MAYBE

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

Strict Trs:
  { active(from(X)) -> from(active(X))
  , active(from(X)) -> mark(cons(X, from(s(X))))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(s(X)) -> s(active(X))
  , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
  , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
  , active(2ndspos(s(N), cons(X, Z))) ->
    mark(2ndspos(s(N), cons2(X, Z)))
  , active(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
    mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
  , active(2ndspos(0(), Z)) -> mark(rnil())
  , active(cons2(X1, X2)) -> cons2(X1, active(X2))
  , active(rcons(X1, X2)) -> rcons(X1, active(X2))
  , active(rcons(X1, X2)) -> rcons(active(X1), X2)
  , active(posrecip(X)) -> posrecip(active(X))
  , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
  , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
  , active(2ndsneg(s(N), cons(X, Z))) ->
    mark(2ndsneg(s(N), cons2(X, Z)))
  , active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
    mark(rcons(negrecip(Y), 2ndspos(N, Z)))
  , active(2ndsneg(0(), Z)) -> mark(rnil())
  , active(negrecip(X)) -> negrecip(active(X))
  , active(pi(X)) -> mark(2ndspos(X, from(0())))
  , active(pi(X)) -> pi(active(X))
  , active(plus(X1, X2)) -> plus(X1, active(X2))
  , active(plus(X1, X2)) -> plus(active(X1), X2)
  , active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
  , active(plus(0(), Y)) -> mark(Y)
  , active(times(X1, X2)) -> times(X1, active(X2))
  , active(times(X1, X2)) -> times(active(X1), X2)
  , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
  , active(times(0(), Y)) -> mark(0())
  , active(square(X)) -> mark(times(X, X))
  , active(square(X)) -> square(active(X))
  , from(mark(X)) -> mark(from(X))
  , from(ok(X)) -> ok(from(X))
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
  , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
  , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))
  , cons2(X1, mark(X2)) -> mark(cons2(X1, X2))
  , cons2(ok(X1), ok(X2)) -> ok(cons2(X1, X2))
  , rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
  , rcons(mark(X1), X2) -> mark(rcons(X1, X2))
  , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
  , posrecip(mark(X)) -> mark(posrecip(X))
  , posrecip(ok(X)) -> ok(posrecip(X))
  , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
  , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
  , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2))
  , negrecip(mark(X)) -> mark(negrecip(X))
  , negrecip(ok(X)) -> ok(negrecip(X))
  , pi(mark(X)) -> mark(pi(X))
  , pi(ok(X)) -> ok(pi(X))
  , plus(X1, mark(X2)) -> mark(plus(X1, X2))
  , plus(mark(X1), X2) -> mark(plus(X1, X2))
  , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
  , times(X1, mark(X2)) -> mark(times(X1, X2))
  , times(mark(X1), X2) -> mark(times(X1, X2))
  , times(ok(X1), ok(X2)) -> ok(times(X1, X2))
  , square(mark(X)) -> mark(square(X))
  , square(ok(X)) -> ok(square(X))
  , proper(from(X)) -> from(proper(X))
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(rnil()) -> ok(rnil())
  , proper(cons2(X1, X2)) -> cons2(proper(X1), proper(X2))
  , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
  , proper(posrecip(X)) -> posrecip(proper(X))
  , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
  , proper(negrecip(X)) -> negrecip(proper(X))
  , proper(pi(X)) -> pi(proper(X))
  , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
  , proper(times(X1, X2)) -> times(proper(X1), proper(X2))
  , proper(square(X)) -> square(proper(X))
  , proper(nil()) -> ok(nil())
  , top(mark(X)) -> top(proper(X))
  , top(ok(X)) -> top(active(X)) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { active^#(from(X)) -> c_1(from^#(active(X)))
     , active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
     , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
     , active^#(s(X)) -> c_4(s^#(active(X)))
     , active^#(2ndspos(X1, X2)) -> c_5(2ndspos^#(X1, active(X2)))
     , active^#(2ndspos(X1, X2)) -> c_6(2ndspos^#(active(X1), X2))
     , active^#(2ndspos(s(N), cons(X, Z))) ->
       c_7(2ndspos^#(s(N), cons2(X, Z)))
     , active^#(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
       c_8(rcons^#(posrecip(Y), 2ndsneg(N, Z)))
     , active^#(2ndspos(0(), Z)) -> c_9()
     , active^#(cons2(X1, X2)) -> c_10(cons2^#(X1, active(X2)))
     , active^#(rcons(X1, X2)) -> c_11(rcons^#(X1, active(X2)))
     , active^#(rcons(X1, X2)) -> c_12(rcons^#(active(X1), X2))
     , active^#(posrecip(X)) -> c_13(posrecip^#(active(X)))
     , active^#(2ndsneg(X1, X2)) -> c_14(2ndsneg^#(X1, active(X2)))
     , active^#(2ndsneg(X1, X2)) -> c_15(2ndsneg^#(active(X1), X2))
     , active^#(2ndsneg(s(N), cons(X, Z))) ->
       c_16(2ndsneg^#(s(N), cons2(X, Z)))
     , active^#(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
       c_17(rcons^#(negrecip(Y), 2ndspos(N, Z)))
     , active^#(2ndsneg(0(), Z)) -> c_18()
     , active^#(negrecip(X)) -> c_19(negrecip^#(active(X)))
     , active^#(pi(X)) -> c_20(2ndspos^#(X, from(0())))
     , active^#(pi(X)) -> c_21(pi^#(active(X)))
     , active^#(plus(X1, X2)) -> c_22(plus^#(X1, active(X2)))
     , active^#(plus(X1, X2)) -> c_23(plus^#(active(X1), X2))
     , active^#(plus(s(X), Y)) -> c_24(s^#(plus(X, Y)))
     , active^#(plus(0(), Y)) -> c_25(Y)
     , active^#(times(X1, X2)) -> c_26(times^#(X1, active(X2)))
     , active^#(times(X1, X2)) -> c_27(times^#(active(X1), X2))
     , active^#(times(s(X), Y)) -> c_28(plus^#(Y, times(X, Y)))
     , active^#(times(0(), Y)) -> c_29()
     , active^#(square(X)) -> c_30(times^#(X, X))
     , active^#(square(X)) -> c_31(square^#(active(X)))
     , from^#(mark(X)) -> c_32(from^#(X))
     , from^#(ok(X)) -> c_33(from^#(X))
     , cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2))
     , s^#(mark(X)) -> c_36(s^#(X))
     , s^#(ok(X)) -> c_37(s^#(X))
     , 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2))
     , 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2))
     , 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2))
     , rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2))
     , rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2))
     , rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2))
     , cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2))
     , cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2))
     , posrecip^#(mark(X)) -> c_46(posrecip^#(X))
     , posrecip^#(ok(X)) -> c_47(posrecip^#(X))
     , 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2))
     , 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2))
     , 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2))
     , negrecip^#(mark(X)) -> c_51(negrecip^#(X))
     , negrecip^#(ok(X)) -> c_52(negrecip^#(X))
     , pi^#(mark(X)) -> c_53(pi^#(X))
     , pi^#(ok(X)) -> c_54(pi^#(X))
     , plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2))
     , plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2))
     , plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2))
     , times^#(X1, mark(X2)) -> c_58(times^#(X1, X2))
     , times^#(mark(X1), X2) -> c_59(times^#(X1, X2))
     , times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2))
     , square^#(mark(X)) -> c_61(square^#(X))
     , square^#(ok(X)) -> c_62(square^#(X))
     , proper^#(from(X)) -> c_63(from^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_64(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_65(s^#(proper(X)))
     , proper^#(2ndspos(X1, X2)) ->
       c_66(2ndspos^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_67()
     , proper^#(rnil()) -> c_68()
     , proper^#(cons2(X1, X2)) -> c_69(cons2^#(proper(X1), proper(X2)))
     , proper^#(rcons(X1, X2)) -> c_70(rcons^#(proper(X1), proper(X2)))
     , proper^#(posrecip(X)) -> c_71(posrecip^#(proper(X)))
     , proper^#(2ndsneg(X1, X2)) ->
       c_72(2ndsneg^#(proper(X1), proper(X2)))
     , proper^#(negrecip(X)) -> c_73(negrecip^#(proper(X)))
     , proper^#(pi(X)) -> c_74(pi^#(proper(X)))
     , proper^#(plus(X1, X2)) -> c_75(plus^#(proper(X1), proper(X2)))
     , proper^#(times(X1, X2)) -> c_76(times^#(proper(X1), proper(X2)))
     , proper^#(square(X)) -> c_77(square^#(proper(X)))
     , proper^#(nil()) -> c_78()
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { active^#(from(X)) -> c_1(from^#(active(X)))
     , active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
     , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
     , active^#(s(X)) -> c_4(s^#(active(X)))
     , active^#(2ndspos(X1, X2)) -> c_5(2ndspos^#(X1, active(X2)))
     , active^#(2ndspos(X1, X2)) -> c_6(2ndspos^#(active(X1), X2))
     , active^#(2ndspos(s(N), cons(X, Z))) ->
       c_7(2ndspos^#(s(N), cons2(X, Z)))
     , active^#(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
       c_8(rcons^#(posrecip(Y), 2ndsneg(N, Z)))
     , active^#(2ndspos(0(), Z)) -> c_9()
     , active^#(cons2(X1, X2)) -> c_10(cons2^#(X1, active(X2)))
     , active^#(rcons(X1, X2)) -> c_11(rcons^#(X1, active(X2)))
     , active^#(rcons(X1, X2)) -> c_12(rcons^#(active(X1), X2))
     , active^#(posrecip(X)) -> c_13(posrecip^#(active(X)))
     , active^#(2ndsneg(X1, X2)) -> c_14(2ndsneg^#(X1, active(X2)))
     , active^#(2ndsneg(X1, X2)) -> c_15(2ndsneg^#(active(X1), X2))
     , active^#(2ndsneg(s(N), cons(X, Z))) ->
       c_16(2ndsneg^#(s(N), cons2(X, Z)))
     , active^#(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
       c_17(rcons^#(negrecip(Y), 2ndspos(N, Z)))
     , active^#(2ndsneg(0(), Z)) -> c_18()
     , active^#(negrecip(X)) -> c_19(negrecip^#(active(X)))
     , active^#(pi(X)) -> c_20(2ndspos^#(X, from(0())))
     , active^#(pi(X)) -> c_21(pi^#(active(X)))
     , active^#(plus(X1, X2)) -> c_22(plus^#(X1, active(X2)))
     , active^#(plus(X1, X2)) -> c_23(plus^#(active(X1), X2))
     , active^#(plus(s(X), Y)) -> c_24(s^#(plus(X, Y)))
     , active^#(plus(0(), Y)) -> c_25(Y)
     , active^#(times(X1, X2)) -> c_26(times^#(X1, active(X2)))
     , active^#(times(X1, X2)) -> c_27(times^#(active(X1), X2))
     , active^#(times(s(X), Y)) -> c_28(plus^#(Y, times(X, Y)))
     , active^#(times(0(), Y)) -> c_29()
     , active^#(square(X)) -> c_30(times^#(X, X))
     , active^#(square(X)) -> c_31(square^#(active(X)))
     , from^#(mark(X)) -> c_32(from^#(X))
     , from^#(ok(X)) -> c_33(from^#(X))
     , cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2))
     , s^#(mark(X)) -> c_36(s^#(X))
     , s^#(ok(X)) -> c_37(s^#(X))
     , 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2))
     , 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2))
     , 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2))
     , rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2))
     , rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2))
     , rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2))
     , cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2))
     , cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2))
     , posrecip^#(mark(X)) -> c_46(posrecip^#(X))
     , posrecip^#(ok(X)) -> c_47(posrecip^#(X))
     , 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2))
     , 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2))
     , 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2))
     , negrecip^#(mark(X)) -> c_51(negrecip^#(X))
     , negrecip^#(ok(X)) -> c_52(negrecip^#(X))
     , pi^#(mark(X)) -> c_53(pi^#(X))
     , pi^#(ok(X)) -> c_54(pi^#(X))
     , plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2))
     , plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2))
     , plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2))
     , times^#(X1, mark(X2)) -> c_58(times^#(X1, X2))
     , times^#(mark(X1), X2) -> c_59(times^#(X1, X2))
     , times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2))
     , square^#(mark(X)) -> c_61(square^#(X))
     , square^#(ok(X)) -> c_62(square^#(X))
     , proper^#(from(X)) -> c_63(from^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_64(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_65(s^#(proper(X)))
     , proper^#(2ndspos(X1, X2)) ->
       c_66(2ndspos^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_67()
     , proper^#(rnil()) -> c_68()
     , proper^#(cons2(X1, X2)) -> c_69(cons2^#(proper(X1), proper(X2)))
     , proper^#(rcons(X1, X2)) -> c_70(rcons^#(proper(X1), proper(X2)))
     , proper^#(posrecip(X)) -> c_71(posrecip^#(proper(X)))
     , proper^#(2ndsneg(X1, X2)) ->
       c_72(2ndsneg^#(proper(X1), proper(X2)))
     , proper^#(negrecip(X)) -> c_73(negrecip^#(proper(X)))
     , proper^#(pi(X)) -> c_74(pi^#(proper(X)))
     , proper^#(plus(X1, X2)) -> c_75(plus^#(proper(X1), proper(X2)))
     , proper^#(times(X1, X2)) -> c_76(times^#(proper(X1), proper(X2)))
     , proper^#(square(X)) -> c_77(square^#(proper(X)))
     , proper^#(nil()) -> c_78()
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   Strict Trs:
     { active(from(X)) -> from(active(X))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
     , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
     , active(2ndspos(s(N), cons(X, Z))) ->
       mark(2ndspos(s(N), cons2(X, Z)))
     , active(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
       mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
     , active(2ndspos(0(), Z)) -> mark(rnil())
     , active(cons2(X1, X2)) -> cons2(X1, active(X2))
     , active(rcons(X1, X2)) -> rcons(X1, active(X2))
     , active(rcons(X1, X2)) -> rcons(active(X1), X2)
     , active(posrecip(X)) -> posrecip(active(X))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
     , active(2ndsneg(s(N), cons(X, Z))) ->
       mark(2ndsneg(s(N), cons2(X, Z)))
     , active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
       mark(rcons(negrecip(Y), 2ndspos(N, Z)))
     , active(2ndsneg(0(), Z)) -> mark(rnil())
     , active(negrecip(X)) -> negrecip(active(X))
     , active(pi(X)) -> mark(2ndspos(X, from(0())))
     , active(pi(X)) -> pi(active(X))
     , active(plus(X1, X2)) -> plus(X1, active(X2))
     , active(plus(X1, X2)) -> plus(active(X1), X2)
     , active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
     , active(plus(0(), Y)) -> mark(Y)
     , active(times(X1, X2)) -> times(X1, active(X2))
     , active(times(X1, X2)) -> times(active(X1), X2)
     , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
     , active(times(0(), Y)) -> mark(0())
     , active(square(X)) -> mark(times(X, X))
     , active(square(X)) -> square(active(X))
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
     , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
     , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))
     , cons2(X1, mark(X2)) -> mark(cons2(X1, X2))
     , cons2(ok(X1), ok(X2)) -> ok(cons2(X1, X2))
     , rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
     , rcons(mark(X1), X2) -> mark(rcons(X1, X2))
     , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
     , posrecip(mark(X)) -> mark(posrecip(X))
     , posrecip(ok(X)) -> ok(posrecip(X))
     , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2))
     , negrecip(mark(X)) -> mark(negrecip(X))
     , negrecip(ok(X)) -> ok(negrecip(X))
     , pi(mark(X)) -> mark(pi(X))
     , pi(ok(X)) -> ok(pi(X))
     , plus(X1, mark(X2)) -> mark(plus(X1, X2))
     , plus(mark(X1), X2) -> mark(plus(X1, X2))
     , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
     , times(X1, mark(X2)) -> mark(times(X1, X2))
     , times(mark(X1), X2) -> mark(times(X1, X2))
     , times(ok(X1), ok(X2)) -> ok(times(X1, X2))
     , square(mark(X)) -> mark(square(X))
     , square(ok(X)) -> ok(square(X))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(rnil()) -> ok(rnil())
     , proper(cons2(X1, X2)) -> cons2(proper(X1), proper(X2))
     , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
     , proper(posrecip(X)) -> posrecip(proper(X))
     , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
     , proper(negrecip(X)) -> negrecip(proper(X))
     , proper(pi(X)) -> pi(proper(X))
     , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
     , proper(times(X1, X2)) -> times(proper(X1), proper(X2))
     , proper(square(X)) -> square(proper(X))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Consider the dependency graph:
   
     1: active^#(from(X)) -> c_1(from^#(active(X)))
        -->_1 from^#(ok(X)) -> c_33(from^#(X)) :33
        -->_1 from^#(mark(X)) -> c_32(from^#(X)) :32
     
     2: active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2)) :35
        -->_1 cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2)) :34
     
     3: active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2)) :35
        -->_1 cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2)) :34
     
     4: active^#(s(X)) -> c_4(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_37(s^#(X)) :37
        -->_1 s^#(mark(X)) -> c_36(s^#(X)) :36
     
     5: active^#(2ndspos(X1, X2)) -> c_5(2ndspos^#(X1, active(X2)))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     6: active^#(2ndspos(X1, X2)) -> c_6(2ndspos^#(active(X1), X2))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     7: active^#(2ndspos(s(N), cons(X, Z))) ->
        c_7(2ndspos^#(s(N), cons2(X, Z)))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     8: active^#(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
        c_8(rcons^#(posrecip(Y), 2ndsneg(N, Z)))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     9: active^#(2ndspos(0(), Z)) -> c_9()
     
     10: active^#(cons2(X1, X2)) -> c_10(cons2^#(X1, active(X2)))
        -->_1 cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2)) :45
        -->_1 cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2)) :44
     
     11: active^#(rcons(X1, X2)) -> c_11(rcons^#(X1, active(X2)))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     12: active^#(rcons(X1, X2)) -> c_12(rcons^#(active(X1), X2))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     13: active^#(posrecip(X)) -> c_13(posrecip^#(active(X)))
        -->_1 posrecip^#(ok(X)) -> c_47(posrecip^#(X)) :47
        -->_1 posrecip^#(mark(X)) -> c_46(posrecip^#(X)) :46
     
     14: active^#(2ndsneg(X1, X2)) -> c_14(2ndsneg^#(X1, active(X2)))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     15: active^#(2ndsneg(X1, X2)) -> c_15(2ndsneg^#(active(X1), X2))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     16: active^#(2ndsneg(s(N), cons(X, Z))) ->
         c_16(2ndsneg^#(s(N), cons2(X, Z)))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     17: active^#(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
         c_17(rcons^#(negrecip(Y), 2ndspos(N, Z)))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     18: active^#(2ndsneg(0(), Z)) -> c_18()
     
     19: active^#(negrecip(X)) -> c_19(negrecip^#(active(X)))
        -->_1 negrecip^#(ok(X)) -> c_52(negrecip^#(X)) :52
        -->_1 negrecip^#(mark(X)) -> c_51(negrecip^#(X)) :51
     
     20: active^#(pi(X)) -> c_20(2ndspos^#(X, from(0())))
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
     
     21: active^#(pi(X)) -> c_21(pi^#(active(X)))
        -->_1 pi^#(ok(X)) -> c_54(pi^#(X)) :54
        -->_1 pi^#(mark(X)) -> c_53(pi^#(X)) :53
     
     22: active^#(plus(X1, X2)) -> c_22(plus^#(X1, active(X2)))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     23: active^#(plus(X1, X2)) -> c_23(plus^#(active(X1), X2))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     24: active^#(plus(s(X), Y)) -> c_24(s^#(plus(X, Y)))
        -->_1 s^#(ok(X)) -> c_37(s^#(X)) :37
        -->_1 s^#(mark(X)) -> c_36(s^#(X)) :36
     
     25: active^#(plus(0(), Y)) -> c_25(Y)
        -->_1 top^#(ok(X)) -> c_80(top^#(active(X))) :80
        -->_1 top^#(mark(X)) -> c_79(top^#(proper(X))) :79
        -->_1 proper^#(square(X)) -> c_77(square^#(proper(X))) :77
        -->_1 proper^#(times(X1, X2)) ->
              c_76(times^#(proper(X1), proper(X2))) :76
        -->_1 proper^#(plus(X1, X2)) ->
              c_75(plus^#(proper(X1), proper(X2))) :75
        -->_1 proper^#(pi(X)) -> c_74(pi^#(proper(X))) :74
        -->_1 proper^#(negrecip(X)) -> c_73(negrecip^#(proper(X))) :73
        -->_1 proper^#(2ndsneg(X1, X2)) ->
              c_72(2ndsneg^#(proper(X1), proper(X2))) :72
        -->_1 proper^#(posrecip(X)) -> c_71(posrecip^#(proper(X))) :71
        -->_1 proper^#(rcons(X1, X2)) ->
              c_70(rcons^#(proper(X1), proper(X2))) :70
        -->_1 proper^#(cons2(X1, X2)) ->
              c_69(cons2^#(proper(X1), proper(X2))) :69
        -->_1 proper^#(2ndspos(X1, X2)) ->
              c_66(2ndspos^#(proper(X1), proper(X2))) :66
        -->_1 proper^#(s(X)) -> c_65(s^#(proper(X))) :65
        -->_1 proper^#(cons(X1, X2)) ->
              c_64(cons^#(proper(X1), proper(X2))) :64
        -->_1 proper^#(from(X)) -> c_63(from^#(proper(X))) :63
        -->_1 square^#(ok(X)) -> c_62(square^#(X)) :62
        -->_1 square^#(mark(X)) -> c_61(square^#(X)) :61
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
        -->_1 pi^#(ok(X)) -> c_54(pi^#(X)) :54
        -->_1 pi^#(mark(X)) -> c_53(pi^#(X)) :53
        -->_1 negrecip^#(ok(X)) -> c_52(negrecip^#(X)) :52
        -->_1 negrecip^#(mark(X)) -> c_51(negrecip^#(X)) :51
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
        -->_1 posrecip^#(ok(X)) -> c_47(posrecip^#(X)) :47
        -->_1 posrecip^#(mark(X)) -> c_46(posrecip^#(X)) :46
        -->_1 cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2)) :45
        -->_1 cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2)) :44
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
        -->_1 s^#(ok(X)) -> c_37(s^#(X)) :37
        -->_1 s^#(mark(X)) -> c_36(s^#(X)) :36
        -->_1 cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2)) :35
        -->_1 cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2)) :34
        -->_1 from^#(ok(X)) -> c_33(from^#(X)) :33
        -->_1 from^#(mark(X)) -> c_32(from^#(X)) :32
        -->_1 active^#(square(X)) -> c_31(square^#(active(X))) :31
        -->_1 active^#(square(X)) -> c_30(times^#(X, X)) :30
        -->_1 active^#(times(s(X), Y)) -> c_28(plus^#(Y, times(X, Y))) :28
        -->_1 active^#(times(X1, X2)) -> c_27(times^#(active(X1), X2)) :27
        -->_1 active^#(times(X1, X2)) -> c_26(times^#(X1, active(X2))) :26
        -->_1 proper^#(nil()) -> c_78() :78
        -->_1 proper^#(rnil()) -> c_68() :68
        -->_1 proper^#(0()) -> c_67() :67
        -->_1 active^#(times(0(), Y)) -> c_29() :29
        -->_1 active^#(plus(0(), Y)) -> c_25(Y) :25
        -->_1 active^#(plus(s(X), Y)) -> c_24(s^#(plus(X, Y))) :24
        -->_1 active^#(plus(X1, X2)) -> c_23(plus^#(active(X1), X2)) :23
        -->_1 active^#(plus(X1, X2)) -> c_22(plus^#(X1, active(X2))) :22
        -->_1 active^#(pi(X)) -> c_21(pi^#(active(X))) :21
        -->_1 active^#(pi(X)) -> c_20(2ndspos^#(X, from(0()))) :20
        -->_1 active^#(negrecip(X)) -> c_19(negrecip^#(active(X))) :19
        -->_1 active^#(2ndsneg(0(), Z)) -> c_18() :18
        -->_1 active^#(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
              c_17(rcons^#(negrecip(Y), 2ndspos(N, Z))) :17
        -->_1 active^#(2ndsneg(s(N), cons(X, Z))) ->
              c_16(2ndsneg^#(s(N), cons2(X, Z))) :16
        -->_1 active^#(2ndsneg(X1, X2)) ->
              c_15(2ndsneg^#(active(X1), X2)) :15
        -->_1 active^#(2ndsneg(X1, X2)) ->
              c_14(2ndsneg^#(X1, active(X2))) :14
        -->_1 active^#(posrecip(X)) -> c_13(posrecip^#(active(X))) :13
        -->_1 active^#(rcons(X1, X2)) -> c_12(rcons^#(active(X1), X2)) :12
        -->_1 active^#(rcons(X1, X2)) -> c_11(rcons^#(X1, active(X2))) :11
        -->_1 active^#(cons2(X1, X2)) -> c_10(cons2^#(X1, active(X2))) :10
        -->_1 active^#(2ndspos(0(), Z)) -> c_9() :9
        -->_1 active^#(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
              c_8(rcons^#(posrecip(Y), 2ndsneg(N, Z))) :8
        -->_1 active^#(2ndspos(s(N), cons(X, Z))) ->
              c_7(2ndspos^#(s(N), cons2(X, Z))) :7
        -->_1 active^#(2ndspos(X1, X2)) ->
              c_6(2ndspos^#(active(X1), X2)) :6
        -->_1 active^#(2ndspos(X1, X2)) ->
              c_5(2ndspos^#(X1, active(X2))) :5
        -->_1 active^#(s(X)) -> c_4(s^#(active(X))) :4
        -->_1 active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) :3
        -->_1 active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) :2
        -->_1 active^#(from(X)) -> c_1(from^#(active(X))) :1
     
     26: active^#(times(X1, X2)) -> c_26(times^#(X1, active(X2)))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     27: active^#(times(X1, X2)) -> c_27(times^#(active(X1), X2))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     28: active^#(times(s(X), Y)) -> c_28(plus^#(Y, times(X, Y)))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     29: active^#(times(0(), Y)) -> c_29()
     
     30: active^#(square(X)) -> c_30(times^#(X, X))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     31: active^#(square(X)) -> c_31(square^#(active(X)))
        -->_1 square^#(ok(X)) -> c_62(square^#(X)) :62
        -->_1 square^#(mark(X)) -> c_61(square^#(X)) :61
     
     32: from^#(mark(X)) -> c_32(from^#(X))
        -->_1 from^#(ok(X)) -> c_33(from^#(X)) :33
        -->_1 from^#(mark(X)) -> c_32(from^#(X)) :32
     
     33: from^#(ok(X)) -> c_33(from^#(X))
        -->_1 from^#(ok(X)) -> c_33(from^#(X)) :33
        -->_1 from^#(mark(X)) -> c_32(from^#(X)) :32
     
     34: cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2)) :35
        -->_1 cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2)) :34
     
     35: cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2)) :35
        -->_1 cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2)) :34
     
     36: s^#(mark(X)) -> c_36(s^#(X))
        -->_1 s^#(ok(X)) -> c_37(s^#(X)) :37
        -->_1 s^#(mark(X)) -> c_36(s^#(X)) :36
     
     37: s^#(ok(X)) -> c_37(s^#(X))
        -->_1 s^#(ok(X)) -> c_37(s^#(X)) :37
        -->_1 s^#(mark(X)) -> c_36(s^#(X)) :36
     
     38: 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     39: 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     40: 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     41: rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     42: rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     43: rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     44: cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2))
        -->_1 cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2)) :45
        -->_1 cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2)) :44
     
     45: cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2))
        -->_1 cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2)) :45
        -->_1 cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2)) :44
     
     46: posrecip^#(mark(X)) -> c_46(posrecip^#(X))
        -->_1 posrecip^#(ok(X)) -> c_47(posrecip^#(X)) :47
        -->_1 posrecip^#(mark(X)) -> c_46(posrecip^#(X)) :46
     
     47: posrecip^#(ok(X)) -> c_47(posrecip^#(X))
        -->_1 posrecip^#(ok(X)) -> c_47(posrecip^#(X)) :47
        -->_1 posrecip^#(mark(X)) -> c_46(posrecip^#(X)) :46
     
     48: 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     49: 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     50: 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     51: negrecip^#(mark(X)) -> c_51(negrecip^#(X))
        -->_1 negrecip^#(ok(X)) -> c_52(negrecip^#(X)) :52
        -->_1 negrecip^#(mark(X)) -> c_51(negrecip^#(X)) :51
     
     52: negrecip^#(ok(X)) -> c_52(negrecip^#(X))
        -->_1 negrecip^#(ok(X)) -> c_52(negrecip^#(X)) :52
        -->_1 negrecip^#(mark(X)) -> c_51(negrecip^#(X)) :51
     
     53: pi^#(mark(X)) -> c_53(pi^#(X))
        -->_1 pi^#(ok(X)) -> c_54(pi^#(X)) :54
        -->_1 pi^#(mark(X)) -> c_53(pi^#(X)) :53
     
     54: pi^#(ok(X)) -> c_54(pi^#(X))
        -->_1 pi^#(ok(X)) -> c_54(pi^#(X)) :54
        -->_1 pi^#(mark(X)) -> c_53(pi^#(X)) :53
     
     55: plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     56: plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     57: plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     58: times^#(X1, mark(X2)) -> c_58(times^#(X1, X2))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     59: times^#(mark(X1), X2) -> c_59(times^#(X1, X2))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     60: times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     61: square^#(mark(X)) -> c_61(square^#(X))
        -->_1 square^#(ok(X)) -> c_62(square^#(X)) :62
        -->_1 square^#(mark(X)) -> c_61(square^#(X)) :61
     
     62: square^#(ok(X)) -> c_62(square^#(X))
        -->_1 square^#(ok(X)) -> c_62(square^#(X)) :62
        -->_1 square^#(mark(X)) -> c_61(square^#(X)) :61
     
     63: proper^#(from(X)) -> c_63(from^#(proper(X)))
        -->_1 from^#(ok(X)) -> c_33(from^#(X)) :33
        -->_1 from^#(mark(X)) -> c_32(from^#(X)) :32
     
     64: proper^#(cons(X1, X2)) -> c_64(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2)) :35
        -->_1 cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2)) :34
     
     65: proper^#(s(X)) -> c_65(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_37(s^#(X)) :37
        -->_1 s^#(mark(X)) -> c_36(s^#(X)) :36
     
     66: proper^#(2ndspos(X1, X2)) ->
         c_66(2ndspos^#(proper(X1), proper(X2)))
        -->_1 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2)) :40
        -->_1 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2)) :39
        -->_1 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2)) :38
     
     67: proper^#(0()) -> c_67()
     
     68: proper^#(rnil()) -> c_68()
     
     69: proper^#(cons2(X1, X2)) ->
         c_69(cons2^#(proper(X1), proper(X2)))
        -->_1 cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2)) :45
        -->_1 cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2)) :44
     
     70: proper^#(rcons(X1, X2)) ->
         c_70(rcons^#(proper(X1), proper(X2)))
        -->_1 rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2)) :43
        -->_1 rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2)) :42
        -->_1 rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2)) :41
     
     71: proper^#(posrecip(X)) -> c_71(posrecip^#(proper(X)))
        -->_1 posrecip^#(ok(X)) -> c_47(posrecip^#(X)) :47
        -->_1 posrecip^#(mark(X)) -> c_46(posrecip^#(X)) :46
     
     72: proper^#(2ndsneg(X1, X2)) ->
         c_72(2ndsneg^#(proper(X1), proper(X2)))
        -->_1 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2)) :50
        -->_1 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2)) :49
        -->_1 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2)) :48
     
     73: proper^#(negrecip(X)) -> c_73(negrecip^#(proper(X)))
        -->_1 negrecip^#(ok(X)) -> c_52(negrecip^#(X)) :52
        -->_1 negrecip^#(mark(X)) -> c_51(negrecip^#(X)) :51
     
     74: proper^#(pi(X)) -> c_74(pi^#(proper(X)))
        -->_1 pi^#(ok(X)) -> c_54(pi^#(X)) :54
        -->_1 pi^#(mark(X)) -> c_53(pi^#(X)) :53
     
     75: proper^#(plus(X1, X2)) -> c_75(plus^#(proper(X1), proper(X2)))
        -->_1 plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2)) :57
        -->_1 plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2)) :56
        -->_1 plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2)) :55
     
     76: proper^#(times(X1, X2)) ->
         c_76(times^#(proper(X1), proper(X2)))
        -->_1 times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2)) :60
        -->_1 times^#(mark(X1), X2) -> c_59(times^#(X1, X2)) :59
        -->_1 times^#(X1, mark(X2)) -> c_58(times^#(X1, X2)) :58
     
     77: proper^#(square(X)) -> c_77(square^#(proper(X)))
        -->_1 square^#(ok(X)) -> c_62(square^#(X)) :62
        -->_1 square^#(mark(X)) -> c_61(square^#(X)) :61
     
     78: proper^#(nil()) -> c_78()
     
     79: top^#(mark(X)) -> c_79(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_80(top^#(active(X))) :80
        -->_1 top^#(mark(X)) -> c_79(top^#(proper(X))) :79
     
     80: top^#(ok(X)) -> c_80(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_80(top^#(active(X))) :80
        -->_1 top^#(mark(X)) -> c_79(top^#(proper(X))) :79
     
   
   Only the nodes
   {32,33,34,35,36,37,38,40,39,41,43,42,44,45,46,47,48,50,49,51,52,53,54,55,57,56,58,60,59,61,62,67,68,78,79,80}
   are reachable from nodes
   {32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,67,68,78,79,80}
   that start derivation from marked basic terms. The nodes not
   reachable are removed from the problem.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(mark(X)) -> c_32(from^#(X))
     , from^#(ok(X)) -> c_33(from^#(X))
     , cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2))
     , s^#(mark(X)) -> c_36(s^#(X))
     , s^#(ok(X)) -> c_37(s^#(X))
     , 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2))
     , 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2))
     , 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2))
     , rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2))
     , rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2))
     , rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2))
     , cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2))
     , cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2))
     , posrecip^#(mark(X)) -> c_46(posrecip^#(X))
     , posrecip^#(ok(X)) -> c_47(posrecip^#(X))
     , 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2))
     , 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2))
     , 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2))
     , negrecip^#(mark(X)) -> c_51(negrecip^#(X))
     , negrecip^#(ok(X)) -> c_52(negrecip^#(X))
     , pi^#(mark(X)) -> c_53(pi^#(X))
     , pi^#(ok(X)) -> c_54(pi^#(X))
     , plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2))
     , plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2))
     , plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2))
     , times^#(X1, mark(X2)) -> c_58(times^#(X1, X2))
     , times^#(mark(X1), X2) -> c_59(times^#(X1, X2))
     , times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2))
     , square^#(mark(X)) -> c_61(square^#(X))
     , square^#(ok(X)) -> c_62(square^#(X))
     , proper^#(0()) -> c_67()
     , proper^#(rnil()) -> c_68()
     , proper^#(nil()) -> c_78()
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   Strict Trs:
     { active(from(X)) -> from(active(X))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
     , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
     , active(2ndspos(s(N), cons(X, Z))) ->
       mark(2ndspos(s(N), cons2(X, Z)))
     , active(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
       mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
     , active(2ndspos(0(), Z)) -> mark(rnil())
     , active(cons2(X1, X2)) -> cons2(X1, active(X2))
     , active(rcons(X1, X2)) -> rcons(X1, active(X2))
     , active(rcons(X1, X2)) -> rcons(active(X1), X2)
     , active(posrecip(X)) -> posrecip(active(X))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
     , active(2ndsneg(s(N), cons(X, Z))) ->
       mark(2ndsneg(s(N), cons2(X, Z)))
     , active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
       mark(rcons(negrecip(Y), 2ndspos(N, Z)))
     , active(2ndsneg(0(), Z)) -> mark(rnil())
     , active(negrecip(X)) -> negrecip(active(X))
     , active(pi(X)) -> mark(2ndspos(X, from(0())))
     , active(pi(X)) -> pi(active(X))
     , active(plus(X1, X2)) -> plus(X1, active(X2))
     , active(plus(X1, X2)) -> plus(active(X1), X2)
     , active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
     , active(plus(0(), Y)) -> mark(Y)
     , active(times(X1, X2)) -> times(X1, active(X2))
     , active(times(X1, X2)) -> times(active(X1), X2)
     , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
     , active(times(0(), Y)) -> mark(0())
     , active(square(X)) -> mark(times(X, X))
     , active(square(X)) -> square(active(X))
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
     , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
     , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))
     , cons2(X1, mark(X2)) -> mark(cons2(X1, X2))
     , cons2(ok(X1), ok(X2)) -> ok(cons2(X1, X2))
     , rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
     , rcons(mark(X1), X2) -> mark(rcons(X1, X2))
     , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
     , posrecip(mark(X)) -> mark(posrecip(X))
     , posrecip(ok(X)) -> ok(posrecip(X))
     , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2))
     , negrecip(mark(X)) -> mark(negrecip(X))
     , negrecip(ok(X)) -> ok(negrecip(X))
     , pi(mark(X)) -> mark(pi(X))
     , pi(ok(X)) -> ok(pi(X))
     , plus(X1, mark(X2)) -> mark(plus(X1, X2))
     , plus(mark(X1), X2) -> mark(plus(X1, X2))
     , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
     , times(X1, mark(X2)) -> mark(times(X1, X2))
     , times(mark(X1), X2) -> mark(times(X1, X2))
     , times(ok(X1), ok(X2)) -> ok(times(X1, X2))
     , square(mark(X)) -> mark(square(X))
     , square(ok(X)) -> ok(square(X))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(rnil()) -> ok(rnil())
     , proper(cons2(X1, X2)) -> cons2(proper(X1), proper(X2))
     , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
     , proper(posrecip(X)) -> posrecip(proper(X))
     , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
     , proper(negrecip(X)) -> negrecip(proper(X))
     , proper(pi(X)) -> pi(proper(X))
     , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
     , proper(times(X1, X2)) -> times(proper(X1), proper(X2))
     , proper(square(X)) -> square(proper(X))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {32,33,34} by applications
   of Pre({32,33,34}) = {}. Here rules are labeled as follows:
   
     DPs:
       { 1: from^#(mark(X)) -> c_32(from^#(X))
       , 2: from^#(ok(X)) -> c_33(from^#(X))
       , 3: cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2))
       , 4: cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2))
       , 5: s^#(mark(X)) -> c_36(s^#(X))
       , 6: s^#(ok(X)) -> c_37(s^#(X))
       , 7: 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2))
       , 8: 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2))
       , 9: 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2))
       , 10: rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2))
       , 11: rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2))
       , 12: rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2))
       , 13: cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2))
       , 14: cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2))
       , 15: posrecip^#(mark(X)) -> c_46(posrecip^#(X))
       , 16: posrecip^#(ok(X)) -> c_47(posrecip^#(X))
       , 17: 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2))
       , 18: 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2))
       , 19: 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2))
       , 20: negrecip^#(mark(X)) -> c_51(negrecip^#(X))
       , 21: negrecip^#(ok(X)) -> c_52(negrecip^#(X))
       , 22: pi^#(mark(X)) -> c_53(pi^#(X))
       , 23: pi^#(ok(X)) -> c_54(pi^#(X))
       , 24: plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2))
       , 25: plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2))
       , 26: plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2))
       , 27: times^#(X1, mark(X2)) -> c_58(times^#(X1, X2))
       , 28: times^#(mark(X1), X2) -> c_59(times^#(X1, X2))
       , 29: times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2))
       , 30: square^#(mark(X)) -> c_61(square^#(X))
       , 31: square^#(ok(X)) -> c_62(square^#(X))
       , 32: proper^#(0()) -> c_67()
       , 33: proper^#(rnil()) -> c_68()
       , 34: proper^#(nil()) -> c_78()
       , 35: top^#(mark(X)) -> c_79(top^#(proper(X)))
       , 36: top^#(ok(X)) -> c_80(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(mark(X)) -> c_32(from^#(X))
     , from^#(ok(X)) -> c_33(from^#(X))
     , cons^#(mark(X1), X2) -> c_34(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_35(cons^#(X1, X2))
     , s^#(mark(X)) -> c_36(s^#(X))
     , s^#(ok(X)) -> c_37(s^#(X))
     , 2ndspos^#(X1, mark(X2)) -> c_38(2ndspos^#(X1, X2))
     , 2ndspos^#(mark(X1), X2) -> c_39(2ndspos^#(X1, X2))
     , 2ndspos^#(ok(X1), ok(X2)) -> c_40(2ndspos^#(X1, X2))
     , rcons^#(X1, mark(X2)) -> c_43(rcons^#(X1, X2))
     , rcons^#(mark(X1), X2) -> c_44(rcons^#(X1, X2))
     , rcons^#(ok(X1), ok(X2)) -> c_45(rcons^#(X1, X2))
     , cons2^#(X1, mark(X2)) -> c_41(cons2^#(X1, X2))
     , cons2^#(ok(X1), ok(X2)) -> c_42(cons2^#(X1, X2))
     , posrecip^#(mark(X)) -> c_46(posrecip^#(X))
     , posrecip^#(ok(X)) -> c_47(posrecip^#(X))
     , 2ndsneg^#(X1, mark(X2)) -> c_48(2ndsneg^#(X1, X2))
     , 2ndsneg^#(mark(X1), X2) -> c_49(2ndsneg^#(X1, X2))
     , 2ndsneg^#(ok(X1), ok(X2)) -> c_50(2ndsneg^#(X1, X2))
     , negrecip^#(mark(X)) -> c_51(negrecip^#(X))
     , negrecip^#(ok(X)) -> c_52(negrecip^#(X))
     , pi^#(mark(X)) -> c_53(pi^#(X))
     , pi^#(ok(X)) -> c_54(pi^#(X))
     , plus^#(X1, mark(X2)) -> c_55(plus^#(X1, X2))
     , plus^#(mark(X1), X2) -> c_56(plus^#(X1, X2))
     , plus^#(ok(X1), ok(X2)) -> c_57(plus^#(X1, X2))
     , times^#(X1, mark(X2)) -> c_58(times^#(X1, X2))
     , times^#(mark(X1), X2) -> c_59(times^#(X1, X2))
     , times^#(ok(X1), ok(X2)) -> c_60(times^#(X1, X2))
     , square^#(mark(X)) -> c_61(square^#(X))
     , square^#(ok(X)) -> c_62(square^#(X))
     , top^#(mark(X)) -> c_79(top^#(proper(X)))
     , top^#(ok(X)) -> c_80(top^#(active(X))) }
   Strict Trs:
     { active(from(X)) -> from(active(X))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
     , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
     , active(2ndspos(s(N), cons(X, Z))) ->
       mark(2ndspos(s(N), cons2(X, Z)))
     , active(2ndspos(s(N), cons2(X, cons(Y, Z)))) ->
       mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
     , active(2ndspos(0(), Z)) -> mark(rnil())
     , active(cons2(X1, X2)) -> cons2(X1, active(X2))
     , active(rcons(X1, X2)) -> rcons(X1, active(X2))
     , active(rcons(X1, X2)) -> rcons(active(X1), X2)
     , active(posrecip(X)) -> posrecip(active(X))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
     , active(2ndsneg(s(N), cons(X, Z))) ->
       mark(2ndsneg(s(N), cons2(X, Z)))
     , active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) ->
       mark(rcons(negrecip(Y), 2ndspos(N, Z)))
     , active(2ndsneg(0(), Z)) -> mark(rnil())
     , active(negrecip(X)) -> negrecip(active(X))
     , active(pi(X)) -> mark(2ndspos(X, from(0())))
     , active(pi(X)) -> pi(active(X))
     , active(plus(X1, X2)) -> plus(X1, active(X2))
     , active(plus(X1, X2)) -> plus(active(X1), X2)
     , active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
     , active(plus(0(), Y)) -> mark(Y)
     , active(times(X1, X2)) -> times(X1, active(X2))
     , active(times(X1, X2)) -> times(active(X1), X2)
     , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
     , active(times(0(), Y)) -> mark(0())
     , active(square(X)) -> mark(times(X, X))
     , active(square(X)) -> square(active(X))
     , from(mark(X)) -> mark(from(X))
     , from(ok(X)) -> ok(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , s(ok(X)) -> ok(s(X))
     , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
     , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
     , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))
     , cons2(X1, mark(X2)) -> mark(cons2(X1, X2))
     , cons2(ok(X1), ok(X2)) -> ok(cons2(X1, X2))
     , rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
     , rcons(mark(X1), X2) -> mark(rcons(X1, X2))
     , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
     , posrecip(mark(X)) -> mark(posrecip(X))
     , posrecip(ok(X)) -> ok(posrecip(X))
     , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2))
     , negrecip(mark(X)) -> mark(negrecip(X))
     , negrecip(ok(X)) -> ok(negrecip(X))
     , pi(mark(X)) -> mark(pi(X))
     , pi(ok(X)) -> ok(pi(X))
     , plus(X1, mark(X2)) -> mark(plus(X1, X2))
     , plus(mark(X1), X2) -> mark(plus(X1, X2))
     , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
     , times(X1, mark(X2)) -> mark(times(X1, X2))
     , times(mark(X1), X2) -> mark(times(X1, X2))
     , times(ok(X1), ok(X2)) -> ok(times(X1, X2))
     , square(mark(X)) -> mark(square(X))
     , square(ok(X)) -> ok(square(X))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(rnil()) -> ok(rnil())
     , proper(cons2(X1, X2)) -> cons2(proper(X1), proper(X2))
     , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
     , proper(posrecip(X)) -> posrecip(proper(X))
     , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
     , proper(negrecip(X)) -> negrecip(proper(X))
     , proper(pi(X)) -> pi(proper(X))
     , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
     , proper(times(X1, X2)) -> times(proper(X1), proper(X2))
     , proper(square(X)) -> square(proper(X))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { proper^#(0()) -> c_67()
     , proper^#(rnil()) -> c_68()
     , proper^#(nil()) -> c_78() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..