MAYBE

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

Strict Trs:
  { active(from(X)) -> from(active(X))
  , active(from(X)) -> mark(cons(X, from(s(X))))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(s(X)) -> s(active(X))
  , active(head(X)) -> head(active(X))
  , active(head(cons(X, XS))) -> mark(X)
  , active(2nd(X)) -> 2nd(active(X))
  , active(2nd(cons(X, XS))) -> mark(head(XS))
  , active(take(X1, X2)) -> take(X1, active(X2))
  , active(take(X1, X2)) -> take(active(X1), X2)
  , active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
  , active(take(0(), XS)) -> mark(nil())
  , active(sel(X1, X2)) -> sel(X1, active(X2))
  , active(sel(X1, X2)) -> sel(active(X1), X2)
  , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
  , active(sel(0(), cons(X, XS))) -> mark(X)
  , from(mark(X)) -> mark(from(X))
  , from(ok(X)) -> ok(from(X))
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , head(mark(X)) -> mark(head(X))
  , head(ok(X)) -> ok(head(X))
  , 2nd(mark(X)) -> mark(2nd(X))
  , 2nd(ok(X)) -> ok(2nd(X))
  , 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))
  , sel(X1, mark(X2)) -> mark(sel(X1, X2))
  , sel(mark(X1), X2) -> mark(sel(X1, X2))
  , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  , proper(from(X)) -> from(proper(X))
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(head(X)) -> head(proper(X))
  , proper(2nd(X)) -> 2nd(proper(X))
  , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(nil()) -> ok(nil())
  , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  , 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^#(from(X)) -> c_1(from^#(active(X)))
     , active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
     , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
     , active^#(s(X)) -> c_4(s^#(active(X)))
     , active^#(head(X)) -> c_5(head^#(active(X)))
     , active^#(head(cons(X, XS))) -> c_6(X)
     , active^#(2nd(X)) -> c_7(2nd^#(active(X)))
     , active^#(2nd(cons(X, XS))) -> c_8(head^#(XS))
     , active^#(take(X1, X2)) -> c_9(take^#(X1, active(X2)))
     , active^#(take(X1, X2)) -> c_10(take^#(active(X1), X2))
     , active^#(take(s(N), cons(X, XS))) -> c_11(cons^#(X, take(N, XS)))
     , active^#(take(0(), XS)) -> c_12()
     , active^#(sel(X1, X2)) -> c_13(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_14(sel^#(active(X1), X2))
     , active^#(sel(s(N), cons(X, XS))) -> c_15(sel^#(N, XS))
     , active^#(sel(0(), cons(X, XS))) -> c_16(X)
     , from^#(mark(X)) -> c_17(from^#(X))
     , from^#(ok(X)) -> c_18(from^#(X))
     , cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2))
     , s^#(mark(X)) -> c_21(s^#(X))
     , s^#(ok(X)) -> c_22(s^#(X))
     , head^#(mark(X)) -> c_23(head^#(X))
     , head^#(ok(X)) -> c_24(head^#(X))
     , 2nd^#(mark(X)) -> c_25(2nd^#(X))
     , 2nd^#(ok(X)) -> c_26(2nd^#(X))
     , take^#(X1, mark(X2)) -> c_27(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_28(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2))
     , proper^#(from(X)) -> c_33(from^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_34(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_35(s^#(proper(X)))
     , proper^#(head(X)) -> c_36(head^#(proper(X)))
     , proper^#(2nd(X)) -> c_37(2nd^#(proper(X)))
     , proper^#(take(X1, X2)) -> c_38(take^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_39()
     , proper^#(nil()) -> c_40()
     , proper^#(sel(X1, X2)) -> c_41(sel^#(proper(X1), proper(X2)))
     , top^#(mark(X)) -> c_42(top^#(proper(X)))
     , top^#(ok(X)) -> c_43(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^#(from(X)) -> c_1(from^#(active(X)))
     , active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
     , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
     , active^#(s(X)) -> c_4(s^#(active(X)))
     , active^#(head(X)) -> c_5(head^#(active(X)))
     , active^#(head(cons(X, XS))) -> c_6(X)
     , active^#(2nd(X)) -> c_7(2nd^#(active(X)))
     , active^#(2nd(cons(X, XS))) -> c_8(head^#(XS))
     , active^#(take(X1, X2)) -> c_9(take^#(X1, active(X2)))
     , active^#(take(X1, X2)) -> c_10(take^#(active(X1), X2))
     , active^#(take(s(N), cons(X, XS))) -> c_11(cons^#(X, take(N, XS)))
     , active^#(take(0(), XS)) -> c_12()
     , active^#(sel(X1, X2)) -> c_13(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_14(sel^#(active(X1), X2))
     , active^#(sel(s(N), cons(X, XS))) -> c_15(sel^#(N, XS))
     , active^#(sel(0(), cons(X, XS))) -> c_16(X)
     , from^#(mark(X)) -> c_17(from^#(X))
     , from^#(ok(X)) -> c_18(from^#(X))
     , cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2))
     , s^#(mark(X)) -> c_21(s^#(X))
     , s^#(ok(X)) -> c_22(s^#(X))
     , head^#(mark(X)) -> c_23(head^#(X))
     , head^#(ok(X)) -> c_24(head^#(X))
     , 2nd^#(mark(X)) -> c_25(2nd^#(X))
     , 2nd^#(ok(X)) -> c_26(2nd^#(X))
     , take^#(X1, mark(X2)) -> c_27(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_28(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2))
     , proper^#(from(X)) -> c_33(from^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_34(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_35(s^#(proper(X)))
     , proper^#(head(X)) -> c_36(head^#(proper(X)))
     , proper^#(2nd(X)) -> c_37(2nd^#(proper(X)))
     , proper^#(take(X1, X2)) -> c_38(take^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_39()
     , proper^#(nil()) -> c_40()
     , proper^#(sel(X1, X2)) -> c_41(sel^#(proper(X1), proper(X2)))
     , top^#(mark(X)) -> c_42(top^#(proper(X)))
     , top^#(ok(X)) -> c_43(top^#(active(X))) }
   Strict Trs:
     { active(from(X)) -> from(active(X))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(head(X)) -> head(active(X))
     , active(head(cons(X, XS))) -> mark(X)
     , active(2nd(X)) -> 2nd(active(X))
     , active(2nd(cons(X, XS))) -> mark(head(XS))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
     , active(take(0(), XS)) -> mark(nil())
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , head(mark(X)) -> mark(head(X))
     , head(ok(X)) -> ok(head(X))
     , 2nd(mark(X)) -> mark(2nd(X))
     , 2nd(ok(X)) -> ok(2nd(X))
     , 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))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(head(X)) -> head(proper(X))
     , proper(2nd(X)) -> 2nd(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Consider the dependency graph:
   
     1: active^#(from(X)) -> c_1(from^#(active(X)))
        -->_1 from^#(ok(X)) -> c_18(from^#(X)) :18
        -->_1 from^#(mark(X)) -> c_17(from^#(X)) :17
     
     2: active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
     
     3: active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
     
     4: active^#(s(X)) -> c_4(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_22(s^#(X)) :22
        -->_1 s^#(mark(X)) -> c_21(s^#(X)) :21
     
     5: active^#(head(X)) -> c_5(head^#(active(X)))
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
     
     6: active^#(head(cons(X, XS))) -> c_6(X)
        -->_1 top^#(ok(X)) -> c_43(top^#(active(X))) :43
        -->_1 top^#(mark(X)) -> c_42(top^#(proper(X))) :42
        -->_1 proper^#(sel(X1, X2)) ->
              c_41(sel^#(proper(X1), proper(X2))) :41
        -->_1 proper^#(take(X1, X2)) ->
              c_38(take^#(proper(X1), proper(X2))) :38
        -->_1 proper^#(2nd(X)) -> c_37(2nd^#(proper(X))) :37
        -->_1 proper^#(head(X)) -> c_36(head^#(proper(X))) :36
        -->_1 proper^#(s(X)) -> c_35(s^#(proper(X))) :35
        -->_1 proper^#(cons(X1, X2)) ->
              c_34(cons^#(proper(X1), proper(X2))) :34
        -->_1 proper^#(from(X)) -> c_33(from^#(proper(X))) :33
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
        -->_1 2nd^#(ok(X)) -> c_26(2nd^#(X)) :26
        -->_1 2nd^#(mark(X)) -> c_25(2nd^#(X)) :25
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
        -->_1 s^#(ok(X)) -> c_22(s^#(X)) :22
        -->_1 s^#(mark(X)) -> c_21(s^#(X)) :21
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
        -->_1 from^#(ok(X)) -> c_18(from^#(X)) :18
        -->_1 from^#(mark(X)) -> c_17(from^#(X)) :17
        -->_1 active^#(sel(0(), cons(X, XS))) -> c_16(X) :16
        -->_1 active^#(sel(s(N), cons(X, XS))) -> c_15(sel^#(N, XS)) :15
        -->_1 active^#(sel(X1, X2)) -> c_14(sel^#(active(X1), X2)) :14
        -->_1 active^#(sel(X1, X2)) -> c_13(sel^#(X1, active(X2))) :13
        -->_1 active^#(take(s(N), cons(X, XS))) ->
              c_11(cons^#(X, take(N, XS))) :11
        -->_1 active^#(take(X1, X2)) -> c_10(take^#(active(X1), X2)) :10
        -->_1 active^#(take(X1, X2)) -> c_9(take^#(X1, active(X2))) :9
        -->_1 active^#(2nd(cons(X, XS))) -> c_8(head^#(XS)) :8
        -->_1 active^#(2nd(X)) -> c_7(2nd^#(active(X))) :7
        -->_1 proper^#(nil()) -> c_40() :40
        -->_1 proper^#(0()) -> c_39() :39
        -->_1 active^#(take(0(), XS)) -> c_12() :12
        -->_1 active^#(head(cons(X, XS))) -> c_6(X) :6
        -->_1 active^#(head(X)) -> c_5(head^#(active(X))) :5
        -->_1 active^#(s(X)) -> c_4(s^#(active(X))) :4
        -->_1 active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) :3
        -->_1 active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) :2
        -->_1 active^#(from(X)) -> c_1(from^#(active(X))) :1
     
     7: active^#(2nd(X)) -> c_7(2nd^#(active(X)))
        -->_1 2nd^#(ok(X)) -> c_26(2nd^#(X)) :26
        -->_1 2nd^#(mark(X)) -> c_25(2nd^#(X)) :25
     
     8: active^#(2nd(cons(X, XS))) -> c_8(head^#(XS))
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
     
     9: active^#(take(X1, X2)) -> c_9(take^#(X1, active(X2)))
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
     
     10: active^#(take(X1, X2)) -> c_10(take^#(active(X1), X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
     
     11: active^#(take(s(N), cons(X, XS))) ->
         c_11(cons^#(X, take(N, XS)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
     
     12: active^#(take(0(), XS)) -> c_12()
     
     13: active^#(sel(X1, X2)) -> c_13(sel^#(X1, active(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     14: active^#(sel(X1, X2)) -> c_14(sel^#(active(X1), X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     15: active^#(sel(s(N), cons(X, XS))) -> c_15(sel^#(N, XS))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     16: active^#(sel(0(), cons(X, XS))) -> c_16(X)
        -->_1 top^#(ok(X)) -> c_43(top^#(active(X))) :43
        -->_1 top^#(mark(X)) -> c_42(top^#(proper(X))) :42
        -->_1 proper^#(sel(X1, X2)) ->
              c_41(sel^#(proper(X1), proper(X2))) :41
        -->_1 proper^#(take(X1, X2)) ->
              c_38(take^#(proper(X1), proper(X2))) :38
        -->_1 proper^#(2nd(X)) -> c_37(2nd^#(proper(X))) :37
        -->_1 proper^#(head(X)) -> c_36(head^#(proper(X))) :36
        -->_1 proper^#(s(X)) -> c_35(s^#(proper(X))) :35
        -->_1 proper^#(cons(X1, X2)) ->
              c_34(cons^#(proper(X1), proper(X2))) :34
        -->_1 proper^#(from(X)) -> c_33(from^#(proper(X))) :33
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
        -->_1 2nd^#(ok(X)) -> c_26(2nd^#(X)) :26
        -->_1 2nd^#(mark(X)) -> c_25(2nd^#(X)) :25
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
        -->_1 s^#(ok(X)) -> c_22(s^#(X)) :22
        -->_1 s^#(mark(X)) -> c_21(s^#(X)) :21
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
        -->_1 from^#(ok(X)) -> c_18(from^#(X)) :18
        -->_1 from^#(mark(X)) -> c_17(from^#(X)) :17
        -->_1 proper^#(nil()) -> c_40() :40
        -->_1 proper^#(0()) -> c_39() :39
        -->_1 active^#(sel(0(), cons(X, XS))) -> c_16(X) :16
        -->_1 active^#(sel(s(N), cons(X, XS))) -> c_15(sel^#(N, XS)) :15
        -->_1 active^#(sel(X1, X2)) -> c_14(sel^#(active(X1), X2)) :14
        -->_1 active^#(sel(X1, X2)) -> c_13(sel^#(X1, active(X2))) :13
        -->_1 active^#(take(0(), XS)) -> c_12() :12
        -->_1 active^#(take(s(N), cons(X, XS))) ->
              c_11(cons^#(X, take(N, XS))) :11
        -->_1 active^#(take(X1, X2)) -> c_10(take^#(active(X1), X2)) :10
        -->_1 active^#(take(X1, X2)) -> c_9(take^#(X1, active(X2))) :9
        -->_1 active^#(2nd(cons(X, XS))) -> c_8(head^#(XS)) :8
        -->_1 active^#(2nd(X)) -> c_7(2nd^#(active(X))) :7
        -->_1 active^#(head(cons(X, XS))) -> c_6(X) :6
        -->_1 active^#(head(X)) -> c_5(head^#(active(X))) :5
        -->_1 active^#(s(X)) -> c_4(s^#(active(X))) :4
        -->_1 active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) :3
        -->_1 active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) :2
        -->_1 active^#(from(X)) -> c_1(from^#(active(X))) :1
     
     17: from^#(mark(X)) -> c_17(from^#(X))
        -->_1 from^#(ok(X)) -> c_18(from^#(X)) :18
        -->_1 from^#(mark(X)) -> c_17(from^#(X)) :17
     
     18: from^#(ok(X)) -> c_18(from^#(X))
        -->_1 from^#(ok(X)) -> c_18(from^#(X)) :18
        -->_1 from^#(mark(X)) -> c_17(from^#(X)) :17
     
     19: cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
     
     20: cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
     
     21: s^#(mark(X)) -> c_21(s^#(X))
        -->_1 s^#(ok(X)) -> c_22(s^#(X)) :22
        -->_1 s^#(mark(X)) -> c_21(s^#(X)) :21
     
     22: s^#(ok(X)) -> c_22(s^#(X))
        -->_1 s^#(ok(X)) -> c_22(s^#(X)) :22
        -->_1 s^#(mark(X)) -> c_21(s^#(X)) :21
     
     23: head^#(mark(X)) -> c_23(head^#(X))
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
     
     24: head^#(ok(X)) -> c_24(head^#(X))
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
     
     25: 2nd^#(mark(X)) -> c_25(2nd^#(X))
        -->_1 2nd^#(ok(X)) -> c_26(2nd^#(X)) :26
        -->_1 2nd^#(mark(X)) -> c_25(2nd^#(X)) :25
     
     26: 2nd^#(ok(X)) -> c_26(2nd^#(X))
        -->_1 2nd^#(ok(X)) -> c_26(2nd^#(X)) :26
        -->_1 2nd^#(mark(X)) -> c_25(2nd^#(X)) :25
     
     27: take^#(X1, mark(X2)) -> c_27(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
     
     28: take^#(mark(X1), X2) -> c_28(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
     
     29: take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
     
     30: sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     31: sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     32: sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     33: proper^#(from(X)) -> c_33(from^#(proper(X)))
        -->_1 from^#(ok(X)) -> c_18(from^#(X)) :18
        -->_1 from^#(mark(X)) -> c_17(from^#(X)) :17
     
     34: proper^#(cons(X1, X2)) -> c_34(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2)) :20
        -->_1 cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2)) :19
     
     35: proper^#(s(X)) -> c_35(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_22(s^#(X)) :22
        -->_1 s^#(mark(X)) -> c_21(s^#(X)) :21
     
     36: proper^#(head(X)) -> c_36(head^#(proper(X)))
        -->_1 head^#(ok(X)) -> c_24(head^#(X)) :24
        -->_1 head^#(mark(X)) -> c_23(head^#(X)) :23
     
     37: proper^#(2nd(X)) -> c_37(2nd^#(proper(X)))
        -->_1 2nd^#(ok(X)) -> c_26(2nd^#(X)) :26
        -->_1 2nd^#(mark(X)) -> c_25(2nd^#(X)) :25
     
     38: proper^#(take(X1, X2)) -> c_38(take^#(proper(X1), proper(X2)))
        -->_1 take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2)) :29
        -->_1 take^#(mark(X1), X2) -> c_28(take^#(X1, X2)) :28
        -->_1 take^#(X1, mark(X2)) -> c_27(take^#(X1, X2)) :27
     
     39: proper^#(0()) -> c_39()
     
     40: proper^#(nil()) -> c_40()
     
     41: proper^#(sel(X1, X2)) -> c_41(sel^#(proper(X1), proper(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2)) :32
        -->_1 sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2)) :31
        -->_1 sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2)) :30
     
     42: top^#(mark(X)) -> c_42(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_43(top^#(active(X))) :43
        -->_1 top^#(mark(X)) -> c_42(top^#(proper(X))) :42
     
     43: top^#(ok(X)) -> c_43(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_43(top^#(active(X))) :43
        -->_1 top^#(mark(X)) -> c_42(top^#(proper(X))) :42
     
   
   Only the nodes
   {17,18,19,20,21,22,23,24,25,26,27,29,28,30,32,31,39,40,42,43} are
   reachable from nodes
   {17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,39,40,42,43} 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:
     { from^#(mark(X)) -> c_17(from^#(X))
     , from^#(ok(X)) -> c_18(from^#(X))
     , cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2))
     , s^#(mark(X)) -> c_21(s^#(X))
     , s^#(ok(X)) -> c_22(s^#(X))
     , head^#(mark(X)) -> c_23(head^#(X))
     , head^#(ok(X)) -> c_24(head^#(X))
     , 2nd^#(mark(X)) -> c_25(2nd^#(X))
     , 2nd^#(ok(X)) -> c_26(2nd^#(X))
     , take^#(X1, mark(X2)) -> c_27(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_28(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2))
     , proper^#(0()) -> c_39()
     , proper^#(nil()) -> c_40()
     , top^#(mark(X)) -> c_42(top^#(proper(X)))
     , top^#(ok(X)) -> c_43(top^#(active(X))) }
   Strict Trs:
     { active(from(X)) -> from(active(X))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(head(X)) -> head(active(X))
     , active(head(cons(X, XS))) -> mark(X)
     , active(2nd(X)) -> 2nd(active(X))
     , active(2nd(cons(X, XS))) -> mark(head(XS))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
     , active(take(0(), XS)) -> mark(nil())
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , head(mark(X)) -> mark(head(X))
     , head(ok(X)) -> ok(head(X))
     , 2nd(mark(X)) -> mark(2nd(X))
     , 2nd(ok(X)) -> ok(2nd(X))
     , 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))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(head(X)) -> head(proper(X))
     , proper(2nd(X)) -> 2nd(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {17,18} by applications of
   Pre({17,18}) = {}. Here rules are labeled as follows:
   
     DPs:
       { 1: from^#(mark(X)) -> c_17(from^#(X))
       , 2: from^#(ok(X)) -> c_18(from^#(X))
       , 3: cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2))
       , 4: cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2))
       , 5: s^#(mark(X)) -> c_21(s^#(X))
       , 6: s^#(ok(X)) -> c_22(s^#(X))
       , 7: head^#(mark(X)) -> c_23(head^#(X))
       , 8: head^#(ok(X)) -> c_24(head^#(X))
       , 9: 2nd^#(mark(X)) -> c_25(2nd^#(X))
       , 10: 2nd^#(ok(X)) -> c_26(2nd^#(X))
       , 11: take^#(X1, mark(X2)) -> c_27(take^#(X1, X2))
       , 12: take^#(mark(X1), X2) -> c_28(take^#(X1, X2))
       , 13: take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2))
       , 14: sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2))
       , 15: sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2))
       , 16: sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2))
       , 17: proper^#(0()) -> c_39()
       , 18: proper^#(nil()) -> c_40()
       , 19: top^#(mark(X)) -> c_42(top^#(proper(X)))
       , 20: top^#(ok(X)) -> c_43(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(mark(X)) -> c_17(from^#(X))
     , from^#(ok(X)) -> c_18(from^#(X))
     , cons^#(mark(X1), X2) -> c_19(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_20(cons^#(X1, X2))
     , s^#(mark(X)) -> c_21(s^#(X))
     , s^#(ok(X)) -> c_22(s^#(X))
     , head^#(mark(X)) -> c_23(head^#(X))
     , head^#(ok(X)) -> c_24(head^#(X))
     , 2nd^#(mark(X)) -> c_25(2nd^#(X))
     , 2nd^#(ok(X)) -> c_26(2nd^#(X))
     , take^#(X1, mark(X2)) -> c_27(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_28(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_29(take^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_30(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_31(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_32(sel^#(X1, X2))
     , top^#(mark(X)) -> c_42(top^#(proper(X)))
     , top^#(ok(X)) -> c_43(top^#(active(X))) }
   Strict Trs:
     { active(from(X)) -> from(active(X))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(head(X)) -> head(active(X))
     , active(head(cons(X, XS))) -> mark(X)
     , active(2nd(X)) -> 2nd(active(X))
     , active(2nd(cons(X, XS))) -> mark(head(XS))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
     , active(take(0(), XS)) -> mark(nil())
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , head(mark(X)) -> mark(head(X))
     , head(ok(X)) -> ok(head(X))
     , 2nd(mark(X)) -> mark(2nd(X))
     , 2nd(ok(X)) -> ok(2nd(X))
     , 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))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(head(X)) -> head(proper(X))
     , proper(2nd(X)) -> 2nd(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { proper^#(0()) -> c_39()
     , proper^#(nil()) -> c_40() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..