MAYBE

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

Strict Trs:
  { active(sel(X1, X2)) -> sel(X1, active(X2))
  , active(sel(X1, X2)) -> sel(active(X1), X2)
  , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  , active(sel(0(), cons(X, Z))) -> mark(X)
  , active(s(X)) -> s(active(X))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(first(X1, X2)) -> first(X1, active(X2))
  , active(first(X1, X2)) -> first(active(X1), X2)
  , active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  , active(first(0(), Z)) -> mark(nil())
  , active(from(X)) -> mark(cons(X, from(s(X))))
  , active(from(X)) -> from(active(X))
  , active(sel1(X1, X2)) -> sel1(X1, active(X2))
  , active(sel1(X1, X2)) -> sel1(active(X1), X2)
  , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  , active(sel1(0(), cons(X, Z))) -> mark(quote(X))
  , active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  , active(quote(s(X))) -> mark(s1(quote(X)))
  , active(quote(0())) -> mark(01())
  , active(first1(X1, X2)) -> first1(X1, active(X2))
  , active(first1(X1, X2)) -> first1(active(X1), X2)
  , active(first1(s(X), cons(Y, Z))) ->
    mark(cons1(quote(Y), first1(X, Z)))
  , active(first1(0(), Z)) -> mark(nil1())
  , active(cons1(X1, X2)) -> cons1(X1, active(X2))
  , active(cons1(X1, X2)) -> cons1(active(X1), X2)
  , active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  , active(quote1(first(X, Z))) -> mark(first1(X, Z))
  , active(quote1(nil())) -> mark(nil1())
  , active(s1(X)) -> s1(active(X))
  , active(unquote(X)) -> unquote(active(X))
  , active(unquote(01())) -> mark(0())
  , active(unquote(s1(X))) -> mark(s(unquote(X)))
  , active(unquote1(X)) -> unquote1(active(X))
  , active(unquote1(nil1())) -> mark(nil())
  , active(unquote1(cons1(X, Z))) ->
    mark(fcons(unquote(X), unquote1(Z)))
  , active(fcons(X, Z)) -> mark(cons(X, Z))
  , active(fcons(X1, X2)) -> fcons(X1, active(X2))
  , active(fcons(X1, X2)) -> fcons(active(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))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , first(X1, mark(X2)) -> mark(first(X1, X2))
  , first(mark(X1), X2) -> mark(first(X1, X2))
  , first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  , from(mark(X)) -> mark(from(X))
  , from(ok(X)) -> ok(from(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(ok(X)) -> ok(quote(X))
  , first1(X1, mark(X2)) -> mark(first1(X1, X2))
  , first1(mark(X1), X2) -> mark(first1(X1, X2))
  , first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  , cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  , cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  , cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  , quote1(ok(X)) -> ok(quote1(X))
  , s1(mark(X)) -> mark(s1(X))
  , s1(ok(X)) -> ok(s1(X))
  , unquote(mark(X)) -> mark(unquote(X))
  , unquote(ok(X)) -> ok(unquote(X))
  , unquote1(mark(X)) -> mark(unquote1(X))
  , unquote1(ok(X)) -> ok(unquote1(X))
  , fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  , fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  , fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  , proper(nil()) -> ok(nil())
  , proper(from(X)) -> from(proper(X))
  , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  , proper(quote(X)) -> quote(proper(X))
  , proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  , proper(nil1()) -> ok(nil1())
  , proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  , proper(01()) -> ok(01())
  , proper(quote1(X)) -> quote1(proper(X))
  , proper(s1(X)) -> s1(proper(X))
  , proper(unquote(X)) -> unquote(proper(X))
  , proper(unquote1(X)) -> unquote1(proper(X))
  , proper(fcons(X1, X2)) -> fcons(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) '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) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) '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
      
      2) '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
      
   

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^#(sel(X1, X2)) -> c_1(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_2(sel^#(active(X1), X2))
     , active^#(sel(s(X), cons(Y, Z))) -> c_3(sel^#(X, Z))
     , active^#(sel(0(), cons(X, Z))) -> c_4(X)
     , active^#(s(X)) -> c_5(s^#(active(X)))
     , active^#(cons(X1, X2)) -> c_6(cons^#(active(X1), X2))
     , active^#(first(X1, X2)) -> c_7(first^#(X1, active(X2)))
     , active^#(first(X1, X2)) -> c_8(first^#(active(X1), X2))
     , active^#(first(s(X), cons(Y, Z))) -> c_9(cons^#(Y, first(X, Z)))
     , active^#(first(0(), Z)) -> c_10()
     , active^#(from(X)) -> c_11(cons^#(X, from(s(X))))
     , active^#(from(X)) -> c_12(from^#(active(X)))
     , active^#(sel1(X1, X2)) -> c_13(sel1^#(X1, active(X2)))
     , active^#(sel1(X1, X2)) -> c_14(sel1^#(active(X1), X2))
     , active^#(sel1(s(X), cons(Y, Z))) -> c_15(sel1^#(X, Z))
     , active^#(sel1(0(), cons(X, Z))) -> c_16(quote^#(X))
     , active^#(quote(sel(X, Z))) -> c_17(sel1^#(X, Z))
     , active^#(quote(s(X))) -> c_18(s1^#(quote(X)))
     , active^#(quote(0())) -> c_19()
     , active^#(first1(X1, X2)) -> c_20(first1^#(X1, active(X2)))
     , active^#(first1(X1, X2)) -> c_21(first1^#(active(X1), X2))
     , active^#(first1(s(X), cons(Y, Z))) ->
       c_22(cons1^#(quote(Y), first1(X, Z)))
     , active^#(first1(0(), Z)) -> c_23()
     , active^#(cons1(X1, X2)) -> c_24(cons1^#(X1, active(X2)))
     , active^#(cons1(X1, X2)) -> c_25(cons1^#(active(X1), X2))
     , active^#(quote1(cons(X, Z))) ->
       c_26(cons1^#(quote(X), quote1(Z)))
     , active^#(quote1(first(X, Z))) -> c_27(first1^#(X, Z))
     , active^#(quote1(nil())) -> c_28()
     , active^#(s1(X)) -> c_29(s1^#(active(X)))
     , active^#(unquote(X)) -> c_30(unquote^#(active(X)))
     , active^#(unquote(01())) -> c_31()
     , active^#(unquote(s1(X))) -> c_32(s^#(unquote(X)))
     , active^#(unquote1(X)) -> c_33(unquote1^#(active(X)))
     , active^#(unquote1(nil1())) -> c_34()
     , active^#(unquote1(cons1(X, Z))) ->
       c_35(fcons^#(unquote(X), unquote1(Z)))
     , active^#(fcons(X, Z)) -> c_36(cons^#(X, Z))
     , active^#(fcons(X1, X2)) -> c_37(fcons^#(X1, active(X2)))
     , active^#(fcons(X1, X2)) -> c_38(fcons^#(active(X1), X2))
     , sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2))
     , s^#(mark(X)) -> c_42(s^#(X))
     , s^#(ok(X)) -> c_43(s^#(X))
     , cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2))
     , first^#(X1, mark(X2)) -> c_46(first^#(X1, X2))
     , first^#(mark(X1), X2) -> c_47(first^#(X1, X2))
     , first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2))
     , from^#(mark(X)) -> c_49(from^#(X))
     , from^#(ok(X)) -> c_50(from^#(X))
     , sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2))
     , quote^#(ok(X)) -> c_54(quote^#(X))
     , s1^#(mark(X)) -> c_62(s1^#(X))
     , s1^#(ok(X)) -> c_63(s1^#(X))
     , first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2))
     , first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2))
     , first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2))
     , cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2))
     , cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2))
     , cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2))
     , unquote^#(mark(X)) -> c_64(unquote^#(X))
     , unquote^#(ok(X)) -> c_65(unquote^#(X))
     , unquote1^#(mark(X)) -> c_66(unquote1^#(X))
     , unquote1^#(ok(X)) -> c_67(unquote1^#(X))
     , fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2))
     , fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2))
     , fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2))
     , quote1^#(ok(X)) -> c_61(quote1^#(X))
     , proper^#(sel(X1, X2)) -> c_71(sel^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_72(s^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_73(cons^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_74()
     , proper^#(first(X1, X2)) -> c_75(first^#(proper(X1), proper(X2)))
     , proper^#(nil()) -> c_76()
     , proper^#(from(X)) -> c_77(from^#(proper(X)))
     , proper^#(sel1(X1, X2)) -> c_78(sel1^#(proper(X1), proper(X2)))
     , proper^#(quote(X)) -> c_79(quote^#(proper(X)))
     , proper^#(first1(X1, X2)) ->
       c_80(first1^#(proper(X1), proper(X2)))
     , proper^#(nil1()) -> c_81()
     , proper^#(cons1(X1, X2)) -> c_82(cons1^#(proper(X1), proper(X2)))
     , proper^#(01()) -> c_83()
     , proper^#(quote1(X)) -> c_84(quote1^#(proper(X)))
     , proper^#(s1(X)) -> c_85(s1^#(proper(X)))
     , proper^#(unquote(X)) -> c_86(unquote^#(proper(X)))
     , proper^#(unquote1(X)) -> c_87(unquote1^#(proper(X)))
     , proper^#(fcons(X1, X2)) -> c_88(fcons^#(proper(X1), proper(X2)))
     , top^#(mark(X)) -> c_89(top^#(proper(X)))
     , top^#(ok(X)) -> c_90(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^#(sel(X1, X2)) -> c_1(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_2(sel^#(active(X1), X2))
     , active^#(sel(s(X), cons(Y, Z))) -> c_3(sel^#(X, Z))
     , active^#(sel(0(), cons(X, Z))) -> c_4(X)
     , active^#(s(X)) -> c_5(s^#(active(X)))
     , active^#(cons(X1, X2)) -> c_6(cons^#(active(X1), X2))
     , active^#(first(X1, X2)) -> c_7(first^#(X1, active(X2)))
     , active^#(first(X1, X2)) -> c_8(first^#(active(X1), X2))
     , active^#(first(s(X), cons(Y, Z))) -> c_9(cons^#(Y, first(X, Z)))
     , active^#(first(0(), Z)) -> c_10()
     , active^#(from(X)) -> c_11(cons^#(X, from(s(X))))
     , active^#(from(X)) -> c_12(from^#(active(X)))
     , active^#(sel1(X1, X2)) -> c_13(sel1^#(X1, active(X2)))
     , active^#(sel1(X1, X2)) -> c_14(sel1^#(active(X1), X2))
     , active^#(sel1(s(X), cons(Y, Z))) -> c_15(sel1^#(X, Z))
     , active^#(sel1(0(), cons(X, Z))) -> c_16(quote^#(X))
     , active^#(quote(sel(X, Z))) -> c_17(sel1^#(X, Z))
     , active^#(quote(s(X))) -> c_18(s1^#(quote(X)))
     , active^#(quote(0())) -> c_19()
     , active^#(first1(X1, X2)) -> c_20(first1^#(X1, active(X2)))
     , active^#(first1(X1, X2)) -> c_21(first1^#(active(X1), X2))
     , active^#(first1(s(X), cons(Y, Z))) ->
       c_22(cons1^#(quote(Y), first1(X, Z)))
     , active^#(first1(0(), Z)) -> c_23()
     , active^#(cons1(X1, X2)) -> c_24(cons1^#(X1, active(X2)))
     , active^#(cons1(X1, X2)) -> c_25(cons1^#(active(X1), X2))
     , active^#(quote1(cons(X, Z))) ->
       c_26(cons1^#(quote(X), quote1(Z)))
     , active^#(quote1(first(X, Z))) -> c_27(first1^#(X, Z))
     , active^#(quote1(nil())) -> c_28()
     , active^#(s1(X)) -> c_29(s1^#(active(X)))
     , active^#(unquote(X)) -> c_30(unquote^#(active(X)))
     , active^#(unquote(01())) -> c_31()
     , active^#(unquote(s1(X))) -> c_32(s^#(unquote(X)))
     , active^#(unquote1(X)) -> c_33(unquote1^#(active(X)))
     , active^#(unquote1(nil1())) -> c_34()
     , active^#(unquote1(cons1(X, Z))) ->
       c_35(fcons^#(unquote(X), unquote1(Z)))
     , active^#(fcons(X, Z)) -> c_36(cons^#(X, Z))
     , active^#(fcons(X1, X2)) -> c_37(fcons^#(X1, active(X2)))
     , active^#(fcons(X1, X2)) -> c_38(fcons^#(active(X1), X2))
     , sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2))
     , s^#(mark(X)) -> c_42(s^#(X))
     , s^#(ok(X)) -> c_43(s^#(X))
     , cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2))
     , first^#(X1, mark(X2)) -> c_46(first^#(X1, X2))
     , first^#(mark(X1), X2) -> c_47(first^#(X1, X2))
     , first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2))
     , from^#(mark(X)) -> c_49(from^#(X))
     , from^#(ok(X)) -> c_50(from^#(X))
     , sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2))
     , quote^#(ok(X)) -> c_54(quote^#(X))
     , s1^#(mark(X)) -> c_62(s1^#(X))
     , s1^#(ok(X)) -> c_63(s1^#(X))
     , first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2))
     , first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2))
     , first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2))
     , cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2))
     , cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2))
     , cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2))
     , unquote^#(mark(X)) -> c_64(unquote^#(X))
     , unquote^#(ok(X)) -> c_65(unquote^#(X))
     , unquote1^#(mark(X)) -> c_66(unquote1^#(X))
     , unquote1^#(ok(X)) -> c_67(unquote1^#(X))
     , fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2))
     , fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2))
     , fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2))
     , quote1^#(ok(X)) -> c_61(quote1^#(X))
     , proper^#(sel(X1, X2)) -> c_71(sel^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_72(s^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_73(cons^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_74()
     , proper^#(first(X1, X2)) -> c_75(first^#(proper(X1), proper(X2)))
     , proper^#(nil()) -> c_76()
     , proper^#(from(X)) -> c_77(from^#(proper(X)))
     , proper^#(sel1(X1, X2)) -> c_78(sel1^#(proper(X1), proper(X2)))
     , proper^#(quote(X)) -> c_79(quote^#(proper(X)))
     , proper^#(first1(X1, X2)) ->
       c_80(first1^#(proper(X1), proper(X2)))
     , proper^#(nil1()) -> c_81()
     , proper^#(cons1(X1, X2)) -> c_82(cons1^#(proper(X1), proper(X2)))
     , proper^#(01()) -> c_83()
     , proper^#(quote1(X)) -> c_84(quote1^#(proper(X)))
     , proper^#(s1(X)) -> c_85(s1^#(proper(X)))
     , proper^#(unquote(X)) -> c_86(unquote^#(proper(X)))
     , proper^#(unquote1(X)) -> c_87(unquote1^#(proper(X)))
     , proper^#(fcons(X1, X2)) -> c_88(fcons^#(proper(X1), proper(X2)))
     , top^#(mark(X)) -> c_89(top^#(proper(X)))
     , top^#(ok(X)) -> c_90(top^#(active(X))) }
   Strict Trs:
     { active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(sel(0(), cons(X, Z))) -> mark(X)
     , active(s(X)) -> s(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(first(X1, X2)) -> first(X1, active(X2))
     , active(first(X1, X2)) -> first(active(X1), X2)
     , active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
     , active(first(0(), Z)) -> mark(nil())
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(from(X)) -> from(active(X))
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(sel1(0(), cons(X, Z))) -> mark(quote(X))
     , active(quote(sel(X, Z))) -> mark(sel1(X, Z))
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(0())) -> mark(01())
     , active(first1(X1, X2)) -> first1(X1, active(X2))
     , active(first1(X1, X2)) -> first1(active(X1), X2)
     , active(first1(s(X), cons(Y, Z))) ->
       mark(cons1(quote(Y), first1(X, Z)))
     , active(first1(0(), Z)) -> mark(nil1())
     , active(cons1(X1, X2)) -> cons1(X1, active(X2))
     , active(cons1(X1, X2)) -> cons1(active(X1), X2)
     , active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
     , active(quote1(first(X, Z))) -> mark(first1(X, Z))
     , active(quote1(nil())) -> mark(nil1())
     , active(s1(X)) -> s1(active(X))
     , active(unquote(X)) -> unquote(active(X))
     , active(unquote(01())) -> mark(0())
     , active(unquote(s1(X))) -> mark(s(unquote(X)))
     , active(unquote1(X)) -> unquote1(active(X))
     , active(unquote1(nil1())) -> mark(nil())
     , active(unquote1(cons1(X, Z))) ->
       mark(fcons(unquote(X), unquote1(Z)))
     , active(fcons(X, Z)) -> mark(cons(X, Z))
     , active(fcons(X1, X2)) -> fcons(X1, active(X2))
     , active(fcons(X1, X2)) -> fcons(active(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))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , first(X1, mark(X2)) -> mark(first(X1, X2))
     , first(mark(X1), X2) -> mark(first(X1, X2))
     , first(ok(X1), ok(X2)) -> ok(first(X1, X2))
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(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(ok(X)) -> ok(quote(X))
     , first1(X1, mark(X2)) -> mark(first1(X1, X2))
     , first1(mark(X1), X2) -> mark(first1(X1, X2))
     , first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
     , cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
     , cons1(mark(X1), X2) -> mark(cons1(X1, X2))
     , cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
     , quote1(ok(X)) -> ok(quote1(X))
     , s1(mark(X)) -> mark(s1(X))
     , s1(ok(X)) -> ok(s1(X))
     , unquote(mark(X)) -> mark(unquote(X))
     , unquote(ok(X)) -> ok(unquote(X))
     , unquote1(mark(X)) -> mark(unquote1(X))
     , unquote1(ok(X)) -> ok(unquote1(X))
     , fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
     , fcons(mark(X1), X2) -> mark(fcons(X1, X2))
     , fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(first(X1, X2)) -> first(proper(X1), proper(X2))
     , proper(nil()) -> ok(nil())
     , proper(from(X)) -> from(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
     , proper(nil1()) -> ok(nil1())
     , proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
     , proper(01()) -> ok(01())
     , proper(quote1(X)) -> quote1(proper(X))
     , proper(s1(X)) -> s1(proper(X))
     , proper(unquote(X)) -> unquote(proper(X))
     , proper(unquote1(X)) -> unquote1(proper(X))
     , proper(fcons(X1, X2)) -> fcons(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^#(sel(X1, X2)) -> c_1(sel^#(X1, active(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     2: active^#(sel(X1, X2)) -> c_2(sel^#(active(X1), X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     3: active^#(sel(s(X), cons(Y, Z))) -> c_3(sel^#(X, Z))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     4: active^#(sel(0(), cons(X, Z))) -> c_4(X)
        -->_1 top^#(ok(X)) -> c_90(top^#(active(X))) :90
        -->_1 top^#(mark(X)) -> c_89(top^#(proper(X))) :89
        -->_1 proper^#(fcons(X1, X2)) ->
              c_88(fcons^#(proper(X1), proper(X2))) :88
        -->_1 proper^#(unquote1(X)) -> c_87(unquote1^#(proper(X))) :87
        -->_1 proper^#(unquote(X)) -> c_86(unquote^#(proper(X))) :86
        -->_1 proper^#(s1(X)) -> c_85(s1^#(proper(X))) :85
        -->_1 proper^#(quote1(X)) -> c_84(quote1^#(proper(X))) :84
        -->_1 proper^#(cons1(X1, X2)) ->
              c_82(cons1^#(proper(X1), proper(X2))) :82
        -->_1 proper^#(first1(X1, X2)) ->
              c_80(first1^#(proper(X1), proper(X2))) :80
        -->_1 proper^#(quote(X)) -> c_79(quote^#(proper(X))) :79
        -->_1 proper^#(sel1(X1, X2)) ->
              c_78(sel1^#(proper(X1), proper(X2))) :78
        -->_1 proper^#(from(X)) -> c_77(from^#(proper(X))) :77
        -->_1 proper^#(first(X1, X2)) ->
              c_75(first^#(proper(X1), proper(X2))) :75
        -->_1 proper^#(cons(X1, X2)) ->
              c_73(cons^#(proper(X1), proper(X2))) :73
        -->_1 proper^#(s(X)) -> c_72(s^#(proper(X))) :72
        -->_1 proper^#(sel(X1, X2)) ->
              c_71(sel^#(proper(X1), proper(X2))) :71
        -->_1 quote1^#(ok(X)) -> c_61(quote1^#(X)) :70
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
        -->_1 unquote1^#(ok(X)) -> c_67(unquote1^#(X)) :66
        -->_1 unquote1^#(mark(X)) -> c_66(unquote1^#(X)) :65
        -->_1 unquote^#(ok(X)) -> c_65(unquote^#(X)) :64
        -->_1 unquote^#(mark(X)) -> c_64(unquote^#(X)) :63
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
        -->_1 s1^#(ok(X)) -> c_63(s1^#(X)) :56
        -->_1 s1^#(mark(X)) -> c_62(s1^#(X)) :55
        -->_1 quote^#(ok(X)) -> c_54(quote^#(X)) :54
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
        -->_1 from^#(ok(X)) -> c_50(from^#(X)) :50
        -->_1 from^#(mark(X)) -> c_49(from^#(X)) :49
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
        -->_1 s^#(ok(X)) -> c_43(s^#(X)) :43
        -->_1 s^#(mark(X)) -> c_42(s^#(X)) :42
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
        -->_1 active^#(fcons(X1, X2)) -> c_38(fcons^#(active(X1), X2)) :38
        -->_1 active^#(fcons(X1, X2)) -> c_37(fcons^#(X1, active(X2))) :37
        -->_1 active^#(fcons(X, Z)) -> c_36(cons^#(X, Z)) :36
        -->_1 active^#(unquote1(cons1(X, Z))) ->
              c_35(fcons^#(unquote(X), unquote1(Z))) :35
        -->_1 active^#(unquote1(X)) -> c_33(unquote1^#(active(X))) :33
        -->_1 active^#(unquote(s1(X))) -> c_32(s^#(unquote(X))) :32
        -->_1 active^#(unquote(X)) -> c_30(unquote^#(active(X))) :30
        -->_1 active^#(s1(X)) -> c_29(s1^#(active(X))) :29
        -->_1 active^#(quote1(first(X, Z))) -> c_27(first1^#(X, Z)) :27
        -->_1 active^#(quote1(cons(X, Z))) ->
              c_26(cons1^#(quote(X), quote1(Z))) :26
        -->_1 active^#(cons1(X1, X2)) -> c_25(cons1^#(active(X1), X2)) :25
        -->_1 active^#(cons1(X1, X2)) -> c_24(cons1^#(X1, active(X2))) :24
        -->_1 active^#(first1(s(X), cons(Y, Z))) ->
              c_22(cons1^#(quote(Y), first1(X, Z))) :22
        -->_1 active^#(first1(X1, X2)) ->
              c_21(first1^#(active(X1), X2)) :21
        -->_1 active^#(first1(X1, X2)) ->
              c_20(first1^#(X1, active(X2))) :20
        -->_1 active^#(quote(s(X))) -> c_18(s1^#(quote(X))) :18
        -->_1 active^#(quote(sel(X, Z))) -> c_17(sel1^#(X, Z)) :17
        -->_1 active^#(sel1(0(), cons(X, Z))) -> c_16(quote^#(X)) :16
        -->_1 active^#(sel1(s(X), cons(Y, Z))) -> c_15(sel1^#(X, Z)) :15
        -->_1 active^#(sel1(X1, X2)) -> c_14(sel1^#(active(X1), X2)) :14
        -->_1 active^#(sel1(X1, X2)) -> c_13(sel1^#(X1, active(X2))) :13
        -->_1 active^#(from(X)) -> c_12(from^#(active(X))) :12
        -->_1 active^#(from(X)) -> c_11(cons^#(X, from(s(X)))) :11
        -->_1 active^#(first(s(X), cons(Y, Z))) ->
              c_9(cons^#(Y, first(X, Z))) :9
        -->_1 active^#(first(X1, X2)) -> c_8(first^#(active(X1), X2)) :8
        -->_1 active^#(first(X1, X2)) -> c_7(first^#(X1, active(X2))) :7
        -->_1 active^#(cons(X1, X2)) -> c_6(cons^#(active(X1), X2)) :6
        -->_1 active^#(s(X)) -> c_5(s^#(active(X))) :5
        -->_1 proper^#(01()) -> c_83() :83
        -->_1 proper^#(nil1()) -> c_81() :81
        -->_1 proper^#(nil()) -> c_76() :76
        -->_1 proper^#(0()) -> c_74() :74
        -->_1 active^#(unquote1(nil1())) -> c_34() :34
        -->_1 active^#(unquote(01())) -> c_31() :31
        -->_1 active^#(quote1(nil())) -> c_28() :28
        -->_1 active^#(first1(0(), Z)) -> c_23() :23
        -->_1 active^#(quote(0())) -> c_19() :19
        -->_1 active^#(first(0(), Z)) -> c_10() :10
        -->_1 active^#(sel(0(), cons(X, Z))) -> c_4(X) :4
        -->_1 active^#(sel(s(X), cons(Y, Z))) -> c_3(sel^#(X, Z)) :3
        -->_1 active^#(sel(X1, X2)) -> c_2(sel^#(active(X1), X2)) :2
        -->_1 active^#(sel(X1, X2)) -> c_1(sel^#(X1, active(X2))) :1
     
     5: active^#(s(X)) -> c_5(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_43(s^#(X)) :43
        -->_1 s^#(mark(X)) -> c_42(s^#(X)) :42
     
     6: active^#(cons(X1, X2)) -> c_6(cons^#(active(X1), X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     7: active^#(first(X1, X2)) -> c_7(first^#(X1, active(X2)))
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
     
     8: active^#(first(X1, X2)) -> c_8(first^#(active(X1), X2))
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
     
     9: active^#(first(s(X), cons(Y, Z))) -> c_9(cons^#(Y, first(X, Z)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     10: active^#(first(0(), Z)) -> c_10()
     
     11: active^#(from(X)) -> c_11(cons^#(X, from(s(X))))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     12: active^#(from(X)) -> c_12(from^#(active(X)))
        -->_1 from^#(ok(X)) -> c_50(from^#(X)) :50
        -->_1 from^#(mark(X)) -> c_49(from^#(X)) :49
     
     13: active^#(sel1(X1, X2)) -> c_13(sel1^#(X1, active(X2)))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     14: active^#(sel1(X1, X2)) -> c_14(sel1^#(active(X1), X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     15: active^#(sel1(s(X), cons(Y, Z))) -> c_15(sel1^#(X, Z))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     16: active^#(sel1(0(), cons(X, Z))) -> c_16(quote^#(X))
        -->_1 quote^#(ok(X)) -> c_54(quote^#(X)) :54
     
     17: active^#(quote(sel(X, Z))) -> c_17(sel1^#(X, Z))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     18: active^#(quote(s(X))) -> c_18(s1^#(quote(X)))
        -->_1 s1^#(ok(X)) -> c_63(s1^#(X)) :56
        -->_1 s1^#(mark(X)) -> c_62(s1^#(X)) :55
     
     19: active^#(quote(0())) -> c_19()
     
     20: active^#(first1(X1, X2)) -> c_20(first1^#(X1, active(X2)))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     21: active^#(first1(X1, X2)) -> c_21(first1^#(active(X1), X2))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     22: active^#(first1(s(X), cons(Y, Z))) ->
         c_22(cons1^#(quote(Y), first1(X, Z)))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     23: active^#(first1(0(), Z)) -> c_23()
     
     24: active^#(cons1(X1, X2)) -> c_24(cons1^#(X1, active(X2)))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     25: active^#(cons1(X1, X2)) -> c_25(cons1^#(active(X1), X2))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     26: active^#(quote1(cons(X, Z))) ->
         c_26(cons1^#(quote(X), quote1(Z)))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     27: active^#(quote1(first(X, Z))) -> c_27(first1^#(X, Z))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     28: active^#(quote1(nil())) -> c_28()
     
     29: active^#(s1(X)) -> c_29(s1^#(active(X)))
        -->_1 s1^#(ok(X)) -> c_63(s1^#(X)) :56
        -->_1 s1^#(mark(X)) -> c_62(s1^#(X)) :55
     
     30: active^#(unquote(X)) -> c_30(unquote^#(active(X)))
        -->_1 unquote^#(ok(X)) -> c_65(unquote^#(X)) :64
        -->_1 unquote^#(mark(X)) -> c_64(unquote^#(X)) :63
     
     31: active^#(unquote(01())) -> c_31()
     
     32: active^#(unquote(s1(X))) -> c_32(s^#(unquote(X)))
        -->_1 s^#(ok(X)) -> c_43(s^#(X)) :43
        -->_1 s^#(mark(X)) -> c_42(s^#(X)) :42
     
     33: active^#(unquote1(X)) -> c_33(unquote1^#(active(X)))
        -->_1 unquote1^#(ok(X)) -> c_67(unquote1^#(X)) :66
        -->_1 unquote1^#(mark(X)) -> c_66(unquote1^#(X)) :65
     
     34: active^#(unquote1(nil1())) -> c_34()
     
     35: active^#(unquote1(cons1(X, Z))) ->
         c_35(fcons^#(unquote(X), unquote1(Z)))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     36: active^#(fcons(X, Z)) -> c_36(cons^#(X, Z))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     37: active^#(fcons(X1, X2)) -> c_37(fcons^#(X1, active(X2)))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     38: active^#(fcons(X1, X2)) -> c_38(fcons^#(active(X1), X2))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     39: sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     40: sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     41: sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     42: s^#(mark(X)) -> c_42(s^#(X))
        -->_1 s^#(ok(X)) -> c_43(s^#(X)) :43
        -->_1 s^#(mark(X)) -> c_42(s^#(X)) :42
     
     43: s^#(ok(X)) -> c_43(s^#(X))
        -->_1 s^#(ok(X)) -> c_43(s^#(X)) :43
        -->_1 s^#(mark(X)) -> c_42(s^#(X)) :42
     
     44: cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     45: cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     46: first^#(X1, mark(X2)) -> c_46(first^#(X1, X2))
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
     
     47: first^#(mark(X1), X2) -> c_47(first^#(X1, X2))
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
     
     48: first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2))
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
     
     49: from^#(mark(X)) -> c_49(from^#(X))
        -->_1 from^#(ok(X)) -> c_50(from^#(X)) :50
        -->_1 from^#(mark(X)) -> c_49(from^#(X)) :49
     
     50: from^#(ok(X)) -> c_50(from^#(X))
        -->_1 from^#(ok(X)) -> c_50(from^#(X)) :50
        -->_1 from^#(mark(X)) -> c_49(from^#(X)) :49
     
     51: sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     52: sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     53: sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     54: quote^#(ok(X)) -> c_54(quote^#(X))
        -->_1 quote^#(ok(X)) -> c_54(quote^#(X)) :54
     
     55: s1^#(mark(X)) -> c_62(s1^#(X))
        -->_1 s1^#(ok(X)) -> c_63(s1^#(X)) :56
        -->_1 s1^#(mark(X)) -> c_62(s1^#(X)) :55
     
     56: s1^#(ok(X)) -> c_63(s1^#(X))
        -->_1 s1^#(ok(X)) -> c_63(s1^#(X)) :56
        -->_1 s1^#(mark(X)) -> c_62(s1^#(X)) :55
     
     57: first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     58: first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     59: first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     60: cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     61: cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     62: cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     63: unquote^#(mark(X)) -> c_64(unquote^#(X))
        -->_1 unquote^#(ok(X)) -> c_65(unquote^#(X)) :64
        -->_1 unquote^#(mark(X)) -> c_64(unquote^#(X)) :63
     
     64: unquote^#(ok(X)) -> c_65(unquote^#(X))
        -->_1 unquote^#(ok(X)) -> c_65(unquote^#(X)) :64
        -->_1 unquote^#(mark(X)) -> c_64(unquote^#(X)) :63
     
     65: unquote1^#(mark(X)) -> c_66(unquote1^#(X))
        -->_1 unquote1^#(ok(X)) -> c_67(unquote1^#(X)) :66
        -->_1 unquote1^#(mark(X)) -> c_66(unquote1^#(X)) :65
     
     66: unquote1^#(ok(X)) -> c_67(unquote1^#(X))
        -->_1 unquote1^#(ok(X)) -> c_67(unquote1^#(X)) :66
        -->_1 unquote1^#(mark(X)) -> c_66(unquote1^#(X)) :65
     
     67: fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     68: fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     69: fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     70: quote1^#(ok(X)) -> c_61(quote1^#(X))
        -->_1 quote1^#(ok(X)) -> c_61(quote1^#(X)) :70
     
     71: proper^#(sel(X1, X2)) -> c_71(sel^#(proper(X1), proper(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2)) :41
        -->_1 sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2)) :40
        -->_1 sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2)) :39
     
     72: proper^#(s(X)) -> c_72(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_43(s^#(X)) :43
        -->_1 s^#(mark(X)) -> c_42(s^#(X)) :42
     
     73: proper^#(cons(X1, X2)) -> c_73(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2)) :45
        -->_1 cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2)) :44
     
     74: proper^#(0()) -> c_74()
     
     75: proper^#(first(X1, X2)) ->
         c_75(first^#(proper(X1), proper(X2)))
        -->_1 first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2)) :48
        -->_1 first^#(mark(X1), X2) -> c_47(first^#(X1, X2)) :47
        -->_1 first^#(X1, mark(X2)) -> c_46(first^#(X1, X2)) :46
     
     76: proper^#(nil()) -> c_76()
     
     77: proper^#(from(X)) -> c_77(from^#(proper(X)))
        -->_1 from^#(ok(X)) -> c_50(from^#(X)) :50
        -->_1 from^#(mark(X)) -> c_49(from^#(X)) :49
     
     78: proper^#(sel1(X1, X2)) -> c_78(sel1^#(proper(X1), proper(X2)))
        -->_1 sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2)) :53
        -->_1 sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2)) :52
        -->_1 sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2)) :51
     
     79: proper^#(quote(X)) -> c_79(quote^#(proper(X)))
        -->_1 quote^#(ok(X)) -> c_54(quote^#(X)) :54
     
     80: proper^#(first1(X1, X2)) ->
         c_80(first1^#(proper(X1), proper(X2)))
        -->_1 first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2)) :59
        -->_1 first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2)) :58
        -->_1 first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2)) :57
     
     81: proper^#(nil1()) -> c_81()
     
     82: proper^#(cons1(X1, X2)) ->
         c_82(cons1^#(proper(X1), proper(X2)))
        -->_1 cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2)) :62
        -->_1 cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2)) :61
        -->_1 cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2)) :60
     
     83: proper^#(01()) -> c_83()
     
     84: proper^#(quote1(X)) -> c_84(quote1^#(proper(X)))
        -->_1 quote1^#(ok(X)) -> c_61(quote1^#(X)) :70
     
     85: proper^#(s1(X)) -> c_85(s1^#(proper(X)))
        -->_1 s1^#(ok(X)) -> c_63(s1^#(X)) :56
        -->_1 s1^#(mark(X)) -> c_62(s1^#(X)) :55
     
     86: proper^#(unquote(X)) -> c_86(unquote^#(proper(X)))
        -->_1 unquote^#(ok(X)) -> c_65(unquote^#(X)) :64
        -->_1 unquote^#(mark(X)) -> c_64(unquote^#(X)) :63
     
     87: proper^#(unquote1(X)) -> c_87(unquote1^#(proper(X)))
        -->_1 unquote1^#(ok(X)) -> c_67(unquote1^#(X)) :66
        -->_1 unquote1^#(mark(X)) -> c_66(unquote1^#(X)) :65
     
     88: proper^#(fcons(X1, X2)) ->
         c_88(fcons^#(proper(X1), proper(X2)))
        -->_1 fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2)) :69
        -->_1 fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2)) :68
        -->_1 fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2)) :67
     
     89: top^#(mark(X)) -> c_89(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_90(top^#(active(X))) :90
        -->_1 top^#(mark(X)) -> c_89(top^#(proper(X))) :89
     
     90: top^#(ok(X)) -> c_90(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_90(top^#(active(X))) :90
        -->_1 top^#(mark(X)) -> c_89(top^#(proper(X))) :89
     
   
   Only the nodes
   {39,41,40,42,43,44,45,46,48,47,49,50,51,53,52,54,55,56,57,59,58,60,62,61,63,64,65,66,67,69,68,70,74,76,81,83,89,90}
   are reachable from nodes
   {39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,74,76,81,83,89,90}
   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:
     { sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2))
     , s^#(mark(X)) -> c_42(s^#(X))
     , s^#(ok(X)) -> c_43(s^#(X))
     , cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2))
     , first^#(X1, mark(X2)) -> c_46(first^#(X1, X2))
     , first^#(mark(X1), X2) -> c_47(first^#(X1, X2))
     , first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2))
     , from^#(mark(X)) -> c_49(from^#(X))
     , from^#(ok(X)) -> c_50(from^#(X))
     , sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2))
     , quote^#(ok(X)) -> c_54(quote^#(X))
     , s1^#(mark(X)) -> c_62(s1^#(X))
     , s1^#(ok(X)) -> c_63(s1^#(X))
     , first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2))
     , first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2))
     , first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2))
     , cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2))
     , cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2))
     , cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2))
     , unquote^#(mark(X)) -> c_64(unquote^#(X))
     , unquote^#(ok(X)) -> c_65(unquote^#(X))
     , unquote1^#(mark(X)) -> c_66(unquote1^#(X))
     , unquote1^#(ok(X)) -> c_67(unquote1^#(X))
     , fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2))
     , fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2))
     , fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2))
     , quote1^#(ok(X)) -> c_61(quote1^#(X))
     , proper^#(0()) -> c_74()
     , proper^#(nil()) -> c_76()
     , proper^#(nil1()) -> c_81()
     , proper^#(01()) -> c_83()
     , top^#(mark(X)) -> c_89(top^#(proper(X)))
     , top^#(ok(X)) -> c_90(top^#(active(X))) }
   Strict Trs:
     { active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(sel(0(), cons(X, Z))) -> mark(X)
     , active(s(X)) -> s(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(first(X1, X2)) -> first(X1, active(X2))
     , active(first(X1, X2)) -> first(active(X1), X2)
     , active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
     , active(first(0(), Z)) -> mark(nil())
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(from(X)) -> from(active(X))
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(sel1(0(), cons(X, Z))) -> mark(quote(X))
     , active(quote(sel(X, Z))) -> mark(sel1(X, Z))
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(0())) -> mark(01())
     , active(first1(X1, X2)) -> first1(X1, active(X2))
     , active(first1(X1, X2)) -> first1(active(X1), X2)
     , active(first1(s(X), cons(Y, Z))) ->
       mark(cons1(quote(Y), first1(X, Z)))
     , active(first1(0(), Z)) -> mark(nil1())
     , active(cons1(X1, X2)) -> cons1(X1, active(X2))
     , active(cons1(X1, X2)) -> cons1(active(X1), X2)
     , active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
     , active(quote1(first(X, Z))) -> mark(first1(X, Z))
     , active(quote1(nil())) -> mark(nil1())
     , active(s1(X)) -> s1(active(X))
     , active(unquote(X)) -> unquote(active(X))
     , active(unquote(01())) -> mark(0())
     , active(unquote(s1(X))) -> mark(s(unquote(X)))
     , active(unquote1(X)) -> unquote1(active(X))
     , active(unquote1(nil1())) -> mark(nil())
     , active(unquote1(cons1(X, Z))) ->
       mark(fcons(unquote(X), unquote1(Z)))
     , active(fcons(X, Z)) -> mark(cons(X, Z))
     , active(fcons(X1, X2)) -> fcons(X1, active(X2))
     , active(fcons(X1, X2)) -> fcons(active(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))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , first(X1, mark(X2)) -> mark(first(X1, X2))
     , first(mark(X1), X2) -> mark(first(X1, X2))
     , first(ok(X1), ok(X2)) -> ok(first(X1, X2))
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(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(ok(X)) -> ok(quote(X))
     , first1(X1, mark(X2)) -> mark(first1(X1, X2))
     , first1(mark(X1), X2) -> mark(first1(X1, X2))
     , first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
     , cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
     , cons1(mark(X1), X2) -> mark(cons1(X1, X2))
     , cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
     , quote1(ok(X)) -> ok(quote1(X))
     , s1(mark(X)) -> mark(s1(X))
     , s1(ok(X)) -> ok(s1(X))
     , unquote(mark(X)) -> mark(unquote(X))
     , unquote(ok(X)) -> ok(unquote(X))
     , unquote1(mark(X)) -> mark(unquote1(X))
     , unquote1(ok(X)) -> ok(unquote1(X))
     , fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
     , fcons(mark(X1), X2) -> mark(fcons(X1, X2))
     , fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(first(X1, X2)) -> first(proper(X1), proper(X2))
     , proper(nil()) -> ok(nil())
     , proper(from(X)) -> from(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
     , proper(nil1()) -> ok(nil1())
     , proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
     , proper(01()) -> ok(01())
     , proper(quote1(X)) -> quote1(proper(X))
     , proper(s1(X)) -> s1(proper(X))
     , proper(unquote(X)) -> unquote(proper(X))
     , proper(unquote1(X)) -> unquote1(proper(X))
     , proper(fcons(X1, X2)) -> fcons(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 {33,34,35,36} by
   applications of Pre({33,34,35,36}) = {}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2))
       , 2: sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2))
       , 3: sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2))
       , 4: s^#(mark(X)) -> c_42(s^#(X))
       , 5: s^#(ok(X)) -> c_43(s^#(X))
       , 6: cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2))
       , 7: cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2))
       , 8: first^#(X1, mark(X2)) -> c_46(first^#(X1, X2))
       , 9: first^#(mark(X1), X2) -> c_47(first^#(X1, X2))
       , 10: first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2))
       , 11: from^#(mark(X)) -> c_49(from^#(X))
       , 12: from^#(ok(X)) -> c_50(from^#(X))
       , 13: sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2))
       , 14: sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2))
       , 15: sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2))
       , 16: quote^#(ok(X)) -> c_54(quote^#(X))
       , 17: s1^#(mark(X)) -> c_62(s1^#(X))
       , 18: s1^#(ok(X)) -> c_63(s1^#(X))
       , 19: first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2))
       , 20: first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2))
       , 21: first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2))
       , 22: cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2))
       , 23: cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2))
       , 24: cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2))
       , 25: unquote^#(mark(X)) -> c_64(unquote^#(X))
       , 26: unquote^#(ok(X)) -> c_65(unquote^#(X))
       , 27: unquote1^#(mark(X)) -> c_66(unquote1^#(X))
       , 28: unquote1^#(ok(X)) -> c_67(unquote1^#(X))
       , 29: fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2))
       , 30: fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2))
       , 31: fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2))
       , 32: quote1^#(ok(X)) -> c_61(quote1^#(X))
       , 33: proper^#(0()) -> c_74()
       , 34: proper^#(nil()) -> c_76()
       , 35: proper^#(nil1()) -> c_81()
       , 36: proper^#(01()) -> c_83()
       , 37: top^#(mark(X)) -> c_89(top^#(proper(X)))
       , 38: top^#(ok(X)) -> c_90(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { sel^#(X1, mark(X2)) -> c_39(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_40(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_41(sel^#(X1, X2))
     , s^#(mark(X)) -> c_42(s^#(X))
     , s^#(ok(X)) -> c_43(s^#(X))
     , cons^#(mark(X1), X2) -> c_44(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_45(cons^#(X1, X2))
     , first^#(X1, mark(X2)) -> c_46(first^#(X1, X2))
     , first^#(mark(X1), X2) -> c_47(first^#(X1, X2))
     , first^#(ok(X1), ok(X2)) -> c_48(first^#(X1, X2))
     , from^#(mark(X)) -> c_49(from^#(X))
     , from^#(ok(X)) -> c_50(from^#(X))
     , sel1^#(X1, mark(X2)) -> c_51(sel1^#(X1, X2))
     , sel1^#(mark(X1), X2) -> c_52(sel1^#(X1, X2))
     , sel1^#(ok(X1), ok(X2)) -> c_53(sel1^#(X1, X2))
     , quote^#(ok(X)) -> c_54(quote^#(X))
     , s1^#(mark(X)) -> c_62(s1^#(X))
     , s1^#(ok(X)) -> c_63(s1^#(X))
     , first1^#(X1, mark(X2)) -> c_55(first1^#(X1, X2))
     , first1^#(mark(X1), X2) -> c_56(first1^#(X1, X2))
     , first1^#(ok(X1), ok(X2)) -> c_57(first1^#(X1, X2))
     , cons1^#(X1, mark(X2)) -> c_58(cons1^#(X1, X2))
     , cons1^#(mark(X1), X2) -> c_59(cons1^#(X1, X2))
     , cons1^#(ok(X1), ok(X2)) -> c_60(cons1^#(X1, X2))
     , unquote^#(mark(X)) -> c_64(unquote^#(X))
     , unquote^#(ok(X)) -> c_65(unquote^#(X))
     , unquote1^#(mark(X)) -> c_66(unquote1^#(X))
     , unquote1^#(ok(X)) -> c_67(unquote1^#(X))
     , fcons^#(X1, mark(X2)) -> c_68(fcons^#(X1, X2))
     , fcons^#(mark(X1), X2) -> c_69(fcons^#(X1, X2))
     , fcons^#(ok(X1), ok(X2)) -> c_70(fcons^#(X1, X2))
     , quote1^#(ok(X)) -> c_61(quote1^#(X))
     , top^#(mark(X)) -> c_89(top^#(proper(X)))
     , top^#(ok(X)) -> c_90(top^#(active(X))) }
   Strict Trs:
     { active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(sel(0(), cons(X, Z))) -> mark(X)
     , active(s(X)) -> s(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(first(X1, X2)) -> first(X1, active(X2))
     , active(first(X1, X2)) -> first(active(X1), X2)
     , active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
     , active(first(0(), Z)) -> mark(nil())
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(from(X)) -> from(active(X))
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(sel1(0(), cons(X, Z))) -> mark(quote(X))
     , active(quote(sel(X, Z))) -> mark(sel1(X, Z))
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(0())) -> mark(01())
     , active(first1(X1, X2)) -> first1(X1, active(X2))
     , active(first1(X1, X2)) -> first1(active(X1), X2)
     , active(first1(s(X), cons(Y, Z))) ->
       mark(cons1(quote(Y), first1(X, Z)))
     , active(first1(0(), Z)) -> mark(nil1())
     , active(cons1(X1, X2)) -> cons1(X1, active(X2))
     , active(cons1(X1, X2)) -> cons1(active(X1), X2)
     , active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
     , active(quote1(first(X, Z))) -> mark(first1(X, Z))
     , active(quote1(nil())) -> mark(nil1())
     , active(s1(X)) -> s1(active(X))
     , active(unquote(X)) -> unquote(active(X))
     , active(unquote(01())) -> mark(0())
     , active(unquote(s1(X))) -> mark(s(unquote(X)))
     , active(unquote1(X)) -> unquote1(active(X))
     , active(unquote1(nil1())) -> mark(nil())
     , active(unquote1(cons1(X, Z))) ->
       mark(fcons(unquote(X), unquote1(Z)))
     , active(fcons(X, Z)) -> mark(cons(X, Z))
     , active(fcons(X1, X2)) -> fcons(X1, active(X2))
     , active(fcons(X1, X2)) -> fcons(active(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))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , first(X1, mark(X2)) -> mark(first(X1, X2))
     , first(mark(X1), X2) -> mark(first(X1, X2))
     , first(ok(X1), ok(X2)) -> ok(first(X1, X2))
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(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(ok(X)) -> ok(quote(X))
     , first1(X1, mark(X2)) -> mark(first1(X1, X2))
     , first1(mark(X1), X2) -> mark(first1(X1, X2))
     , first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
     , cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
     , cons1(mark(X1), X2) -> mark(cons1(X1, X2))
     , cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
     , quote1(ok(X)) -> ok(quote1(X))
     , s1(mark(X)) -> mark(s1(X))
     , s1(ok(X)) -> ok(s1(X))
     , unquote(mark(X)) -> mark(unquote(X))
     , unquote(ok(X)) -> ok(unquote(X))
     , unquote1(mark(X)) -> mark(unquote1(X))
     , unquote1(ok(X)) -> ok(unquote1(X))
     , fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
     , fcons(mark(X1), X2) -> mark(fcons(X1, X2))
     , fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(first(X1, X2)) -> first(proper(X1), proper(X2))
     , proper(nil()) -> ok(nil())
     , proper(from(X)) -> from(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
     , proper(nil1()) -> ok(nil1())
     , proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
     , proper(01()) -> ok(01())
     , proper(quote1(X)) -> quote1(proper(X))
     , proper(s1(X)) -> s1(proper(X))
     , proper(unquote(X)) -> unquote(proper(X))
     , proper(unquote1(X)) -> unquote1(proper(X))
     , proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { proper^#(0()) -> c_74()
     , proper^#(nil()) -> c_76()
     , proper^#(nil1()) -> c_81()
     , proper^#(01()) -> c_83() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..