MAYBE

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

Strict Trs:
  { active(dbl(X)) -> dbl(active(X))
  , active(dbl(0())) -> mark(0())
  , active(dbl(s(X))) -> mark(s(s(dbl(X))))
  , active(dbls(X)) -> dbls(active(X))
  , active(dbls(nil())) -> mark(nil())
  , active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
  , active(sel(X1, X2)) -> sel(X1, active(X2))
  , active(sel(X1, X2)) -> sel(active(X1), X2)
  , active(sel(0(), cons(X, Y))) -> mark(X)
  , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  , active(indx(X1, X2)) -> indx(active(X1), X2)
  , active(indx(nil(), X)) -> mark(nil())
  , active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
  , active(from(X)) -> mark(cons(X, from(s(X))))
  , active(dbl1(X)) -> dbl1(active(X))
  , active(dbl1(0())) -> mark(01())
  , active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
  , active(s1(X)) -> s1(active(X))
  , active(sel1(X1, X2)) -> sel1(X1, active(X2))
  , active(sel1(X1, X2)) -> sel1(active(X1), X2)
  , active(sel1(0(), cons(X, Y))) -> mark(X)
  , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  , active(quote(X)) -> quote(active(X))
  , active(quote(dbl(X))) -> mark(dbl1(X))
  , active(quote(0())) -> mark(01())
  , active(quote(s(X))) -> mark(s1(quote(X)))
  , active(quote(sel(X, Y))) -> mark(sel1(X, Y))
  , dbl(mark(X)) -> mark(dbl(X))
  , dbl(ok(X)) -> ok(dbl(X))
  , s(ok(X)) -> ok(s(X))
  , dbls(mark(X)) -> mark(dbls(X))
  , dbls(ok(X)) -> ok(dbls(X))
  , cons(ok(X1), ok(X2)) -> ok(cons(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))
  , indx(mark(X1), X2) -> mark(indx(X1, X2))
  , indx(ok(X1), ok(X2)) -> ok(indx(X1, X2))
  , from(ok(X)) -> ok(from(X))
  , dbl1(mark(X)) -> mark(dbl1(X))
  , dbl1(ok(X)) -> ok(dbl1(X))
  , s1(mark(X)) -> mark(s1(X))
  , s1(ok(X)) -> ok(s1(X))
  , sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  , sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  , sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  , quote(mark(X)) -> mark(quote(X))
  , quote(ok(X)) -> ok(quote(X))
  , proper(dbl(X)) -> dbl(proper(X))
  , proper(0()) -> ok(0())
  , proper(s(X)) -> s(proper(X))
  , proper(dbls(X)) -> dbls(proper(X))
  , proper(nil()) -> ok(nil())
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  , proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
  , proper(from(X)) -> from(proper(X))
  , proper(dbl1(X)) -> dbl1(proper(X))
  , proper(01()) -> ok(01())
  , proper(s1(X)) -> s1(proper(X))
  , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  , proper(quote(X)) -> quote(proper(X))
  , 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^#(dbl(X)) -> c_1(dbl^#(active(X)))
     , active^#(dbl(0())) -> c_2()
     , active^#(dbl(s(X))) -> c_3(s^#(s(dbl(X))))
     , active^#(dbls(X)) -> c_4(dbls^#(active(X)))
     , active^#(dbls(nil())) -> c_5()
     , active^#(dbls(cons(X, Y))) -> c_6(cons^#(dbl(X), dbls(Y)))
     , active^#(sel(X1, X2)) -> c_7(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_8(sel^#(active(X1), X2))
     , active^#(sel(0(), cons(X, Y))) -> c_9(X)
     , active^#(sel(s(X), cons(Y, Z))) -> c_10(sel^#(X, Z))
     , active^#(indx(X1, X2)) -> c_11(indx^#(active(X1), X2))
     , active^#(indx(nil(), X)) -> c_12()
     , active^#(indx(cons(X, Y), Z)) ->
       c_13(cons^#(sel(X, Z), indx(Y, Z)))
     , active^#(from(X)) -> c_14(cons^#(X, from(s(X))))
     , active^#(dbl1(X)) -> c_15(dbl1^#(active(X)))
     , active^#(dbl1(0())) -> c_16()
     , active^#(dbl1(s(X))) -> c_17(s1^#(s1(dbl1(X))))
     , active^#(s1(X)) -> c_18(s1^#(active(X)))
     , active^#(sel1(X1, X2)) -> c_19(sel1^#(X1, active(X2)))
     , active^#(sel1(X1, X2)) -> c_20(sel1^#(active(X1), X2))
     , active^#(sel1(0(), cons(X, Y))) -> c_21(X)
     , active^#(sel1(s(X), cons(Y, Z))) -> c_22(sel1^#(X, Z))
     , active^#(quote(X)) -> c_23(quote^#(active(X)))
     , active^#(quote(dbl(X))) -> c_24(dbl1^#(X))
     , active^#(quote(0())) -> c_25()
     , active^#(quote(s(X))) -> c_26(s1^#(quote(X)))
     , active^#(quote(sel(X, Y))) -> c_27(sel1^#(X, Y))
     , dbl^#(mark(X)) -> c_28(dbl^#(X))
     , dbl^#(ok(X)) -> c_29(dbl^#(X))
     , s^#(ok(X)) -> c_30(s^#(X))
     , dbls^#(mark(X)) -> c_31(dbls^#(X))
     , dbls^#(ok(X)) -> c_32(dbls^#(X))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2))
     , indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2))
     , indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2))
     , dbl1^#(mark(X)) -> c_40(dbl1^#(X))
     , dbl1^#(ok(X)) -> c_41(dbl1^#(X))
     , s1^#(mark(X)) -> c_42(s1^#(X))
     , s1^#(ok(X)) -> c_43(s1^#(X))
     , sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2))
     , quote^#(mark(X)) -> c_47(quote^#(X))
     , quote^#(ok(X)) -> c_48(quote^#(X))
     , from^#(ok(X)) -> c_39(from^#(X))
     , proper^#(dbl(X)) -> c_49(dbl^#(proper(X)))
     , proper^#(0()) -> c_50()
     , proper^#(s(X)) -> c_51(s^#(proper(X)))
     , proper^#(dbls(X)) -> c_52(dbls^#(proper(X)))
     , proper^#(nil()) -> c_53()
     , proper^#(cons(X1, X2)) -> c_54(cons^#(proper(X1), proper(X2)))
     , proper^#(sel(X1, X2)) -> c_55(sel^#(proper(X1), proper(X2)))
     , proper^#(indx(X1, X2)) -> c_56(indx^#(proper(X1), proper(X2)))
     , proper^#(from(X)) -> c_57(from^#(proper(X)))
     , proper^#(dbl1(X)) -> c_58(dbl1^#(proper(X)))
     , proper^#(01()) -> c_59()
     , proper^#(s1(X)) -> c_60(s1^#(proper(X)))
     , proper^#(sel1(X1, X2)) -> c_61(sel1^#(proper(X1), proper(X2)))
     , proper^#(quote(X)) -> c_62(quote^#(proper(X)))
     , top^#(mark(X)) -> c_63(top^#(proper(X)))
     , top^#(ok(X)) -> c_64(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^#(dbl(X)) -> c_1(dbl^#(active(X)))
     , active^#(dbl(0())) -> c_2()
     , active^#(dbl(s(X))) -> c_3(s^#(s(dbl(X))))
     , active^#(dbls(X)) -> c_4(dbls^#(active(X)))
     , active^#(dbls(nil())) -> c_5()
     , active^#(dbls(cons(X, Y))) -> c_6(cons^#(dbl(X), dbls(Y)))
     , active^#(sel(X1, X2)) -> c_7(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_8(sel^#(active(X1), X2))
     , active^#(sel(0(), cons(X, Y))) -> c_9(X)
     , active^#(sel(s(X), cons(Y, Z))) -> c_10(sel^#(X, Z))
     , active^#(indx(X1, X2)) -> c_11(indx^#(active(X1), X2))
     , active^#(indx(nil(), X)) -> c_12()
     , active^#(indx(cons(X, Y), Z)) ->
       c_13(cons^#(sel(X, Z), indx(Y, Z)))
     , active^#(from(X)) -> c_14(cons^#(X, from(s(X))))
     , active^#(dbl1(X)) -> c_15(dbl1^#(active(X)))
     , active^#(dbl1(0())) -> c_16()
     , active^#(dbl1(s(X))) -> c_17(s1^#(s1(dbl1(X))))
     , active^#(s1(X)) -> c_18(s1^#(active(X)))
     , active^#(sel1(X1, X2)) -> c_19(sel1^#(X1, active(X2)))
     , active^#(sel1(X1, X2)) -> c_20(sel1^#(active(X1), X2))
     , active^#(sel1(0(), cons(X, Y))) -> c_21(X)
     , active^#(sel1(s(X), cons(Y, Z))) -> c_22(sel1^#(X, Z))
     , active^#(quote(X)) -> c_23(quote^#(active(X)))
     , active^#(quote(dbl(X))) -> c_24(dbl1^#(X))
     , active^#(quote(0())) -> c_25()
     , active^#(quote(s(X))) -> c_26(s1^#(quote(X)))
     , active^#(quote(sel(X, Y))) -> c_27(sel1^#(X, Y))
     , dbl^#(mark(X)) -> c_28(dbl^#(X))
     , dbl^#(ok(X)) -> c_29(dbl^#(X))
     , s^#(ok(X)) -> c_30(s^#(X))
     , dbls^#(mark(X)) -> c_31(dbls^#(X))
     , dbls^#(ok(X)) -> c_32(dbls^#(X))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2))
     , indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2))
     , indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2))
     , dbl1^#(mark(X)) -> c_40(dbl1^#(X))
     , dbl1^#(ok(X)) -> c_41(dbl1^#(X))
     , s1^#(mark(X)) -> c_42(s1^#(X))
     , s1^#(ok(X)) -> c_43(s1^#(X))
     , sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2))
     , quote^#(mark(X)) -> c_47(quote^#(X))
     , quote^#(ok(X)) -> c_48(quote^#(X))
     , from^#(ok(X)) -> c_39(from^#(X))
     , proper^#(dbl(X)) -> c_49(dbl^#(proper(X)))
     , proper^#(0()) -> c_50()
     , proper^#(s(X)) -> c_51(s^#(proper(X)))
     , proper^#(dbls(X)) -> c_52(dbls^#(proper(X)))
     , proper^#(nil()) -> c_53()
     , proper^#(cons(X1, X2)) -> c_54(cons^#(proper(X1), proper(X2)))
     , proper^#(sel(X1, X2)) -> c_55(sel^#(proper(X1), proper(X2)))
     , proper^#(indx(X1, X2)) -> c_56(indx^#(proper(X1), proper(X2)))
     , proper^#(from(X)) -> c_57(from^#(proper(X)))
     , proper^#(dbl1(X)) -> c_58(dbl1^#(proper(X)))
     , proper^#(01()) -> c_59()
     , proper^#(s1(X)) -> c_60(s1^#(proper(X)))
     , proper^#(sel1(X1, X2)) -> c_61(sel1^#(proper(X1), proper(X2)))
     , proper^#(quote(X)) -> c_62(quote^#(proper(X)))
     , top^#(mark(X)) -> c_63(top^#(proper(X)))
     , top^#(ok(X)) -> c_64(top^#(active(X))) }
   Strict Trs:
     { active(dbl(X)) -> dbl(active(X))
     , active(dbl(0())) -> mark(0())
     , active(dbl(s(X))) -> mark(s(s(dbl(X))))
     , active(dbls(X)) -> dbls(active(X))
     , active(dbls(nil())) -> mark(nil())
     , active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(0(), cons(X, Y))) -> mark(X)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(indx(X1, X2)) -> indx(active(X1), X2)
     , active(indx(nil(), X)) -> mark(nil())
     , active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(dbl1(X)) -> dbl1(active(X))
     , active(dbl1(0())) -> mark(01())
     , active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
     , active(s1(X)) -> s1(active(X))
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(0(), cons(X, Y))) -> mark(X)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(quote(X)) -> quote(active(X))
     , active(quote(dbl(X))) -> mark(dbl1(X))
     , active(quote(0())) -> mark(01())
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(sel(X, Y))) -> mark(sel1(X, Y))
     , dbl(mark(X)) -> mark(dbl(X))
     , dbl(ok(X)) -> ok(dbl(X))
     , s(ok(X)) -> ok(s(X))
     , dbls(mark(X)) -> mark(dbls(X))
     , dbls(ok(X)) -> ok(dbls(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(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))
     , indx(mark(X1), X2) -> mark(indx(X1, X2))
     , indx(ok(X1), ok(X2)) -> ok(indx(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , dbl1(mark(X)) -> mark(dbl1(X))
     , dbl1(ok(X)) -> ok(dbl1(X))
     , s1(mark(X)) -> mark(s1(X))
     , s1(ok(X)) -> ok(s1(X))
     , sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
     , sel1(mark(X1), X2) -> mark(sel1(X1, X2))
     , sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
     , quote(mark(X)) -> mark(quote(X))
     , quote(ok(X)) -> ok(quote(X))
     , proper(dbl(X)) -> dbl(proper(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(dbls(X)) -> dbls(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(dbl1(X)) -> dbl1(proper(X))
     , proper(01()) -> ok(01())
     , proper(s1(X)) -> s1(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Consider the dependency graph:
   
     1: active^#(dbl(X)) -> c_1(dbl^#(active(X)))
        -->_1 dbl^#(ok(X)) -> c_29(dbl^#(X)) :29
        -->_1 dbl^#(mark(X)) -> c_28(dbl^#(X)) :28
     
     2: active^#(dbl(0())) -> c_2()
     
     3: active^#(dbl(s(X))) -> c_3(s^#(s(dbl(X))))
        -->_1 s^#(ok(X)) -> c_30(s^#(X)) :30
     
     4: active^#(dbls(X)) -> c_4(dbls^#(active(X)))
        -->_1 dbls^#(ok(X)) -> c_32(dbls^#(X)) :32
        -->_1 dbls^#(mark(X)) -> c_31(dbls^#(X)) :31
     
     5: active^#(dbls(nil())) -> c_5()
     
     6: active^#(dbls(cons(X, Y))) -> c_6(cons^#(dbl(X), dbls(Y)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
     
     7: active^#(sel(X1, X2)) -> c_7(sel^#(X1, active(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     8: active^#(sel(X1, X2)) -> c_8(sel^#(active(X1), X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     9: active^#(sel(0(), cons(X, Y))) -> c_9(X)
        -->_1 top^#(ok(X)) -> c_64(top^#(active(X))) :64
        -->_1 top^#(mark(X)) -> c_63(top^#(proper(X))) :63
        -->_1 proper^#(quote(X)) -> c_62(quote^#(proper(X))) :62
        -->_1 proper^#(sel1(X1, X2)) ->
              c_61(sel1^#(proper(X1), proper(X2))) :61
        -->_1 proper^#(s1(X)) -> c_60(s1^#(proper(X))) :60
        -->_1 proper^#(dbl1(X)) -> c_58(dbl1^#(proper(X))) :58
        -->_1 proper^#(from(X)) -> c_57(from^#(proper(X))) :57
        -->_1 proper^#(indx(X1, X2)) ->
              c_56(indx^#(proper(X1), proper(X2))) :56
        -->_1 proper^#(sel(X1, X2)) ->
              c_55(sel^#(proper(X1), proper(X2))) :55
        -->_1 proper^#(cons(X1, X2)) ->
              c_54(cons^#(proper(X1), proper(X2))) :54
        -->_1 proper^#(dbls(X)) -> c_52(dbls^#(proper(X))) :52
        -->_1 proper^#(s(X)) -> c_51(s^#(proper(X))) :51
        -->_1 proper^#(dbl(X)) -> c_49(dbl^#(proper(X))) :49
        -->_1 from^#(ok(X)) -> c_39(from^#(X)) :48
        -->_1 quote^#(ok(X)) -> c_48(quote^#(X)) :47
        -->_1 quote^#(mark(X)) -> c_47(quote^#(X)) :46
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
        -->_1 indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2)) :38
        -->_1 indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2)) :37
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 dbls^#(ok(X)) -> c_32(dbls^#(X)) :32
        -->_1 dbls^#(mark(X)) -> c_31(dbls^#(X)) :31
        -->_1 s^#(ok(X)) -> c_30(s^#(X)) :30
        -->_1 dbl^#(ok(X)) -> c_29(dbl^#(X)) :29
        -->_1 dbl^#(mark(X)) -> c_28(dbl^#(X)) :28
        -->_1 active^#(quote(sel(X, Y))) -> c_27(sel1^#(X, Y)) :27
        -->_1 active^#(quote(s(X))) -> c_26(s1^#(quote(X))) :26
        -->_1 active^#(quote(dbl(X))) -> c_24(dbl1^#(X)) :24
        -->_1 active^#(quote(X)) -> c_23(quote^#(active(X))) :23
        -->_1 active^#(sel1(s(X), cons(Y, Z))) -> c_22(sel1^#(X, Z)) :22
        -->_1 active^#(sel1(0(), cons(X, Y))) -> c_21(X) :21
        -->_1 active^#(sel1(X1, X2)) -> c_20(sel1^#(active(X1), X2)) :20
        -->_1 active^#(sel1(X1, X2)) -> c_19(sel1^#(X1, active(X2))) :19
        -->_1 active^#(s1(X)) -> c_18(s1^#(active(X))) :18
        -->_1 active^#(dbl1(s(X))) -> c_17(s1^#(s1(dbl1(X)))) :17
        -->_1 active^#(dbl1(X)) -> c_15(dbl1^#(active(X))) :15
        -->_1 active^#(from(X)) -> c_14(cons^#(X, from(s(X)))) :14
        -->_1 active^#(indx(cons(X, Y), Z)) ->
              c_13(cons^#(sel(X, Z), indx(Y, Z))) :13
        -->_1 active^#(indx(X1, X2)) -> c_11(indx^#(active(X1), X2)) :11
        -->_1 active^#(sel(s(X), cons(Y, Z))) -> c_10(sel^#(X, Z)) :10
        -->_1 proper^#(01()) -> c_59() :59
        -->_1 proper^#(nil()) -> c_53() :53
        -->_1 proper^#(0()) -> c_50() :50
        -->_1 active^#(quote(0())) -> c_25() :25
        -->_1 active^#(dbl1(0())) -> c_16() :16
        -->_1 active^#(indx(nil(), X)) -> c_12() :12
        -->_1 active^#(sel(0(), cons(X, Y))) -> c_9(X) :9
        -->_1 active^#(sel(X1, X2)) -> c_8(sel^#(active(X1), X2)) :8
        -->_1 active^#(sel(X1, X2)) -> c_7(sel^#(X1, active(X2))) :7
        -->_1 active^#(dbls(cons(X, Y))) -> c_6(cons^#(dbl(X), dbls(Y))) :6
        -->_1 active^#(dbls(nil())) -> c_5() :5
        -->_1 active^#(dbls(X)) -> c_4(dbls^#(active(X))) :4
        -->_1 active^#(dbl(s(X))) -> c_3(s^#(s(dbl(X)))) :3
        -->_1 active^#(dbl(0())) -> c_2() :2
        -->_1 active^#(dbl(X)) -> c_1(dbl^#(active(X))) :1
     
     10: active^#(sel(s(X), cons(Y, Z))) -> c_10(sel^#(X, Z))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     11: active^#(indx(X1, X2)) -> c_11(indx^#(active(X1), X2))
        -->_1 indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2)) :38
        -->_1 indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2)) :37
     
     12: active^#(indx(nil(), X)) -> c_12()
     
     13: active^#(indx(cons(X, Y), Z)) ->
         c_13(cons^#(sel(X, Z), indx(Y, Z)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
     
     14: active^#(from(X)) -> c_14(cons^#(X, from(s(X))))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
     
     15: active^#(dbl1(X)) -> c_15(dbl1^#(active(X)))
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
     
     16: active^#(dbl1(0())) -> c_16()
     
     17: active^#(dbl1(s(X))) -> c_17(s1^#(s1(dbl1(X))))
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
     
     18: active^#(s1(X)) -> c_18(s1^#(active(X)))
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
     
     19: active^#(sel1(X1, X2)) -> c_19(sel1^#(X1, active(X2)))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     20: active^#(sel1(X1, X2)) -> c_20(sel1^#(active(X1), X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     21: active^#(sel1(0(), cons(X, Y))) -> c_21(X)
        -->_1 top^#(ok(X)) -> c_64(top^#(active(X))) :64
        -->_1 top^#(mark(X)) -> c_63(top^#(proper(X))) :63
        -->_1 proper^#(quote(X)) -> c_62(quote^#(proper(X))) :62
        -->_1 proper^#(sel1(X1, X2)) ->
              c_61(sel1^#(proper(X1), proper(X2))) :61
        -->_1 proper^#(s1(X)) -> c_60(s1^#(proper(X))) :60
        -->_1 proper^#(dbl1(X)) -> c_58(dbl1^#(proper(X))) :58
        -->_1 proper^#(from(X)) -> c_57(from^#(proper(X))) :57
        -->_1 proper^#(indx(X1, X2)) ->
              c_56(indx^#(proper(X1), proper(X2))) :56
        -->_1 proper^#(sel(X1, X2)) ->
              c_55(sel^#(proper(X1), proper(X2))) :55
        -->_1 proper^#(cons(X1, X2)) ->
              c_54(cons^#(proper(X1), proper(X2))) :54
        -->_1 proper^#(dbls(X)) -> c_52(dbls^#(proper(X))) :52
        -->_1 proper^#(s(X)) -> c_51(s^#(proper(X))) :51
        -->_1 proper^#(dbl(X)) -> c_49(dbl^#(proper(X))) :49
        -->_1 from^#(ok(X)) -> c_39(from^#(X)) :48
        -->_1 quote^#(ok(X)) -> c_48(quote^#(X)) :47
        -->_1 quote^#(mark(X)) -> c_47(quote^#(X)) :46
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
        -->_1 indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2)) :38
        -->_1 indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2)) :37
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
        -->_1 dbls^#(ok(X)) -> c_32(dbls^#(X)) :32
        -->_1 dbls^#(mark(X)) -> c_31(dbls^#(X)) :31
        -->_1 s^#(ok(X)) -> c_30(s^#(X)) :30
        -->_1 dbl^#(ok(X)) -> c_29(dbl^#(X)) :29
        -->_1 dbl^#(mark(X)) -> c_28(dbl^#(X)) :28
        -->_1 active^#(quote(sel(X, Y))) -> c_27(sel1^#(X, Y)) :27
        -->_1 active^#(quote(s(X))) -> c_26(s1^#(quote(X))) :26
        -->_1 active^#(quote(dbl(X))) -> c_24(dbl1^#(X)) :24
        -->_1 active^#(quote(X)) -> c_23(quote^#(active(X))) :23
        -->_1 active^#(sel1(s(X), cons(Y, Z))) -> c_22(sel1^#(X, Z)) :22
        -->_1 proper^#(01()) -> c_59() :59
        -->_1 proper^#(nil()) -> c_53() :53
        -->_1 proper^#(0()) -> c_50() :50
        -->_1 active^#(quote(0())) -> c_25() :25
        -->_1 active^#(sel1(0(), cons(X, Y))) -> c_21(X) :21
        -->_1 active^#(sel1(X1, X2)) -> c_20(sel1^#(active(X1), X2)) :20
        -->_1 active^#(sel1(X1, X2)) -> c_19(sel1^#(X1, active(X2))) :19
        -->_1 active^#(s1(X)) -> c_18(s1^#(active(X))) :18
        -->_1 active^#(dbl1(s(X))) -> c_17(s1^#(s1(dbl1(X)))) :17
        -->_1 active^#(dbl1(0())) -> c_16() :16
        -->_1 active^#(dbl1(X)) -> c_15(dbl1^#(active(X))) :15
        -->_1 active^#(from(X)) -> c_14(cons^#(X, from(s(X)))) :14
        -->_1 active^#(indx(cons(X, Y), Z)) ->
              c_13(cons^#(sel(X, Z), indx(Y, Z))) :13
        -->_1 active^#(indx(nil(), X)) -> c_12() :12
        -->_1 active^#(indx(X1, X2)) -> c_11(indx^#(active(X1), X2)) :11
        -->_1 active^#(sel(s(X), cons(Y, Z))) -> c_10(sel^#(X, Z)) :10
        -->_1 active^#(sel(0(), cons(X, Y))) -> c_9(X) :9
        -->_1 active^#(sel(X1, X2)) -> c_8(sel^#(active(X1), X2)) :8
        -->_1 active^#(sel(X1, X2)) -> c_7(sel^#(X1, active(X2))) :7
        -->_1 active^#(dbls(cons(X, Y))) -> c_6(cons^#(dbl(X), dbls(Y))) :6
        -->_1 active^#(dbls(nil())) -> c_5() :5
        -->_1 active^#(dbls(X)) -> c_4(dbls^#(active(X))) :4
        -->_1 active^#(dbl(s(X))) -> c_3(s^#(s(dbl(X)))) :3
        -->_1 active^#(dbl(0())) -> c_2() :2
        -->_1 active^#(dbl(X)) -> c_1(dbl^#(active(X))) :1
     
     22: active^#(sel1(s(X), cons(Y, Z))) -> c_22(sel1^#(X, Z))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     23: active^#(quote(X)) -> c_23(quote^#(active(X)))
        -->_1 quote^#(ok(X)) -> c_48(quote^#(X)) :47
        -->_1 quote^#(mark(X)) -> c_47(quote^#(X)) :46
     
     24: active^#(quote(dbl(X))) -> c_24(dbl1^#(X))
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
     
     25: active^#(quote(0())) -> c_25()
     
     26: active^#(quote(s(X))) -> c_26(s1^#(quote(X)))
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
     
     27: active^#(quote(sel(X, Y))) -> c_27(sel1^#(X, Y))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     28: dbl^#(mark(X)) -> c_28(dbl^#(X))
        -->_1 dbl^#(ok(X)) -> c_29(dbl^#(X)) :29
        -->_1 dbl^#(mark(X)) -> c_28(dbl^#(X)) :28
     
     29: dbl^#(ok(X)) -> c_29(dbl^#(X))
        -->_1 dbl^#(ok(X)) -> c_29(dbl^#(X)) :29
        -->_1 dbl^#(mark(X)) -> c_28(dbl^#(X)) :28
     
     30: s^#(ok(X)) -> c_30(s^#(X)) -->_1 s^#(ok(X)) -> c_30(s^#(X)) :30
     
     31: dbls^#(mark(X)) -> c_31(dbls^#(X))
        -->_1 dbls^#(ok(X)) -> c_32(dbls^#(X)) :32
        -->_1 dbls^#(mark(X)) -> c_31(dbls^#(X)) :31
     
     32: dbls^#(ok(X)) -> c_32(dbls^#(X))
        -->_1 dbls^#(ok(X)) -> c_32(dbls^#(X)) :32
        -->_1 dbls^#(mark(X)) -> c_31(dbls^#(X)) :31
     
     33: cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
     
     34: sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     35: sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     36: sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     37: indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2))
        -->_1 indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2)) :38
        -->_1 indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2)) :37
     
     38: indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2))
        -->_1 indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2)) :38
        -->_1 indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2)) :37
     
     39: dbl1^#(mark(X)) -> c_40(dbl1^#(X))
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
     
     40: dbl1^#(ok(X)) -> c_41(dbl1^#(X))
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
     
     41: s1^#(mark(X)) -> c_42(s1^#(X))
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
     
     42: s1^#(ok(X)) -> c_43(s1^#(X))
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
     
     43: sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     44: sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     45: sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     46: quote^#(mark(X)) -> c_47(quote^#(X))
        -->_1 quote^#(ok(X)) -> c_48(quote^#(X)) :47
        -->_1 quote^#(mark(X)) -> c_47(quote^#(X)) :46
     
     47: quote^#(ok(X)) -> c_48(quote^#(X))
        -->_1 quote^#(ok(X)) -> c_48(quote^#(X)) :47
        -->_1 quote^#(mark(X)) -> c_47(quote^#(X)) :46
     
     48: from^#(ok(X)) -> c_39(from^#(X))
        -->_1 from^#(ok(X)) -> c_39(from^#(X)) :48
     
     49: proper^#(dbl(X)) -> c_49(dbl^#(proper(X)))
        -->_1 dbl^#(ok(X)) -> c_29(dbl^#(X)) :29
        -->_1 dbl^#(mark(X)) -> c_28(dbl^#(X)) :28
     
     50: proper^#(0()) -> c_50()
     
     51: proper^#(s(X)) -> c_51(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_30(s^#(X)) :30
     
     52: proper^#(dbls(X)) -> c_52(dbls^#(proper(X)))
        -->_1 dbls^#(ok(X)) -> c_32(dbls^#(X)) :32
        -->_1 dbls^#(mark(X)) -> c_31(dbls^#(X)) :31
     
     53: proper^#(nil()) -> c_53()
     
     54: proper^#(cons(X1, X2)) -> c_54(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2)) :33
     
     55: proper^#(sel(X1, X2)) -> c_55(sel^#(proper(X1), proper(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2)) :36
        -->_1 sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2)) :35
        -->_1 sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2)) :34
     
     56: proper^#(indx(X1, X2)) -> c_56(indx^#(proper(X1), proper(X2)))
        -->_1 indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2)) :38
        -->_1 indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2)) :37
     
     57: proper^#(from(X)) -> c_57(from^#(proper(X)))
        -->_1 from^#(ok(X)) -> c_39(from^#(X)) :48
     
     58: proper^#(dbl1(X)) -> c_58(dbl1^#(proper(X)))
        -->_1 dbl1^#(ok(X)) -> c_41(dbl1^#(X)) :40
        -->_1 dbl1^#(mark(X)) -> c_40(dbl1^#(X)) :39
     
     59: proper^#(01()) -> c_59()
     
     60: proper^#(s1(X)) -> c_60(s1^#(proper(X)))
        -->_1 s1^#(ok(X)) -> c_43(s1^#(X)) :42
        -->_1 s1^#(mark(X)) -> c_42(s1^#(X)) :41
     
     61: proper^#(sel1(X1, X2)) -> c_61(sel1^#(proper(X1), proper(X2)))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2)) :45
        -->_1 sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2)) :44
        -->_1 sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2)) :43
     
     62: proper^#(quote(X)) -> c_62(quote^#(proper(X)))
        -->_1 quote^#(ok(X)) -> c_48(quote^#(X)) :47
        -->_1 quote^#(mark(X)) -> c_47(quote^#(X)) :46
     
     63: top^#(mark(X)) -> c_63(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_64(top^#(active(X))) :64
        -->_1 top^#(mark(X)) -> c_63(top^#(proper(X))) :63
     
     64: top^#(ok(X)) -> c_64(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_64(top^#(active(X))) :64
        -->_1 top^#(mark(X)) -> c_63(top^#(proper(X))) :63
     
   
   Only the nodes
   {28,29,30,31,32,33,34,36,35,37,38,39,40,41,42,43,45,44,46,47,48,50,53,59,63,64}
   are reachable from nodes
   {28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,50,53,59,63,64}
   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:
     { dbl^#(mark(X)) -> c_28(dbl^#(X))
     , dbl^#(ok(X)) -> c_29(dbl^#(X))
     , s^#(ok(X)) -> c_30(s^#(X))
     , dbls^#(mark(X)) -> c_31(dbls^#(X))
     , dbls^#(ok(X)) -> c_32(dbls^#(X))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2))
     , indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2))
     , indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2))
     , dbl1^#(mark(X)) -> c_40(dbl1^#(X))
     , dbl1^#(ok(X)) -> c_41(dbl1^#(X))
     , s1^#(mark(X)) -> c_42(s1^#(X))
     , s1^#(ok(X)) -> c_43(s1^#(X))
     , sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2))
     , quote^#(mark(X)) -> c_47(quote^#(X))
     , quote^#(ok(X)) -> c_48(quote^#(X))
     , from^#(ok(X)) -> c_39(from^#(X))
     , proper^#(0()) -> c_50()
     , proper^#(nil()) -> c_53()
     , proper^#(01()) -> c_59()
     , top^#(mark(X)) -> c_63(top^#(proper(X)))
     , top^#(ok(X)) -> c_64(top^#(active(X))) }
   Strict Trs:
     { active(dbl(X)) -> dbl(active(X))
     , active(dbl(0())) -> mark(0())
     , active(dbl(s(X))) -> mark(s(s(dbl(X))))
     , active(dbls(X)) -> dbls(active(X))
     , active(dbls(nil())) -> mark(nil())
     , active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(0(), cons(X, Y))) -> mark(X)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(indx(X1, X2)) -> indx(active(X1), X2)
     , active(indx(nil(), X)) -> mark(nil())
     , active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(dbl1(X)) -> dbl1(active(X))
     , active(dbl1(0())) -> mark(01())
     , active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
     , active(s1(X)) -> s1(active(X))
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(0(), cons(X, Y))) -> mark(X)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(quote(X)) -> quote(active(X))
     , active(quote(dbl(X))) -> mark(dbl1(X))
     , active(quote(0())) -> mark(01())
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(sel(X, Y))) -> mark(sel1(X, Y))
     , dbl(mark(X)) -> mark(dbl(X))
     , dbl(ok(X)) -> ok(dbl(X))
     , s(ok(X)) -> ok(s(X))
     , dbls(mark(X)) -> mark(dbls(X))
     , dbls(ok(X)) -> ok(dbls(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(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))
     , indx(mark(X1), X2) -> mark(indx(X1, X2))
     , indx(ok(X1), ok(X2)) -> ok(indx(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , dbl1(mark(X)) -> mark(dbl1(X))
     , dbl1(ok(X)) -> ok(dbl1(X))
     , s1(mark(X)) -> mark(s1(X))
     , s1(ok(X)) -> ok(s1(X))
     , sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
     , sel1(mark(X1), X2) -> mark(sel1(X1, X2))
     , sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
     , quote(mark(X)) -> mark(quote(X))
     , quote(ok(X)) -> ok(quote(X))
     , proper(dbl(X)) -> dbl(proper(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(dbls(X)) -> dbls(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(dbl1(X)) -> dbl1(proper(X))
     , proper(01()) -> ok(01())
     , proper(s1(X)) -> s1(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {22,23,24} by applications
   of Pre({22,23,24}) = {}. Here rules are labeled as follows:
   
     DPs:
       { 1: dbl^#(mark(X)) -> c_28(dbl^#(X))
       , 2: dbl^#(ok(X)) -> c_29(dbl^#(X))
       , 3: s^#(ok(X)) -> c_30(s^#(X))
       , 4: dbls^#(mark(X)) -> c_31(dbls^#(X))
       , 5: dbls^#(ok(X)) -> c_32(dbls^#(X))
       , 6: cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
       , 7: sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2))
       , 8: sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2))
       , 9: sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2))
       , 10: indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2))
       , 11: indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2))
       , 12: dbl1^#(mark(X)) -> c_40(dbl1^#(X))
       , 13: dbl1^#(ok(X)) -> c_41(dbl1^#(X))
       , 14: s1^#(mark(X)) -> c_42(s1^#(X))
       , 15: s1^#(ok(X)) -> c_43(s1^#(X))
       , 16: sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2))
       , 17: sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2))
       , 18: sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2))
       , 19: quote^#(mark(X)) -> c_47(quote^#(X))
       , 20: quote^#(ok(X)) -> c_48(quote^#(X))
       , 21: from^#(ok(X)) -> c_39(from^#(X))
       , 22: proper^#(0()) -> c_50()
       , 23: proper^#(nil()) -> c_53()
       , 24: proper^#(01()) -> c_59()
       , 25: top^#(mark(X)) -> c_63(top^#(proper(X)))
       , 26: top^#(ok(X)) -> c_64(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { dbl^#(mark(X)) -> c_28(dbl^#(X))
     , dbl^#(ok(X)) -> c_29(dbl^#(X))
     , s^#(ok(X)) -> c_30(s^#(X))
     , dbls^#(mark(X)) -> c_31(dbls^#(X))
     , dbls^#(ok(X)) -> c_32(dbls^#(X))
     , cons^#(ok(X1), ok(X2)) -> c_33(cons^#(X1, X2))
     , sel^#(X1, mark(X2)) -> c_34(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_35(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_36(sel^#(X1, X2))
     , indx^#(mark(X1), X2) -> c_37(indx^#(X1, X2))
     , indx^#(ok(X1), ok(X2)) -> c_38(indx^#(X1, X2))
     , dbl1^#(mark(X)) -> c_40(dbl1^#(X))
     , dbl1^#(ok(X)) -> c_41(dbl1^#(X))
     , s1^#(mark(X)) -> c_42(s1^#(X))
     , s1^#(ok(X)) -> c_43(s1^#(X))
     , sel1^#(X1, mark(X2)) -> c_44(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_45(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_46(sel1^#(X1, X2))
     , quote^#(mark(X)) -> c_47(quote^#(X))
     , quote^#(ok(X)) -> c_48(quote^#(X))
     , from^#(ok(X)) -> c_39(from^#(X))
     , top^#(mark(X)) -> c_63(top^#(proper(X)))
     , top^#(ok(X)) -> c_64(top^#(active(X))) }
   Strict Trs:
     { active(dbl(X)) -> dbl(active(X))
     , active(dbl(0())) -> mark(0())
     , active(dbl(s(X))) -> mark(s(s(dbl(X))))
     , active(dbls(X)) -> dbls(active(X))
     , active(dbls(nil())) -> mark(nil())
     , active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(0(), cons(X, Y))) -> mark(X)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(indx(X1, X2)) -> indx(active(X1), X2)
     , active(indx(nil(), X)) -> mark(nil())
     , active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(dbl1(X)) -> dbl1(active(X))
     , active(dbl1(0())) -> mark(01())
     , active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
     , active(s1(X)) -> s1(active(X))
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(0(), cons(X, Y))) -> mark(X)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(quote(X)) -> quote(active(X))
     , active(quote(dbl(X))) -> mark(dbl1(X))
     , active(quote(0())) -> mark(01())
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(sel(X, Y))) -> mark(sel1(X, Y))
     , dbl(mark(X)) -> mark(dbl(X))
     , dbl(ok(X)) -> ok(dbl(X))
     , s(ok(X)) -> ok(s(X))
     , dbls(mark(X)) -> mark(dbls(X))
     , dbls(ok(X)) -> ok(dbls(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(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))
     , indx(mark(X1), X2) -> mark(indx(X1, X2))
     , indx(ok(X1), ok(X2)) -> ok(indx(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , dbl1(mark(X)) -> mark(dbl1(X))
     , dbl1(ok(X)) -> ok(dbl1(X))
     , s1(mark(X)) -> mark(s1(X))
     , s1(ok(X)) -> ok(s1(X))
     , sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
     , sel1(mark(X1), X2) -> mark(sel1(X1, X2))
     , sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
     , quote(mark(X)) -> mark(quote(X))
     , quote(ok(X)) -> ok(quote(X))
     , proper(dbl(X)) -> dbl(proper(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(dbls(X)) -> dbls(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(dbl1(X)) -> dbl1(proper(X))
     , proper(01()) -> ok(01())
     , proper(s1(X)) -> s1(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { proper^#(0()) -> c_50()
     , proper^#(nil()) -> c_53()
     , proper^#(01()) -> c_59() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..