MAYBE

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

Strict Trs:
  { active(natsFrom(X)) -> natsFrom(active(X))
  , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(s(X)) -> s(active(X))
  , active(fst(X)) -> fst(active(X))
  , active(fst(pair(XS, YS))) -> mark(XS)
  , active(pair(X1, X2)) -> pair(X1, active(X2))
  , active(pair(X1, X2)) -> pair(active(X1), X2)
  , active(snd(X)) -> snd(active(X))
  , active(snd(pair(XS, YS))) -> mark(YS)
  , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
  , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
  , active(splitAt(s(N), cons(X, XS))) ->
    mark(u(splitAt(N, XS), N, X, XS))
  , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
  , active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
  , active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
  , active(head(X)) -> head(active(X))
  , active(head(cons(N, XS))) -> mark(N)
  , active(tail(X)) -> tail(active(X))
  , active(tail(cons(N, XS))) -> mark(XS)
  , active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
  , active(sel(X1, X2)) -> sel(X1, active(X2))
  , active(sel(X1, X2)) -> sel(active(X1), X2)
  , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
  , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
  , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
  , active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
  , active(take(X1, X2)) -> take(X1, active(X2))
  , active(take(X1, X2)) -> take(active(X1), X2)
  , natsFrom(mark(X)) -> mark(natsFrom(X))
  , natsFrom(ok(X)) -> ok(natsFrom(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))
  , fst(mark(X)) -> mark(fst(X))
  , fst(ok(X)) -> ok(fst(X))
  , pair(X1, mark(X2)) -> mark(pair(X1, X2))
  , pair(mark(X1), X2) -> mark(pair(X1, X2))
  , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
  , snd(mark(X)) -> mark(snd(X))
  , snd(ok(X)) -> ok(snd(X))
  , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
  , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
  , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
  , u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
  , u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
  , head(mark(X)) -> mark(head(X))
  , head(ok(X)) -> ok(head(X))
  , tail(mark(X)) -> mark(tail(X))
  , tail(ok(X)) -> ok(tail(X))
  , 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))
  , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
  , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
  , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
  , 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(natsFrom(X)) -> natsFrom(proper(X))
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(fst(X)) -> fst(proper(X))
  , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
  , proper(snd(X)) -> snd(proper(X))
  , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(nil()) -> ok(nil())
  , proper(u(X1, X2, X3, X4)) ->
    u(proper(X1), proper(X2), proper(X3), proper(X4))
  , proper(head(X)) -> head(proper(X))
  , proper(tail(X)) -> tail(proper(X))
  , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
  , proper(take(X1, X2)) -> take(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^#(natsFrom(X)) -> c_1(natsFrom^#(active(X)))
     , active^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N))))
     , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
     , active^#(s(X)) -> c_4(s^#(active(X)))
     , active^#(fst(X)) -> c_5(fst^#(active(X)))
     , active^#(fst(pair(XS, YS))) -> c_6(XS)
     , active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2)))
     , active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2))
     , active^#(snd(X)) -> c_9(snd^#(active(X)))
     , active^#(snd(pair(XS, YS))) -> c_10(YS)
     , active^#(splitAt(X1, X2)) -> c_11(splitAt^#(X1, active(X2)))
     , active^#(splitAt(X1, X2)) -> c_12(splitAt^#(active(X1), X2))
     , active^#(splitAt(s(N), cons(X, XS))) ->
       c_13(u^#(splitAt(N, XS), N, X, XS))
     , active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS))
     , active^#(u(X1, X2, X3, X4)) -> c_15(u^#(active(X1), X2, X3, X4))
     , active^#(u(pair(YS, ZS), N, X, XS)) ->
       c_16(pair^#(cons(X, YS), ZS))
     , active^#(head(X)) -> c_17(head^#(active(X)))
     , active^#(head(cons(N, XS))) -> c_18(N)
     , active^#(tail(X)) -> c_19(tail^#(active(X)))
     , active^#(tail(cons(N, XS))) -> c_20(XS)
     , active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS)))
     , active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2))
     , active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS)))
     , active^#(afterNth(X1, X2)) -> c_25(afterNth^#(X1, active(X2)))
     , active^#(afterNth(X1, X2)) -> c_26(afterNth^#(active(X1), X2))
     , active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS)))
     , active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2)))
     , active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2))
     , natsFrom^#(mark(X)) -> c_30(natsFrom^#(X))
     , natsFrom^#(ok(X)) -> c_31(natsFrom^#(X))
     , cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , s^#(mark(X)) -> c_34(s^#(X))
     , s^#(ok(X)) -> c_35(s^#(X))
     , fst^#(mark(X)) -> c_36(fst^#(X))
     , fst^#(ok(X)) -> c_37(fst^#(X))
     , pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2))
     , pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2))
     , pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2))
     , snd^#(mark(X)) -> c_41(snd^#(X))
     , snd^#(ok(X)) -> c_42(snd^#(X))
     , splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2))
     , splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2))
     , splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2))
     , u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4))
     , u^#(ok(X1), ok(X2), ok(X3), ok(X4)) -> c_47(u^#(X1, X2, X3, X4))
     , head^#(mark(X)) -> c_48(head^#(X))
     , head^#(ok(X)) -> c_49(head^#(X))
     , tail^#(mark(X)) -> c_50(tail^#(X))
     , tail^#(ok(X)) -> c_51(tail^#(X))
     , sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2))
     , afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2))
     , afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2))
     , afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2))
     , take^#(X1, mark(X2)) -> c_58(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_59(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2))
     , proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_62(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_63(s^#(proper(X)))
     , proper^#(fst(X)) -> c_64(fst^#(proper(X)))
     , proper^#(pair(X1, X2)) -> c_65(pair^#(proper(X1), proper(X2)))
     , proper^#(snd(X)) -> c_66(snd^#(proper(X)))
     , proper^#(splitAt(X1, X2)) ->
       c_67(splitAt^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_68()
     , proper^#(nil()) -> c_69()
     , proper^#(u(X1, X2, X3, X4)) ->
       c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(head(X)) -> c_71(head^#(proper(X)))
     , proper^#(tail(X)) -> c_72(tail^#(proper(X)))
     , proper^#(sel(X1, X2)) -> c_73(sel^#(proper(X1), proper(X2)))
     , proper^#(afterNth(X1, X2)) ->
       c_74(afterNth^#(proper(X1), proper(X2)))
     , proper^#(take(X1, X2)) -> c_75(take^#(proper(X1), proper(X2)))
     , top^#(mark(X)) -> c_76(top^#(proper(X)))
     , top^#(ok(X)) -> c_77(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^#(natsFrom(X)) -> c_1(natsFrom^#(active(X)))
     , active^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N))))
     , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
     , active^#(s(X)) -> c_4(s^#(active(X)))
     , active^#(fst(X)) -> c_5(fst^#(active(X)))
     , active^#(fst(pair(XS, YS))) -> c_6(XS)
     , active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2)))
     , active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2))
     , active^#(snd(X)) -> c_9(snd^#(active(X)))
     , active^#(snd(pair(XS, YS))) -> c_10(YS)
     , active^#(splitAt(X1, X2)) -> c_11(splitAt^#(X1, active(X2)))
     , active^#(splitAt(X1, X2)) -> c_12(splitAt^#(active(X1), X2))
     , active^#(splitAt(s(N), cons(X, XS))) ->
       c_13(u^#(splitAt(N, XS), N, X, XS))
     , active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS))
     , active^#(u(X1, X2, X3, X4)) -> c_15(u^#(active(X1), X2, X3, X4))
     , active^#(u(pair(YS, ZS), N, X, XS)) ->
       c_16(pair^#(cons(X, YS), ZS))
     , active^#(head(X)) -> c_17(head^#(active(X)))
     , active^#(head(cons(N, XS))) -> c_18(N)
     , active^#(tail(X)) -> c_19(tail^#(active(X)))
     , active^#(tail(cons(N, XS))) -> c_20(XS)
     , active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS)))
     , active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2))
     , active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS)))
     , active^#(afterNth(X1, X2)) -> c_25(afterNth^#(X1, active(X2)))
     , active^#(afterNth(X1, X2)) -> c_26(afterNth^#(active(X1), X2))
     , active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS)))
     , active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2)))
     , active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2))
     , natsFrom^#(mark(X)) -> c_30(natsFrom^#(X))
     , natsFrom^#(ok(X)) -> c_31(natsFrom^#(X))
     , cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , s^#(mark(X)) -> c_34(s^#(X))
     , s^#(ok(X)) -> c_35(s^#(X))
     , fst^#(mark(X)) -> c_36(fst^#(X))
     , fst^#(ok(X)) -> c_37(fst^#(X))
     , pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2))
     , pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2))
     , pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2))
     , snd^#(mark(X)) -> c_41(snd^#(X))
     , snd^#(ok(X)) -> c_42(snd^#(X))
     , splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2))
     , splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2))
     , splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2))
     , u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4))
     , u^#(ok(X1), ok(X2), ok(X3), ok(X4)) -> c_47(u^#(X1, X2, X3, X4))
     , head^#(mark(X)) -> c_48(head^#(X))
     , head^#(ok(X)) -> c_49(head^#(X))
     , tail^#(mark(X)) -> c_50(tail^#(X))
     , tail^#(ok(X)) -> c_51(tail^#(X))
     , sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2))
     , afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2))
     , afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2))
     , afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2))
     , take^#(X1, mark(X2)) -> c_58(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_59(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2))
     , proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_62(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_63(s^#(proper(X)))
     , proper^#(fst(X)) -> c_64(fst^#(proper(X)))
     , proper^#(pair(X1, X2)) -> c_65(pair^#(proper(X1), proper(X2)))
     , proper^#(snd(X)) -> c_66(snd^#(proper(X)))
     , proper^#(splitAt(X1, X2)) ->
       c_67(splitAt^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_68()
     , proper^#(nil()) -> c_69()
     , proper^#(u(X1, X2, X3, X4)) ->
       c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4)))
     , proper^#(head(X)) -> c_71(head^#(proper(X)))
     , proper^#(tail(X)) -> c_72(tail^#(proper(X)))
     , proper^#(sel(X1, X2)) -> c_73(sel^#(proper(X1), proper(X2)))
     , proper^#(afterNth(X1, X2)) ->
       c_74(afterNth^#(proper(X1), proper(X2)))
     , proper^#(take(X1, X2)) -> c_75(take^#(proper(X1), proper(X2)))
     , top^#(mark(X)) -> c_76(top^#(proper(X)))
     , top^#(ok(X)) -> c_77(top^#(active(X))) }
   Strict Trs:
     { active(natsFrom(X)) -> natsFrom(active(X))
     , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(fst(X)) -> fst(active(X))
     , active(fst(pair(XS, YS))) -> mark(XS)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(snd(X)) -> snd(active(X))
     , active(snd(pair(XS, YS))) -> mark(YS)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(s(N), cons(X, XS))) ->
       mark(u(splitAt(N, XS), N, X, XS))
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
     , active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
     , active(head(X)) -> head(active(X))
     , active(head(cons(N, XS))) -> mark(N)
     , active(tail(X)) -> tail(active(X))
     , active(tail(cons(N, XS))) -> mark(XS)
     , active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , natsFrom(ok(X)) -> ok(natsFrom(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))
     , fst(mark(X)) -> mark(fst(X))
     , fst(ok(X)) -> ok(fst(X))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , snd(mark(X)) -> mark(snd(X))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
     , u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
     , head(mark(X)) -> mark(head(X))
     , head(ok(X)) -> ok(head(X))
     , tail(mark(X)) -> mark(tail(X))
     , tail(ok(X)) -> ok(tail(X))
     , 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))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , 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(natsFrom(X)) -> natsFrom(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(fst(X)) -> fst(proper(X))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(u(X1, X2, X3, X4)) ->
       u(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(head(X)) -> head(proper(X))
     , proper(tail(X)) -> tail(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(take(X1, X2)) -> take(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^#(natsFrom(X)) -> c_1(natsFrom^#(active(X)))
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
     
     2: active^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N))))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
     
     3: active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
     
     4: active^#(s(X)) -> c_4(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
     
     5: active^#(fst(X)) -> c_5(fst^#(active(X)))
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
     
     6: active^#(fst(pair(XS, YS))) -> c_6(XS)
        -->_1 top^#(ok(X)) -> c_77(top^#(active(X))) :77
        -->_1 top^#(mark(X)) -> c_76(top^#(proper(X))) :76
        -->_1 proper^#(take(X1, X2)) ->
              c_75(take^#(proper(X1), proper(X2))) :75
        -->_1 proper^#(afterNth(X1, X2)) ->
              c_74(afterNth^#(proper(X1), proper(X2))) :74
        -->_1 proper^#(sel(X1, X2)) ->
              c_73(sel^#(proper(X1), proper(X2))) :73
        -->_1 proper^#(tail(X)) -> c_72(tail^#(proper(X))) :72
        -->_1 proper^#(head(X)) -> c_71(head^#(proper(X))) :71
        -->_1 proper^#(u(X1, X2, X3, X4)) ->
              c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4))) :70
        -->_1 proper^#(splitAt(X1, X2)) ->
              c_67(splitAt^#(proper(X1), proper(X2))) :67
        -->_1 proper^#(snd(X)) -> c_66(snd^#(proper(X))) :66
        -->_1 proper^#(pair(X1, X2)) ->
              c_65(pair^#(proper(X1), proper(X2))) :65
        -->_1 proper^#(fst(X)) -> c_64(fst^#(proper(X))) :64
        -->_1 proper^#(s(X)) -> c_63(s^#(proper(X))) :63
        -->_1 proper^#(cons(X1, X2)) ->
              c_62(cons^#(proper(X1), proper(X2))) :62
        -->_1 proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X))) :61
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
        -->_1 active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2)) :29
        -->_1 active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2))) :28
        -->_1 active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS))) :27
        -->_1 active^#(afterNth(X1, X2)) ->
              c_26(afterNth^#(active(X1), X2)) :26
        -->_1 active^#(afterNth(X1, X2)) ->
              c_25(afterNth^#(X1, active(X2))) :25
        -->_1 active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS))) :24
        -->_1 active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2)) :23
        -->_1 active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2))) :22
        -->_1 active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS))) :21
        -->_1 active^#(tail(cons(N, XS))) -> c_20(XS) :20
        -->_1 active^#(tail(X)) -> c_19(tail^#(active(X))) :19
        -->_1 active^#(head(cons(N, XS))) -> c_18(N) :18
        -->_1 active^#(head(X)) -> c_17(head^#(active(X))) :17
        -->_1 active^#(u(pair(YS, ZS), N, X, XS)) ->
              c_16(pair^#(cons(X, YS), ZS)) :16
        -->_1 active^#(u(X1, X2, X3, X4)) ->
              c_15(u^#(active(X1), X2, X3, X4)) :15
        -->_1 active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS)) :14
        -->_1 active^#(splitAt(s(N), cons(X, XS))) ->
              c_13(u^#(splitAt(N, XS), N, X, XS)) :13
        -->_1 active^#(splitAt(X1, X2)) ->
              c_12(splitAt^#(active(X1), X2)) :12
        -->_1 active^#(splitAt(X1, X2)) ->
              c_11(splitAt^#(X1, active(X2))) :11
        -->_1 active^#(snd(pair(XS, YS))) -> c_10(YS) :10
        -->_1 active^#(snd(X)) -> c_9(snd^#(active(X))) :9
        -->_1 active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2)) :8
        -->_1 active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2))) :7
        -->_1 proper^#(nil()) -> c_69() :69
        -->_1 proper^#(0()) -> c_68() :68
        -->_1 active^#(fst(pair(XS, YS))) -> c_6(XS) :6
        -->_1 active^#(fst(X)) -> c_5(fst^#(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^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N)))) :2
        -->_1 active^#(natsFrom(X)) -> c_1(natsFrom^#(active(X))) :1
     
     7: active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2)))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     8: active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     9: active^#(snd(X)) -> c_9(snd^#(active(X)))
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
     
     10: active^#(snd(pair(XS, YS))) -> c_10(YS)
        -->_1 top^#(ok(X)) -> c_77(top^#(active(X))) :77
        -->_1 top^#(mark(X)) -> c_76(top^#(proper(X))) :76
        -->_1 proper^#(take(X1, X2)) ->
              c_75(take^#(proper(X1), proper(X2))) :75
        -->_1 proper^#(afterNth(X1, X2)) ->
              c_74(afterNth^#(proper(X1), proper(X2))) :74
        -->_1 proper^#(sel(X1, X2)) ->
              c_73(sel^#(proper(X1), proper(X2))) :73
        -->_1 proper^#(tail(X)) -> c_72(tail^#(proper(X))) :72
        -->_1 proper^#(head(X)) -> c_71(head^#(proper(X))) :71
        -->_1 proper^#(u(X1, X2, X3, X4)) ->
              c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4))) :70
        -->_1 proper^#(splitAt(X1, X2)) ->
              c_67(splitAt^#(proper(X1), proper(X2))) :67
        -->_1 proper^#(snd(X)) -> c_66(snd^#(proper(X))) :66
        -->_1 proper^#(pair(X1, X2)) ->
              c_65(pair^#(proper(X1), proper(X2))) :65
        -->_1 proper^#(fst(X)) -> c_64(fst^#(proper(X))) :64
        -->_1 proper^#(s(X)) -> c_63(s^#(proper(X))) :63
        -->_1 proper^#(cons(X1, X2)) ->
              c_62(cons^#(proper(X1), proper(X2))) :62
        -->_1 proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X))) :61
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
        -->_1 active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2)) :29
        -->_1 active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2))) :28
        -->_1 active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS))) :27
        -->_1 active^#(afterNth(X1, X2)) ->
              c_26(afterNth^#(active(X1), X2)) :26
        -->_1 active^#(afterNth(X1, X2)) ->
              c_25(afterNth^#(X1, active(X2))) :25
        -->_1 active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS))) :24
        -->_1 active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2)) :23
        -->_1 active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2))) :22
        -->_1 active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS))) :21
        -->_1 active^#(tail(cons(N, XS))) -> c_20(XS) :20
        -->_1 active^#(tail(X)) -> c_19(tail^#(active(X))) :19
        -->_1 active^#(head(cons(N, XS))) -> c_18(N) :18
        -->_1 active^#(head(X)) -> c_17(head^#(active(X))) :17
        -->_1 active^#(u(pair(YS, ZS), N, X, XS)) ->
              c_16(pair^#(cons(X, YS), ZS)) :16
        -->_1 active^#(u(X1, X2, X3, X4)) ->
              c_15(u^#(active(X1), X2, X3, X4)) :15
        -->_1 active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS)) :14
        -->_1 active^#(splitAt(s(N), cons(X, XS))) ->
              c_13(u^#(splitAt(N, XS), N, X, XS)) :13
        -->_1 active^#(splitAt(X1, X2)) ->
              c_12(splitAt^#(active(X1), X2)) :12
        -->_1 active^#(splitAt(X1, X2)) ->
              c_11(splitAt^#(X1, active(X2))) :11
        -->_1 proper^#(nil()) -> c_69() :69
        -->_1 proper^#(0()) -> c_68() :68
        -->_1 active^#(snd(pair(XS, YS))) -> c_10(YS) :10
        -->_1 active^#(snd(X)) -> c_9(snd^#(active(X))) :9
        -->_1 active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2)) :8
        -->_1 active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2))) :7
        -->_1 active^#(fst(pair(XS, YS))) -> c_6(XS) :6
        -->_1 active^#(fst(X)) -> c_5(fst^#(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^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N)))) :2
        -->_1 active^#(natsFrom(X)) -> c_1(natsFrom^#(active(X))) :1
     
     11: active^#(splitAt(X1, X2)) -> c_11(splitAt^#(X1, active(X2)))
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
     
     12: active^#(splitAt(X1, X2)) -> c_12(splitAt^#(active(X1), X2))
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
     
     13: active^#(splitAt(s(N), cons(X, XS))) ->
         c_13(u^#(splitAt(N, XS), N, X, XS))
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
     
     14: active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS))
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     15: active^#(u(X1, X2, X3, X4)) ->
         c_15(u^#(active(X1), X2, X3, X4))
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
     
     16: active^#(u(pair(YS, ZS), N, X, XS)) ->
         c_16(pair^#(cons(X, YS), ZS))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     17: active^#(head(X)) -> c_17(head^#(active(X)))
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
     
     18: active^#(head(cons(N, XS))) -> c_18(N)
        -->_1 top^#(ok(X)) -> c_77(top^#(active(X))) :77
        -->_1 top^#(mark(X)) -> c_76(top^#(proper(X))) :76
        -->_1 proper^#(take(X1, X2)) ->
              c_75(take^#(proper(X1), proper(X2))) :75
        -->_1 proper^#(afterNth(X1, X2)) ->
              c_74(afterNth^#(proper(X1), proper(X2))) :74
        -->_1 proper^#(sel(X1, X2)) ->
              c_73(sel^#(proper(X1), proper(X2))) :73
        -->_1 proper^#(tail(X)) -> c_72(tail^#(proper(X))) :72
        -->_1 proper^#(head(X)) -> c_71(head^#(proper(X))) :71
        -->_1 proper^#(u(X1, X2, X3, X4)) ->
              c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4))) :70
        -->_1 proper^#(splitAt(X1, X2)) ->
              c_67(splitAt^#(proper(X1), proper(X2))) :67
        -->_1 proper^#(snd(X)) -> c_66(snd^#(proper(X))) :66
        -->_1 proper^#(pair(X1, X2)) ->
              c_65(pair^#(proper(X1), proper(X2))) :65
        -->_1 proper^#(fst(X)) -> c_64(fst^#(proper(X))) :64
        -->_1 proper^#(s(X)) -> c_63(s^#(proper(X))) :63
        -->_1 proper^#(cons(X1, X2)) ->
              c_62(cons^#(proper(X1), proper(X2))) :62
        -->_1 proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X))) :61
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
        -->_1 active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2)) :29
        -->_1 active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2))) :28
        -->_1 active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS))) :27
        -->_1 active^#(afterNth(X1, X2)) ->
              c_26(afterNth^#(active(X1), X2)) :26
        -->_1 active^#(afterNth(X1, X2)) ->
              c_25(afterNth^#(X1, active(X2))) :25
        -->_1 active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS))) :24
        -->_1 active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2)) :23
        -->_1 active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2))) :22
        -->_1 active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS))) :21
        -->_1 active^#(tail(cons(N, XS))) -> c_20(XS) :20
        -->_1 active^#(tail(X)) -> c_19(tail^#(active(X))) :19
        -->_1 proper^#(nil()) -> c_69() :69
        -->_1 proper^#(0()) -> c_68() :68
        -->_1 active^#(head(cons(N, XS))) -> c_18(N) :18
        -->_1 active^#(head(X)) -> c_17(head^#(active(X))) :17
        -->_1 active^#(u(pair(YS, ZS), N, X, XS)) ->
              c_16(pair^#(cons(X, YS), ZS)) :16
        -->_1 active^#(u(X1, X2, X3, X4)) ->
              c_15(u^#(active(X1), X2, X3, X4)) :15
        -->_1 active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS)) :14
        -->_1 active^#(splitAt(s(N), cons(X, XS))) ->
              c_13(u^#(splitAt(N, XS), N, X, XS)) :13
        -->_1 active^#(splitAt(X1, X2)) ->
              c_12(splitAt^#(active(X1), X2)) :12
        -->_1 active^#(splitAt(X1, X2)) ->
              c_11(splitAt^#(X1, active(X2))) :11
        -->_1 active^#(snd(pair(XS, YS))) -> c_10(YS) :10
        -->_1 active^#(snd(X)) -> c_9(snd^#(active(X))) :9
        -->_1 active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2)) :8
        -->_1 active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2))) :7
        -->_1 active^#(fst(pair(XS, YS))) -> c_6(XS) :6
        -->_1 active^#(fst(X)) -> c_5(fst^#(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^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N)))) :2
        -->_1 active^#(natsFrom(X)) -> c_1(natsFrom^#(active(X))) :1
     
     19: active^#(tail(X)) -> c_19(tail^#(active(X)))
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
     
     20: active^#(tail(cons(N, XS))) -> c_20(XS)
        -->_1 top^#(ok(X)) -> c_77(top^#(active(X))) :77
        -->_1 top^#(mark(X)) -> c_76(top^#(proper(X))) :76
        -->_1 proper^#(take(X1, X2)) ->
              c_75(take^#(proper(X1), proper(X2))) :75
        -->_1 proper^#(afterNth(X1, X2)) ->
              c_74(afterNth^#(proper(X1), proper(X2))) :74
        -->_1 proper^#(sel(X1, X2)) ->
              c_73(sel^#(proper(X1), proper(X2))) :73
        -->_1 proper^#(tail(X)) -> c_72(tail^#(proper(X))) :72
        -->_1 proper^#(head(X)) -> c_71(head^#(proper(X))) :71
        -->_1 proper^#(u(X1, X2, X3, X4)) ->
              c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4))) :70
        -->_1 proper^#(splitAt(X1, X2)) ->
              c_67(splitAt^#(proper(X1), proper(X2))) :67
        -->_1 proper^#(snd(X)) -> c_66(snd^#(proper(X))) :66
        -->_1 proper^#(pair(X1, X2)) ->
              c_65(pair^#(proper(X1), proper(X2))) :65
        -->_1 proper^#(fst(X)) -> c_64(fst^#(proper(X))) :64
        -->_1 proper^#(s(X)) -> c_63(s^#(proper(X))) :63
        -->_1 proper^#(cons(X1, X2)) ->
              c_62(cons^#(proper(X1), proper(X2))) :62
        -->_1 proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X))) :61
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
        -->_1 active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2)) :29
        -->_1 active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2))) :28
        -->_1 active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS))) :27
        -->_1 active^#(afterNth(X1, X2)) ->
              c_26(afterNth^#(active(X1), X2)) :26
        -->_1 active^#(afterNth(X1, X2)) ->
              c_25(afterNth^#(X1, active(X2))) :25
        -->_1 active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS))) :24
        -->_1 active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2)) :23
        -->_1 active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2))) :22
        -->_1 active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS))) :21
        -->_1 proper^#(nil()) -> c_69() :69
        -->_1 proper^#(0()) -> c_68() :68
        -->_1 active^#(tail(cons(N, XS))) -> c_20(XS) :20
        -->_1 active^#(tail(X)) -> c_19(tail^#(active(X))) :19
        -->_1 active^#(head(cons(N, XS))) -> c_18(N) :18
        -->_1 active^#(head(X)) -> c_17(head^#(active(X))) :17
        -->_1 active^#(u(pair(YS, ZS), N, X, XS)) ->
              c_16(pair^#(cons(X, YS), ZS)) :16
        -->_1 active^#(u(X1, X2, X3, X4)) ->
              c_15(u^#(active(X1), X2, X3, X4)) :15
        -->_1 active^#(splitAt(0(), XS)) -> c_14(pair^#(nil(), XS)) :14
        -->_1 active^#(splitAt(s(N), cons(X, XS))) ->
              c_13(u^#(splitAt(N, XS), N, X, XS)) :13
        -->_1 active^#(splitAt(X1, X2)) ->
              c_12(splitAt^#(active(X1), X2)) :12
        -->_1 active^#(splitAt(X1, X2)) ->
              c_11(splitAt^#(X1, active(X2))) :11
        -->_1 active^#(snd(pair(XS, YS))) -> c_10(YS) :10
        -->_1 active^#(snd(X)) -> c_9(snd^#(active(X))) :9
        -->_1 active^#(pair(X1, X2)) -> c_8(pair^#(active(X1), X2)) :8
        -->_1 active^#(pair(X1, X2)) -> c_7(pair^#(X1, active(X2))) :7
        -->_1 active^#(fst(pair(XS, YS))) -> c_6(XS) :6
        -->_1 active^#(fst(X)) -> c_5(fst^#(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^#(natsFrom(N)) -> c_2(cons^#(N, natsFrom(s(N)))) :2
        -->_1 active^#(natsFrom(X)) -> c_1(natsFrom^#(active(X))) :1
     
     21: active^#(sel(N, XS)) -> c_21(head^#(afterNth(N, XS)))
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
     
     22: active^#(sel(X1, X2)) -> c_22(sel^#(X1, active(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
     
     23: active^#(sel(X1, X2)) -> c_23(sel^#(active(X1), X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
     
     24: active^#(afterNth(N, XS)) -> c_24(snd^#(splitAt(N, XS)))
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
     
     25: active^#(afterNth(X1, X2)) -> c_25(afterNth^#(X1, active(X2)))
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
     
     26: active^#(afterNth(X1, X2)) -> c_26(afterNth^#(active(X1), X2))
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
     
     27: active^#(take(N, XS)) -> c_27(fst^#(splitAt(N, XS)))
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
     
     28: active^#(take(X1, X2)) -> c_28(take^#(X1, active(X2)))
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
     
     29: active^#(take(X1, X2)) -> c_29(take^#(active(X1), X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
     
     30: natsFrom^#(mark(X)) -> c_30(natsFrom^#(X))
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
     
     31: natsFrom^#(ok(X)) -> c_31(natsFrom^#(X))
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
     
     32: cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
     
     33: cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
     
     34: s^#(mark(X)) -> c_34(s^#(X))
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
     
     35: s^#(ok(X)) -> c_35(s^#(X))
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
     
     36: fst^#(mark(X)) -> c_36(fst^#(X))
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
     
     37: fst^#(ok(X)) -> c_37(fst^#(X))
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
     
     38: pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     39: pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     40: pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     41: snd^#(mark(X)) -> c_41(snd^#(X))
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
     
     42: snd^#(ok(X)) -> c_42(snd^#(X))
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
     
     43: splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2))
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
     
     44: splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2))
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
     
     45: splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2))
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
     
     46: u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4))
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
     
     47: u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
         c_47(u^#(X1, X2, X3, X4))
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
     
     48: head^#(mark(X)) -> c_48(head^#(X))
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
     
     49: head^#(ok(X)) -> c_49(head^#(X))
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
     
     50: tail^#(mark(X)) -> c_50(tail^#(X))
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
     
     51: tail^#(ok(X)) -> c_51(tail^#(X))
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
     
     52: sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
     
     53: sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
     
     54: sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
     
     55: afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2))
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
     
     56: afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2))
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
     
     57: afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2))
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
     
     58: take^#(X1, mark(X2)) -> c_58(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
     
     59: take^#(mark(X1), X2) -> c_59(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
     
     60: take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2))
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
     
     61: proper^#(natsFrom(X)) -> c_61(natsFrom^#(proper(X)))
        -->_1 natsFrom^#(ok(X)) -> c_31(natsFrom^#(X)) :31
        -->_1 natsFrom^#(mark(X)) -> c_30(natsFrom^#(X)) :30
     
     62: proper^#(cons(X1, X2)) -> c_62(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2)) :32
     
     63: proper^#(s(X)) -> c_63(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_35(s^#(X)) :35
        -->_1 s^#(mark(X)) -> c_34(s^#(X)) :34
     
     64: proper^#(fst(X)) -> c_64(fst^#(proper(X)))
        -->_1 fst^#(ok(X)) -> c_37(fst^#(X)) :37
        -->_1 fst^#(mark(X)) -> c_36(fst^#(X)) :36
     
     65: proper^#(pair(X1, X2)) -> c_65(pair^#(proper(X1), proper(X2)))
        -->_1 pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2)) :40
        -->_1 pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2)) :39
        -->_1 pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2)) :38
     
     66: proper^#(snd(X)) -> c_66(snd^#(proper(X)))
        -->_1 snd^#(ok(X)) -> c_42(snd^#(X)) :42
        -->_1 snd^#(mark(X)) -> c_41(snd^#(X)) :41
     
     67: proper^#(splitAt(X1, X2)) ->
         c_67(splitAt^#(proper(X1), proper(X2)))
        -->_1 splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2)) :45
        -->_1 splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2)) :44
        -->_1 splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2)) :43
     
     68: proper^#(0()) -> c_68()
     
     69: proper^#(nil()) -> c_69()
     
     70: proper^#(u(X1, X2, X3, X4)) ->
         c_70(u^#(proper(X1), proper(X2), proper(X3), proper(X4)))
        -->_1 u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
              c_47(u^#(X1, X2, X3, X4)) :47
        -->_1 u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4)) :46
     
     71: proper^#(head(X)) -> c_71(head^#(proper(X)))
        -->_1 head^#(ok(X)) -> c_49(head^#(X)) :49
        -->_1 head^#(mark(X)) -> c_48(head^#(X)) :48
     
     72: proper^#(tail(X)) -> c_72(tail^#(proper(X)))
        -->_1 tail^#(ok(X)) -> c_51(tail^#(X)) :51
        -->_1 tail^#(mark(X)) -> c_50(tail^#(X)) :50
     
     73: proper^#(sel(X1, X2)) -> c_73(sel^#(proper(X1), proper(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2)) :54
        -->_1 sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2)) :53
        -->_1 sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2)) :52
     
     74: proper^#(afterNth(X1, X2)) ->
         c_74(afterNth^#(proper(X1), proper(X2)))
        -->_1 afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2)) :57
        -->_1 afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2)) :56
        -->_1 afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2)) :55
     
     75: proper^#(take(X1, X2)) -> c_75(take^#(proper(X1), proper(X2)))
        -->_1 take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2)) :60
        -->_1 take^#(mark(X1), X2) -> c_59(take^#(X1, X2)) :59
        -->_1 take^#(X1, mark(X2)) -> c_58(take^#(X1, X2)) :58
     
     76: top^#(mark(X)) -> c_76(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_77(top^#(active(X))) :77
        -->_1 top^#(mark(X)) -> c_76(top^#(proper(X))) :76
     
     77: top^#(ok(X)) -> c_77(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_77(top^#(active(X))) :77
        -->_1 top^#(mark(X)) -> c_76(top^#(proper(X))) :76
     
   
   Only the nodes
   {30,31,32,33,34,35,36,37,38,40,39,41,42,43,45,44,46,47,48,49,50,51,52,54,53,55,57,56,58,60,59,68,69,76,77}
   are reachable from nodes
   {30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,68,69,76,77}
   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:
     { natsFrom^#(mark(X)) -> c_30(natsFrom^#(X))
     , natsFrom^#(ok(X)) -> c_31(natsFrom^#(X))
     , cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , s^#(mark(X)) -> c_34(s^#(X))
     , s^#(ok(X)) -> c_35(s^#(X))
     , fst^#(mark(X)) -> c_36(fst^#(X))
     , fst^#(ok(X)) -> c_37(fst^#(X))
     , pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2))
     , pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2))
     , pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2))
     , snd^#(mark(X)) -> c_41(snd^#(X))
     , snd^#(ok(X)) -> c_42(snd^#(X))
     , splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2))
     , splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2))
     , splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2))
     , u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4))
     , u^#(ok(X1), ok(X2), ok(X3), ok(X4)) -> c_47(u^#(X1, X2, X3, X4))
     , head^#(mark(X)) -> c_48(head^#(X))
     , head^#(ok(X)) -> c_49(head^#(X))
     , tail^#(mark(X)) -> c_50(tail^#(X))
     , tail^#(ok(X)) -> c_51(tail^#(X))
     , sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2))
     , afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2))
     , afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2))
     , afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2))
     , take^#(X1, mark(X2)) -> c_58(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_59(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2))
     , proper^#(0()) -> c_68()
     , proper^#(nil()) -> c_69()
     , top^#(mark(X)) -> c_76(top^#(proper(X)))
     , top^#(ok(X)) -> c_77(top^#(active(X))) }
   Strict Trs:
     { active(natsFrom(X)) -> natsFrom(active(X))
     , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(fst(X)) -> fst(active(X))
     , active(fst(pair(XS, YS))) -> mark(XS)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(snd(X)) -> snd(active(X))
     , active(snd(pair(XS, YS))) -> mark(YS)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(s(N), cons(X, XS))) ->
       mark(u(splitAt(N, XS), N, X, XS))
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
     , active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
     , active(head(X)) -> head(active(X))
     , active(head(cons(N, XS))) -> mark(N)
     , active(tail(X)) -> tail(active(X))
     , active(tail(cons(N, XS))) -> mark(XS)
     , active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , natsFrom(ok(X)) -> ok(natsFrom(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))
     , fst(mark(X)) -> mark(fst(X))
     , fst(ok(X)) -> ok(fst(X))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , snd(mark(X)) -> mark(snd(X))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
     , u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
     , head(mark(X)) -> mark(head(X))
     , head(ok(X)) -> ok(head(X))
     , tail(mark(X)) -> mark(tail(X))
     , tail(ok(X)) -> ok(tail(X))
     , 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))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , 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(natsFrom(X)) -> natsFrom(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(fst(X)) -> fst(proper(X))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(u(X1, X2, X3, X4)) ->
       u(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(head(X)) -> head(proper(X))
     , proper(tail(X)) -> tail(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(take(X1, X2)) -> take(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 {32,33} by applications of
   Pre({32,33}) = {}. Here rules are labeled as follows:
   
     DPs:
       { 1: natsFrom^#(mark(X)) -> c_30(natsFrom^#(X))
       , 2: natsFrom^#(ok(X)) -> c_31(natsFrom^#(X))
       , 3: cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2))
       , 4: cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
       , 5: s^#(mark(X)) -> c_34(s^#(X))
       , 6: s^#(ok(X)) -> c_35(s^#(X))
       , 7: fst^#(mark(X)) -> c_36(fst^#(X))
       , 8: fst^#(ok(X)) -> c_37(fst^#(X))
       , 9: pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2))
       , 10: pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2))
       , 11: pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2))
       , 12: snd^#(mark(X)) -> c_41(snd^#(X))
       , 13: snd^#(ok(X)) -> c_42(snd^#(X))
       , 14: splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2))
       , 15: splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2))
       , 16: splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2))
       , 17: u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4))
       , 18: u^#(ok(X1), ok(X2), ok(X3), ok(X4)) ->
             c_47(u^#(X1, X2, X3, X4))
       , 19: head^#(mark(X)) -> c_48(head^#(X))
       , 20: head^#(ok(X)) -> c_49(head^#(X))
       , 21: tail^#(mark(X)) -> c_50(tail^#(X))
       , 22: tail^#(ok(X)) -> c_51(tail^#(X))
       , 23: sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2))
       , 24: sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2))
       , 25: sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2))
       , 26: afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2))
       , 27: afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2))
       , 28: afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2))
       , 29: take^#(X1, mark(X2)) -> c_58(take^#(X1, X2))
       , 30: take^#(mark(X1), X2) -> c_59(take^#(X1, X2))
       , 31: take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2))
       , 32: proper^#(0()) -> c_68()
       , 33: proper^#(nil()) -> c_69()
       , 34: top^#(mark(X)) -> c_76(top^#(proper(X)))
       , 35: top^#(ok(X)) -> c_77(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { natsFrom^#(mark(X)) -> c_30(natsFrom^#(X))
     , natsFrom^#(ok(X)) -> c_31(natsFrom^#(X))
     , cons^#(mark(X1), X2) -> c_32(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , s^#(mark(X)) -> c_34(s^#(X))
     , s^#(ok(X)) -> c_35(s^#(X))
     , fst^#(mark(X)) -> c_36(fst^#(X))
     , fst^#(ok(X)) -> c_37(fst^#(X))
     , pair^#(X1, mark(X2)) -> c_38(pair^#(X1, X2))
     , pair^#(mark(X1), X2) -> c_39(pair^#(X1, X2))
     , pair^#(ok(X1), ok(X2)) -> c_40(pair^#(X1, X2))
     , snd^#(mark(X)) -> c_41(snd^#(X))
     , snd^#(ok(X)) -> c_42(snd^#(X))
     , splitAt^#(X1, mark(X2)) -> c_43(splitAt^#(X1, X2))
     , splitAt^#(mark(X1), X2) -> c_44(splitAt^#(X1, X2))
     , splitAt^#(ok(X1), ok(X2)) -> c_45(splitAt^#(X1, X2))
     , u^#(mark(X1), X2, X3, X4) -> c_46(u^#(X1, X2, X3, X4))
     , u^#(ok(X1), ok(X2), ok(X3), ok(X4)) -> c_47(u^#(X1, X2, X3, X4))
     , head^#(mark(X)) -> c_48(head^#(X))
     , head^#(ok(X)) -> c_49(head^#(X))
     , tail^#(mark(X)) -> c_50(tail^#(X))
     , tail^#(ok(X)) -> c_51(tail^#(X))
     , sel^#(X1, mark(X2)) -> c_52(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_53(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_54(sel^#(X1, X2))
     , afterNth^#(X1, mark(X2)) -> c_55(afterNth^#(X1, X2))
     , afterNth^#(mark(X1), X2) -> c_56(afterNth^#(X1, X2))
     , afterNth^#(ok(X1), ok(X2)) -> c_57(afterNth^#(X1, X2))
     , take^#(X1, mark(X2)) -> c_58(take^#(X1, X2))
     , take^#(mark(X1), X2) -> c_59(take^#(X1, X2))
     , take^#(ok(X1), ok(X2)) -> c_60(take^#(X1, X2))
     , top^#(mark(X)) -> c_76(top^#(proper(X)))
     , top^#(ok(X)) -> c_77(top^#(active(X))) }
   Strict Trs:
     { active(natsFrom(X)) -> natsFrom(active(X))
     , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(fst(X)) -> fst(active(X))
     , active(fst(pair(XS, YS))) -> mark(XS)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(snd(X)) -> snd(active(X))
     , active(snd(pair(XS, YS))) -> mark(YS)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(s(N), cons(X, XS))) ->
       mark(u(splitAt(N, XS), N, X, XS))
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
     , active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
     , active(head(X)) -> head(active(X))
     , active(head(cons(N, XS))) -> mark(N)
     , active(tail(X)) -> tail(active(X))
     , active(tail(cons(N, XS))) -> mark(XS)
     , active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , natsFrom(ok(X)) -> ok(natsFrom(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))
     , fst(mark(X)) -> mark(fst(X))
     , fst(ok(X)) -> ok(fst(X))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , snd(mark(X)) -> mark(snd(X))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
     , u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
     , head(mark(X)) -> mark(head(X))
     , head(ok(X)) -> ok(head(X))
     , tail(mark(X)) -> mark(tail(X))
     , tail(ok(X)) -> ok(tail(X))
     , 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))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , 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(natsFrom(X)) -> natsFrom(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(fst(X)) -> fst(proper(X))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(u(X1, X2, X3, X4)) ->
       u(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(head(X)) -> head(proper(X))
     , proper(tail(X)) -> tail(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { proper^#(0()) -> c_68()
     , proper^#(nil()) -> c_69() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..