) -> c_35(U23^#(X1, X2, X3, X4))
     , U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_36(U23^#(X1, X2, X3, X4))
     , take^#(X1, mark(X2)) -> c_37(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_38(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2))
     , proper^#(zeros()) -> c_40()
     , proper^#(cons(X1, X2)) -> c_41(cons^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_42()
     , proper^#(U11(X1, X2)) -> c_43(U11^#(proper(X1), proper(X2)))
     , proper^#(tt()) -> c_44()
     , proper^#(U12(X1, X2)) -> c_45(U12^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_46(s^#(proper(X)))
     , proper^#(length(X)) -> c_47(length^#(proper(X)))
     , proper^#(U21(X1, X2, X3, X4)) ->
       c_48(U21^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(U22(X1, X2, X3, X4)) ->
       c_49(U22^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(U23(X1, X2, X3, X4)) ->
       c_50(U23^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(take(X1, X2)) -> c_51(take^#(proper(X1), proper(X2)))
     , proper^#(nil()) -> c_52()
     , top^#(mark(X)) -> c_53(top^#(proper(X)))
     , top^#(ok(X)) -> c_54(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(X1, X2)) -> c_3(U11^#(active(X1), X2))
     , active^#(U11(tt(), L)) -> c_4(U12^#(tt(), L))
     , active^#(U12(X1, X2)) -> c_5(U12^#(active(X1), X2))
     , active^#(U12(tt(), L)) -> c_6(s^#(length(L)))
     , active^#(s(X)) -> c_7(s^#(active(X)))
     , active^#(length(X)) -> c_8(length^#(active(X)))
     , active^#(length(cons(N, L))) -> c_9(U11^#(tt(), L))
     , active^#(length(nil())) -> c_10()
     , active^#(U21(X1, X2, X3, X4)) ->
       c_11(U21^#(active(X1), X2, X3, X4))
     , active^#(U21(tt(), IL, M, N)) -> c_12(U22^#(tt(), IL, M, N))
     , active^#(U22(X1, X2, X3, X4)) ->
       c_13(U22^#(active(X1), X2, X3, X4))
     , active^#(U22(tt(), IL, M, N)) -> c_14(U23^#(tt(), IL, M, N))
     , active^#(U23(X1, X2, X3, X4)) ->
       c_15(U23^#(active(X1), X2, X3, X4))
     , active^#(U23(tt(), IL, M, N)) -> c_16(cons^#(N, take(M, IL)))
     , active^#(take(X1, X2)) -> c_17(take^#(X1, active(X2)))
     , active^#(take(X1, X2)) -> c_18(take^#(active(X1), X2))
     , active^#(take(0(), IL)) -> c_19()
     , active^#(take(s(M), cons(N, IL))) -> c_20(U21^#(tt(), IL, M, N))
     , cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2))
     , U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2))
     , U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2))
     , U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2))
     , U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2))
     , s^#(mark(X)) -> c_27(s^#(X))
     , s^#(ok(X)) -> c_28(s^#(X))
     , length^#(mark(X)) -> c_29(length^#(X))
     , length^#(ok(X)) -> c_30(length^#(X))
     , U21^#(mark(X1), X2, X3, X4) -> c_31(U21^#(X1, X2, X3, X4))
     , U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_32(U21^#(X1, X2, X3, X4))
     , U22^#(mark(X1), X2, X3, X4) -> c_33(U22^#(X1, X2, X3, X4))
     , U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_34(U22^#(X1, X2, X3, X4))
     , U23^#(mark(X1), X2, X3, X4) -> c_35(U23^#(X1, X2, X3, X4))
     , U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_36(U23^#(X1, X2, X3, X4))
     , take^#(X1, mark(X2)) -> c_37(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_38(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2))
     , proper^#(zeros()) -> c_40()
     , proper^#(cons(X1, X2)) -> c_41(cons^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_42()
     , proper^#(U11(X1, X2)) -> c_43(U11^#(proper(X1), proper(X2)))
     , proper^#(tt()) -> c_44()
     , proper^#(U12(X1, X2)) -> c_45(U12^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_46(s^#(proper(X)))
     , proper^#(length(X)) -> c_47(length^#(proper(X)))
     , proper^#(U21(X1, X2, X3, X4)) ->
       c_48(U21^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(U22(X1, X2, X3, X4)) ->
       c_49(U22^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(U23(X1, X2, X3, X4)) ->
       c_50(U23^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(take(X1, X2)) -> c_51(take^#(proper(X1), proper(X2)))
     , proper^#(nil()) -> c_52()
     , top^#(mark(X)) -> c_53(top^#(proper(X)))
     , top^#(ok(X)) -> c_54(top^#(active(X))) }
   Strict Trs:
     { active(zeros()) -> mark(cons(0(), zeros()))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(U11(tt(), L)) -> mark(U12(tt(), L))
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(U12(tt(), L)) -> mark(s(length(L)))
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(length(cons(N, L))) -> mark(U11(tt(), L))
     , active(length(nil())) -> mark(0())
     , active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
     , active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N))
     , active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
     , active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N))
     , active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
     , active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(0(), IL)) -> mark(nil())
     , active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , length(mark(X)) -> mark(length(X))
     , length(ok(X)) -> ok(length(X))
     , U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
     , U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
     , U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
     , U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
     , U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
     , U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X1, X2, X3, X4)) ->
       U21(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U22(X1, X2, X3, X4)) ->
       U22(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U23(X1, X2, X3, X4)) ->
       U23(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , 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_22(cons^#(X1, X2)) :22
        -->_1 cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2)) :21
     
     3: active^#(U11(X1, X2)) -> c_3(U11^#(active(X1), X2))
        -->_1 U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2)) :24
        -->_1 U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2)) :23
     
     4: active^#(U11(tt(), L)) -> c_4(U12^#(tt(), L))
     
     5: active^#(U12(X1, X2)) -> c_5(U12^#(active(X1), X2))
        -->_1 U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2)) :26
        -->_1 U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2)) :25
     
     6: active^#(U12(tt(), L)) -> c_6(s^#(length(L)))
        -->_1 s^#(ok(X)) -> c_28(s^#(X)) :28
        -->_1 s^#(mark(X)) -> c_27(s^#(X)) :27
     
     7: active^#(s(X)) -> c_7(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_28(s^#(X)) :28
        -->_1 s^#(mark(X)) -> c_27(s^#(X)) :27
     
     8: active^#(length(X)) -> c_8(length^#(active(X)))
        -->_1 length^#(ok(X)) -> c_30(length^#(X)) :30
        -->_1 length^#(mark(X)) -> c_29(length^#(X)) :29
     
     9: active^#(length(cons(N, L))) -> c_9(U11^#(tt(), L))
     
     10: active^#(length(nil())) -> c_10()
     
     11: active^#(U21(X1, X2, X3, X4)) ->
         c_11(U21^#(active(X1), X2, X3, X4))
        -->_1 U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_32(U21^#(X1, X2, X3, X4)) :32
        -->_1 U21^#(mark(X1), X2, X3, X4) ->
              c_31(U21^#(X1, X2, X3, X4)) :31
     
     12: active^#(U21(tt(), IL, M, N)) -> c_12(U22^#(tt(), IL, M, N))
     
     13: active^#(U22(X1, X2, X3, X4)) ->
         c_13(U22^#(active(X1), X2, X3, X4))
        -->_1 U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_34(U22^#(X1, X2, X3, X4)) :34
        -->_1 U22^#(mark(X1), X2, X3, X4) ->
              c_33(U22^#(X1, X2, X3, X4)) :33
     
     14: active^#(U22(tt(), IL, M, N)) -> c_14(U23^#(tt(), IL, M, N))
     
     15: active^#(U23(X1, X2, X3, X4)) ->
         c_15(U23^#(active(X1), X2, X3, X4))
        -->_1 U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_36(U23^#(X1, X2, X3, X4)) :36
        -->_1 U23^#(mark(X1), X2, X3, X4) ->
              c_35(U23^#(X1, X2, X3, X4)) :35
     
     16: active^#(U23(tt(), IL, M, N)) -> c_16(cons^#(N, take(M, IL)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2)) :22
        -->_1 cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2)) :21
     
     17: active^#(take(X1, X2)) -> c_17(take^#(X1, active(X2)))
        -->_1 take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2)) :39
        -->_1 take^#(mark(X1), X2) -> c_38(take^#(X1, X2)) :38
        -->_1 take^#(X1, mark(X2)) -> c_37(take^#(X1, X2)) :37
     
     18: active^#(take(X1, X2)) -> c_18(take^#(active(X1), X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2)) :39
        -->_1 take^#(mark(X1), X2) -> c_38(take^#(X1, X2)) :38
        -->_1 take^#(X1, mark(X2)) -> c_37(take^#(X1, X2)) :37
     
     19: active^#(take(0(), IL)) -> c_19()
     
     20: active^#(take(s(M), cons(N, IL))) ->
         c_20(U21^#(tt(), IL, M, N))
     
     21: cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2)) :22
        -->_1 cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2)) :21
     
     22: cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2)) :22
        -->_1 cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2)) :21
     
     23: U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2))
        -->_1 U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2)) :24
        -->_1 U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2)) :23
     
     24: U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2))
        -->_1 U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2)) :24
        -->_1 U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2)) :23
     
     25: U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2))
        -->_1 U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2)) :26
        -->_1 U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2)) :25
     
     26: U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2))
        -->_1 U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2)) :26
        -->_1 U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2)) :25
     
     27: s^#(mark(X)) -> c_27(s^#(X))
        -->_1 s^#(ok(X)) -> c_28(s^#(X)) :28
        -->_1 s^#(mark(X)) -> c_27(s^#(X)) :27
     
     28: s^#(ok(X)) -> c_28(s^#(X))
        -->_1 s^#(ok(X)) -> c_28(s^#(X)) :28
        -->_1 s^#(mark(X)) -> c_27(s^#(X)) :27
     
     29: length^#(mark(X)) -> c_29(length^#(X))
        -->_1 length^#(ok(X)) -> c_30(length^#(X)) :30
        -->_1 length^#(mark(X)) -> c_29(length^#(X)) :29
     
     30: length^#(ok(X)) -> c_30(length^#(X))
        -->_1 length^#(ok(X)) -> c_30(length^#(X)) :30
        -->_1 length^#(mark(X)) -> c_29(length^#(X)) :29
     
     31: U21^#(mark(X1), X2, X3, X4) -> c_31(U21^#(X1, X2, X3, X4))
        -->_1 U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_32(U21^#(X1, X2, X3, X4)) :32
        -->_1 U21^#(mark(X1), X2, X3, X4) ->
              c_31(U21^#(X1, X2, X3, X4)) :31
     
     32: U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
         c_32(U21^#(X1, X2, X3, X4))
        -->_1 U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_32(U21^#(X1, X2, X3, X4)) :32
        -->_1 U21^#(mark(X1), X2, X3, X4) ->
              c_31(U21^#(X1, X2, X3, X4)) :31
     
     33: U22^#(mark(X1), X2, X3, X4) -> c_33(U22^#(X1, X2, X3, X4))
        -->_1 U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_34(U22^#(X1, X2, X3, X4)) :34
        -->_1 U22^#(mark(X1), X2, X3, X4) ->
              c_33(U22^#(X1, X2, X3, X4)) :33
     
     34: U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
         c_34(U22^#(X1, X2, X3, X4))
        -->_1 U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_34(U22^#(X1, X2, X3, X4)) :34
        -->_1 U22^#(mark(X1), X2, X3, X4) ->
              c_33(U22^#(X1, X2, X3, X4)) :33
     
     35: U23^#(mark(X1), X2, X3, X4) -> c_35(U23^#(X1, X2, X3, X4))
        -->_1 U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_36(U23^#(X1, X2, X3, X4)) :36
        -->_1 U23^#(mark(X1), X2, X3, X4) ->
              c_35(U23^#(X1, X2, X3, X4)) :35
     
     36: U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
         c_36(U23^#(X1, X2, X3, X4))
        -->_1 U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_36(U23^#(X1, X2, X3, X4)) :36
        -->_1 U23^#(mark(X1), X2, X3, X4) ->
              c_35(U23^#(X1, X2, X3, X4)) :35
     
     37: take^#(X1, mark(X2)) -> c_37(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2)) :39
        -->_1 take^#(mark(X1), X2) -> c_38(take^#(X1, X2)) :38
        -->_1 take^#(X1, mark(X2)) -> c_37(take^#(X1, X2)) :37
     
     38: take^#(mark(X1), X2) -> c_38(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2)) :39
        -->_1 take^#(mark(X1), X2) -> c_38(take^#(X1, X2)) :38
        -->_1 take^#(X1, mark(X2)) -> c_37(take^#(X1, X2)) :37
     
     39: take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2)) :39
        -->_1 take^#(mark(X1), X2) -> c_38(take^#(X1, X2)) :38
        -->_1 take^#(X1, mark(X2)) -> c_37(take^#(X1, X2)) :37
     
     40: proper^#(zeros()) -> c_40()
     
     41: proper^#(cons(X1, X2)) -> c_41(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2)) :22
        -->_1 cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2)) :21
     
     42: proper^#(0()) -> c_42()
     
     43: proper^#(U11(X1, X2)) -> c_43(U11^#(proper(X1), proper(X2)))
        -->_1 U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2)) :24
        -->_1 U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2)) :23
     
     44: proper^#(tt()) -> c_44()
     
     45: proper^#(U12(X1, X2)) -> c_45(U12^#(proper(X1), proper(X2)))
        -->_1 U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2)) :26
        -->_1 U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2)) :25
     
     46: proper^#(s(X)) -> c_46(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_28(s^#(X)) :28
        -->_1 s^#(mark(X)) -> c_27(s^#(X)) :27
     
     47: proper^#(length(X)) -> c_47(length^#(proper(X)))
        -->_1 length^#(ok(X)) -> c_30(length^#(X)) :30
        -->_1 length^#(mark(X)) -> c_29(length^#(X)) :29
     
     48: proper^#(U21(X1, X2, X3, X4)) ->
         c_48(U21^#(proper(X1), proper(X2), proper(X3), proper(X4)))
        -->_1 U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_32(U21^#(X1, X2, X3, X4)) :32
        -->_1 U21^#(mark(X1), X2, X3, X4) ->
              c_31(U21^#(X1, X2, X3, X4)) :31
     
     49: proper^#(U22(X1, X2, X3, X4)) ->
         c_49(U22^#(proper(X1), proper(X2), proper(X3), proper(X4)))
        -->_1 U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_34(U22^#(X1, X2, X3, X4)) :34
        -->_1 U22^#(mark(X1), X2, X3, X4) ->
              c_33(U22^#(X1, X2, X3, X4)) :33
     
     50: proper^#(U23(X1, X2, X3, X4)) ->
         c_50(U23^#(proper(X1), proper(X2), proper(X3), proper(X4)))
        -->_1 U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_36(U23^#(X1, X2, X3, X4)) :36
        -->_1 U23^#(mark(X1), X2, X3, X4) ->
              c_35(U23^#(X1, X2, X3, X4)) :35
     
     51: proper^#(take(X1, X2)) -> c_51(take^#(proper(X1), proper(X2)))
        -->_1 take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2)) :39
        -->_1 take^#(mark(X1), X2) -> c_38(take^#(X1, X2)) :38
        -->_1 take^#(X1, mark(X2)) -> c_37(take^#(X1, X2)) :37
     
     52: proper^#(nil()) -> c_52()
     
     53: top^#(mark(X)) -> c_53(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_54(top^#(active(X))) :54
        -->_1 top^#(mark(X)) -> c_53(top^#(proper(X))) :53
     
     54: top^#(ok(X)) -> c_54(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_54(top^#(active(X))) :54
        -->_1 top^#(mark(X)) -> c_53(top^#(proper(X))) :53
     
   
   Only the nodes
   {1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,39,38,40,42,44,52,53,54}
   are reachable from nodes
   {1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,44,52,53,54}
   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_21(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2))
     , U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2))
     , U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2))
     , U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2))
     , U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2))
     , s^#(mark(X)) -> c_27(s^#(X))
     , s^#(ok(X)) -> c_28(s^#(X))
     , length^#(mark(X)) -> c_29(length^#(X))
     , length^#(ok(X)) -> c_30(length^#(X))
     , U21^#(mark(X1), X2, X3, X4) -> c_31(U21^#(X1, X2, X3, X4))
     , U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_32(U21^#(X1, X2, X3, X4))
     , U22^#(mark(X1), X2, X3, X4) -> c_33(U22^#(X1, X2, X3, X4))
     , U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_34(U22^#(X1, X2, X3, X4))
     , U23^#(mark(X1), X2, X3, X4) -> c_35(U23^#(X1, X2, X3, X4))
     , U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_36(U23^#(X1, X2, X3, X4))
     , take^#(X1, mark(X2)) -> c_37(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_38(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2))
     , proper^#(zeros()) -> c_40()
     , proper^#(0()) -> c_42()
     , proper^#(tt()) -> c_44()
     , proper^#(nil()) -> c_52()
     , top^#(mark(X)) -> c_53(top^#(proper(X)))
     , top^#(ok(X)) -> c_54(top^#(active(X))) }
   Strict Trs:
     { active(zeros()) -> mark(cons(0(), zeros()))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(U11(tt(), L)) -> mark(U12(tt(), L))
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(U12(tt(), L)) -> mark(s(length(L)))
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(length(cons(N, L))) -> mark(U11(tt(), L))
     , active(length(nil())) -> mark(0())
     , active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
     , active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N))
     , active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
     , active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N))
     , active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
     , active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(0(), IL)) -> mark(nil())
     , active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , length(mark(X)) -> mark(length(X))
     , length(ok(X)) -> ok(length(X))
     , U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
     , U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
     , U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
     , U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
     , U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
     , U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X1, X2, X3, X4)) ->
       U21(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U22(X1, X2, X3, X4)) ->
       U22(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U23(X1, X2, X3, X4)) ->
       U23(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , 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 {1,21,22,23,24} by
   applications of Pre({1,21,22,23,24}) = {}. Here rules are labeled
   as follows:
   
     DPs:
       { 1: active^#(zeros()) -> c_1(cons^#(0(), zeros()))
       , 2: cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2))
       , 3: cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2))
       , 4: U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2))
       , 5: U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2))
       , 6: U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2))
       , 7: U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2))
       , 8: s^#(mark(X)) -> c_27(s^#(X))
       , 9: s^#(ok(X)) -> c_28(s^#(X))
       , 10: length^#(mark(X)) -> c_29(length^#(X))
       , 11: length^#(ok(X)) -> c_30(length^#(X))
       , 12: U21^#(mark(X1), X2, X3, X4) -> c_31(U21^#(X1, X2, X3, X4))
       , 13: U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
             c_32(U21^#(X1, X2, X3, X4))
       , 14: U22^#(mark(X1), X2, X3, X4) -> c_33(U22^#(X1, X2, X3, X4))
       , 15: U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
             c_34(U22^#(X1, X2, X3, X4))
       , 16: U23^#(mark(X1), X2, X3, X4) -> c_35(U23^#(X1, X2, X3, X4))
       , 17: U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
             c_36(U23^#(X1, X2, X3, X4))
       , 18: take^#(X1, mark(X2)) -> c_37(take^#(X1, X2))
       , 19: take^#(mark(X1), X2) -> c_38(take^#(X1, X2))
       , 20: take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2))
       , 21: proper^#(zeros()) -> c_40()
       , 22: proper^#(0()) -> c_42()
       , 23: proper^#(tt()) -> c_44()
       , 24: proper^#(nil()) -> c_52()
       , 25: top^#(mark(X)) -> c_53(top^#(proper(X)))
       , 26: top^#(ok(X)) -> c_54(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cons^#(mark(X1), X2) -> c_21(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_22(cons^#(X1, X2))
     , U11^#(mark(X1), X2) -> c_23(U11^#(X1, X2))
     , U11^#(ok(X1), ok(X2)) -> c_24(U11^#(X1, X2))
     , U12^#(mark(X1), X2) -> c_25(U12^#(X1, X2))
     , U12^#(ok(X1), ok(X2)) -> c_26(U12^#(X1, X2))
     , s^#(mark(X)) -> c_27(s^#(X))
     , s^#(ok(X)) -> c_28(s^#(X))
     , length^#(mark(X)) -> c_29(length^#(X))
     , length^#(ok(X)) -> c_30(length^#(X))
     , U21^#(mark(X1), X2, X3, X4) -> c_31(U21^#(X1, X2, X3, X4))
     , U21^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_32(U21^#(X1, X2, X3, X4))
     , U22^#(mark(X1), X2, X3, X4) -> c_33(U22^#(X1, X2, X3, X4))
     , U22^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_34(U22^#(X1, X2, X3, X4))
     , U23^#(mark(X1), X2, X3, X4) -> c_35(U23^#(X1, X2, X3, X4))
     , U23^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
       c_36(U23^#(X1, X2, X3, X4))
     , take^#(X1, mark(X2)) -> c_37(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_38(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_39(take^#(X1, X2))
     , top^#(mark(X)) -> c_53(top^#(proper(X)))
     , top^#(ok(X)) -> c_54(top^#(active(X))) }
   Strict Trs:
     { active(zeros()) -> mark(cons(0(), zeros()))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(U11(tt(), L)) -> mark(U12(tt(), L))
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(U12(tt(), L)) -> mark(s(length(L)))
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(length(cons(N, L))) -> mark(U11(tt(), L))
     , active(length(nil())) -> mark(0())
     , active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
     , active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N))
     , active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
     , active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N))
     , active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
     , active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(0(), IL)) -> mark(nil())
     , active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , length(mark(X)) -> mark(length(X))
     , length(ok(X)) -> ok(length(X))
     , U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
     , U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
     , U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
     , U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
     , U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
     , U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X1, X2, X3, X4)) ->
       U21(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U22(X1, X2, X3, X4)) ->
       U22(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U23(X1, X2, X3, X4)) ->
       U23(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , 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_40()
     , proper^#(0()) -> c_42()
     , proper^#(tt()) -> c_44()
     , proper^#(nil()) -> c_52() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..