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(sel(X1, X2)) -> sel(X1, active(X2))
  , active(sel(X1, X2)) -> sel(active(X1), X2)
  , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
  , active(sel(0(), cons(X, XS))) -> mark(X)
  , active(minus(X1, X2)) -> minus(X1, active(X2))
  , active(minus(X1, X2)) -> minus(active(X1), X2)
  , active(minus(X, 0())) -> mark(0())
  , active(minus(s(X), s(Y))) -> mark(minus(X, Y))
  , active(quot(X1, X2)) -> quot(X1, active(X2))
  , active(quot(X1, X2)) -> quot(active(X1), X2)
  , active(quot(s(X), s(Y))) -> mark(s(quot(minus(X, Y), s(Y))))
  , active(quot(0(), s(Y))) -> mark(0())
  , active(zWquot(X1, X2)) -> zWquot(X1, active(X2))
  , active(zWquot(X1, X2)) -> zWquot(active(X1), X2)
  , active(zWquot(XS, nil())) -> mark(nil())
  , active(zWquot(cons(X, XS), cons(Y, YS))) ->
    mark(cons(quot(X, Y), zWquot(XS, YS)))
  , active(zWquot(nil(), XS)) -> mark(nil())
  , 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))
  , 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))
  , minus(X1, mark(X2)) -> mark(minus(X1, X2))
  , minus(mark(X1), X2) -> mark(minus(X1, X2))
  , minus(ok(X1), ok(X2)) -> ok(minus(X1, X2))
  , quot(X1, mark(X2)) -> mark(quot(X1, X2))
  , quot(mark(X1), X2) -> mark(quot(X1, X2))
  , quot(ok(X1), ok(X2)) -> ok(quot(X1, X2))
  , zWquot(X1, mark(X2)) -> mark(zWquot(X1, X2))
  , zWquot(mark(X1), X2) -> mark(zWquot(X1, X2))
  , zWquot(ok(X1), ok(X2)) -> ok(zWquot(X1, X2))
  , proper(from(X)) -> from(proper(X))
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(minus(X1, X2)) -> minus(proper(X1), proper(X2))
  , proper(quot(X1, X2)) -> quot(proper(X1), proper(X2))
  , proper(zWquot(X1, X2)) -> zWquot(proper(X1), proper(X2))
  , 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) '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) '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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-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^#(sel(X1, X2)) -> c_5(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_6(sel^#(active(X1), X2))
     , active^#(sel(s(N), cons(X, XS))) -> c_7(sel^#(N, XS))
     , active^#(sel(0(), cons(X, XS))) -> c_8(X)
     , active^#(minus(X1, X2)) -> c_9(minus^#(X1, active(X2)))
     , active^#(minus(X1, X2)) -> c_10(minus^#(active(X1), X2))
     , active^#(minus(X, 0())) -> c_11()
     , active^#(minus(s(X), s(Y))) -> c_12(minus^#(X, Y))
     , active^#(quot(X1, X2)) -> c_13(quot^#(X1, active(X2)))
     , active^#(quot(X1, X2)) -> c_14(quot^#(active(X1), X2))
     , active^#(quot(s(X), s(Y))) -> c_15(s^#(quot(minus(X, Y), s(Y))))
     , active^#(quot(0(), s(Y))) -> c_16()
     , active^#(zWquot(X1, X2)) -> c_17(zWquot^#(X1, active(X2)))
     , active^#(zWquot(X1, X2)) -> c_18(zWquot^#(active(X1), X2))
     , active^#(zWquot(XS, nil())) -> c_19()
     , active^#(zWquot(cons(X, XS), cons(Y, YS))) ->
       c_20(cons^#(quot(X, Y), zWquot(XS, YS)))
     , active^#(zWquot(nil(), XS)) -> c_21()
     , from^#(mark(X)) -> c_22(from^#(X))
     , from^#(ok(X)) -> c_23(from^#(X))
     , cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2))
     , s^#(mark(X)) -> c_26(s^#(X))
     , s^#(ok(X)) -> c_27(s^#(X))
     , sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2))
     , minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2))
     , minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2))
     , minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2))
     , quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2))
     , quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2))
     , quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2))
     , zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2))
     , zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2))
     , zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2))
     , proper^#(from(X)) -> c_40(from^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_41(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_42(s^#(proper(X)))
     , proper^#(sel(X1, X2)) -> c_43(sel^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_44()
     , proper^#(minus(X1, X2)) -> c_45(minus^#(proper(X1), proper(X2)))
     , proper^#(quot(X1, X2)) -> c_46(quot^#(proper(X1), proper(X2)))
     , proper^#(zWquot(X1, X2)) ->
       c_47(zWquot^#(proper(X1), proper(X2)))
     , proper^#(nil()) -> c_48()
     , top^#(mark(X)) -> c_49(top^#(proper(X)))
     , top^#(ok(X)) -> c_50(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^#(sel(X1, X2)) -> c_5(sel^#(X1, active(X2)))
     , active^#(sel(X1, X2)) -> c_6(sel^#(active(X1), X2))
     , active^#(sel(s(N), cons(X, XS))) -> c_7(sel^#(N, XS))
     , active^#(sel(0(), cons(X, XS))) -> c_8(X)
     , active^#(minus(X1, X2)) -> c_9(minus^#(X1, active(X2)))
     , active^#(minus(X1, X2)) -> c_10(minus^#(active(X1), X2))
     , active^#(minus(X, 0())) -> c_11()
     , active^#(minus(s(X), s(Y))) -> c_12(minus^#(X, Y))
     , active^#(quot(X1, X2)) -> c_13(quot^#(X1, active(X2)))
     , active^#(quot(X1, X2)) -> c_14(quot^#(active(X1), X2))
     , active^#(quot(s(X), s(Y))) -> c_15(s^#(quot(minus(X, Y), s(Y))))
     , active^#(quot(0(), s(Y))) -> c_16()
     , active^#(zWquot(X1, X2)) -> c_17(zWquot^#(X1, active(X2)))
     , active^#(zWquot(X1, X2)) -> c_18(zWquot^#(active(X1), X2))
     , active^#(zWquot(XS, nil())) -> c_19()
     , active^#(zWquot(cons(X, XS), cons(Y, YS))) ->
       c_20(cons^#(quot(X, Y), zWquot(XS, YS)))
     , active^#(zWquot(nil(), XS)) -> c_21()
     , from^#(mark(X)) -> c_22(from^#(X))
     , from^#(ok(X)) -> c_23(from^#(X))
     , cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2))
     , s^#(mark(X)) -> c_26(s^#(X))
     , s^#(ok(X)) -> c_27(s^#(X))
     , sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2))
     , minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2))
     , minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2))
     , minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2))
     , quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2))
     , quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2))
     , quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2))
     , zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2))
     , zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2))
     , zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2))
     , proper^#(from(X)) -> c_40(from^#(proper(X)))
     , proper^#(cons(X1, X2)) -> c_41(cons^#(proper(X1), proper(X2)))
     , proper^#(s(X)) -> c_42(s^#(proper(X)))
     , proper^#(sel(X1, X2)) -> c_43(sel^#(proper(X1), proper(X2)))
     , proper^#(0()) -> c_44()
     , proper^#(minus(X1, X2)) -> c_45(minus^#(proper(X1), proper(X2)))
     , proper^#(quot(X1, X2)) -> c_46(quot^#(proper(X1), proper(X2)))
     , proper^#(zWquot(X1, X2)) ->
       c_47(zWquot^#(proper(X1), proper(X2)))
     , proper^#(nil()) -> c_48()
     , top^#(mark(X)) -> c_49(top^#(proper(X)))
     , top^#(ok(X)) -> c_50(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(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , active(minus(X1, X2)) -> minus(X1, active(X2))
     , active(minus(X1, X2)) -> minus(active(X1), X2)
     , active(minus(X, 0())) -> mark(0())
     , active(minus(s(X), s(Y))) -> mark(minus(X, Y))
     , active(quot(X1, X2)) -> quot(X1, active(X2))
     , active(quot(X1, X2)) -> quot(active(X1), X2)
     , active(quot(s(X), s(Y))) -> mark(s(quot(minus(X, Y), s(Y))))
     , active(quot(0(), s(Y))) -> mark(0())
     , active(zWquot(X1, X2)) -> zWquot(X1, active(X2))
     , active(zWquot(X1, X2)) -> zWquot(active(X1), X2)
     , active(zWquot(XS, nil())) -> mark(nil())
     , active(zWquot(cons(X, XS), cons(Y, YS))) ->
       mark(cons(quot(X, Y), zWquot(XS, YS)))
     , active(zWquot(nil(), XS)) -> mark(nil())
     , 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))
     , 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))
     , minus(X1, mark(X2)) -> mark(minus(X1, X2))
     , minus(mark(X1), X2) -> mark(minus(X1, X2))
     , minus(ok(X1), ok(X2)) -> ok(minus(X1, X2))
     , quot(X1, mark(X2)) -> mark(quot(X1, X2))
     , quot(mark(X1), X2) -> mark(quot(X1, X2))
     , quot(ok(X1), ok(X2)) -> ok(quot(X1, X2))
     , zWquot(X1, mark(X2)) -> mark(zWquot(X1, X2))
     , zWquot(mark(X1), X2) -> mark(zWquot(X1, X2))
     , zWquot(ok(X1), ok(X2)) -> ok(zWquot(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(minus(X1, X2)) -> minus(proper(X1), proper(X2))
     , proper(quot(X1, X2)) -> quot(proper(X1), proper(X2))
     , proper(zWquot(X1, X2)) -> zWquot(proper(X1), proper(X2))
     , 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_23(from^#(X)) :23
        -->_1 from^#(mark(X)) -> c_22(from^#(X)) :22
     
     2: active^#(from(X)) -> c_2(cons^#(X, from(s(X))))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
     
     3: active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
     
     4: active^#(s(X)) -> c_4(s^#(active(X)))
        -->_1 s^#(ok(X)) -> c_27(s^#(X)) :27
        -->_1 s^#(mark(X)) -> c_26(s^#(X)) :26
     
     5: active^#(sel(X1, X2)) -> c_5(sel^#(X1, active(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     6: active^#(sel(X1, X2)) -> c_6(sel^#(active(X1), X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     7: active^#(sel(s(N), cons(X, XS))) -> c_7(sel^#(N, XS))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     8: active^#(sel(0(), cons(X, XS))) -> c_8(X)
        -->_1 top^#(ok(X)) -> c_50(top^#(active(X))) :50
        -->_1 top^#(mark(X)) -> c_49(top^#(proper(X))) :49
        -->_1 proper^#(zWquot(X1, X2)) ->
              c_47(zWquot^#(proper(X1), proper(X2))) :47
        -->_1 proper^#(quot(X1, X2)) ->
              c_46(quot^#(proper(X1), proper(X2))) :46
        -->_1 proper^#(minus(X1, X2)) ->
              c_45(minus^#(proper(X1), proper(X2))) :45
        -->_1 proper^#(sel(X1, X2)) ->
              c_43(sel^#(proper(X1), proper(X2))) :43
        -->_1 proper^#(s(X)) -> c_42(s^#(proper(X))) :42
        -->_1 proper^#(cons(X1, X2)) ->
              c_41(cons^#(proper(X1), proper(X2))) :41
        -->_1 proper^#(from(X)) -> c_40(from^#(proper(X))) :40
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
        -->_1 s^#(ok(X)) -> c_27(s^#(X)) :27
        -->_1 s^#(mark(X)) -> c_26(s^#(X)) :26
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
        -->_1 from^#(ok(X)) -> c_23(from^#(X)) :23
        -->_1 from^#(mark(X)) -> c_22(from^#(X)) :22
        -->_1 active^#(zWquot(cons(X, XS), cons(Y, YS))) ->
              c_20(cons^#(quot(X, Y), zWquot(XS, YS))) :20
        -->_1 active^#(zWquot(X1, X2)) ->
              c_18(zWquot^#(active(X1), X2)) :18
        -->_1 active^#(zWquot(X1, X2)) ->
              c_17(zWquot^#(X1, active(X2))) :17
        -->_1 active^#(quot(s(X), s(Y))) ->
              c_15(s^#(quot(minus(X, Y), s(Y)))) :15
        -->_1 active^#(quot(X1, X2)) -> c_14(quot^#(active(X1), X2)) :14
        -->_1 active^#(quot(X1, X2)) -> c_13(quot^#(X1, active(X2))) :13
        -->_1 active^#(minus(s(X), s(Y))) -> c_12(minus^#(X, Y)) :12
        -->_1 active^#(minus(X1, X2)) -> c_10(minus^#(active(X1), X2)) :10
        -->_1 active^#(minus(X1, X2)) -> c_9(minus^#(X1, active(X2))) :9
        -->_1 proper^#(nil()) -> c_48() :48
        -->_1 proper^#(0()) -> c_44() :44
        -->_1 active^#(zWquot(nil(), XS)) -> c_21() :21
        -->_1 active^#(zWquot(XS, nil())) -> c_19() :19
        -->_1 active^#(quot(0(), s(Y))) -> c_16() :16
        -->_1 active^#(minus(X, 0())) -> c_11() :11
        -->_1 active^#(sel(0(), cons(X, XS))) -> c_8(X) :8
        -->_1 active^#(sel(s(N), cons(X, XS))) -> c_7(sel^#(N, XS)) :7
        -->_1 active^#(sel(X1, X2)) -> c_6(sel^#(active(X1), X2)) :6
        -->_1 active^#(sel(X1, X2)) -> c_5(sel^#(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
     
     9: active^#(minus(X1, X2)) -> c_9(minus^#(X1, active(X2)))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     10: active^#(minus(X1, X2)) -> c_10(minus^#(active(X1), X2))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     11: active^#(minus(X, 0())) -> c_11()
     
     12: active^#(minus(s(X), s(Y))) -> c_12(minus^#(X, Y))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     13: active^#(quot(X1, X2)) -> c_13(quot^#(X1, active(X2)))
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
     
     14: active^#(quot(X1, X2)) -> c_14(quot^#(active(X1), X2))
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
     
     15: active^#(quot(s(X), s(Y))) ->
         c_15(s^#(quot(minus(X, Y), s(Y))))
        -->_1 s^#(ok(X)) -> c_27(s^#(X)) :27
        -->_1 s^#(mark(X)) -> c_26(s^#(X)) :26
     
     16: active^#(quot(0(), s(Y))) -> c_16()
     
     17: active^#(zWquot(X1, X2)) -> c_17(zWquot^#(X1, active(X2)))
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
     
     18: active^#(zWquot(X1, X2)) -> c_18(zWquot^#(active(X1), X2))
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
     
     19: active^#(zWquot(XS, nil())) -> c_19()
     
     20: active^#(zWquot(cons(X, XS), cons(Y, YS))) ->
         c_20(cons^#(quot(X, Y), zWquot(XS, YS)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
     
     21: active^#(zWquot(nil(), XS)) -> c_21()
     
     22: from^#(mark(X)) -> c_22(from^#(X))
        -->_1 from^#(ok(X)) -> c_23(from^#(X)) :23
        -->_1 from^#(mark(X)) -> c_22(from^#(X)) :22
     
     23: from^#(ok(X)) -> c_23(from^#(X))
        -->_1 from^#(ok(X)) -> c_23(from^#(X)) :23
        -->_1 from^#(mark(X)) -> c_22(from^#(X)) :22
     
     24: cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
     
     25: cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
     
     26: s^#(mark(X)) -> c_26(s^#(X))
        -->_1 s^#(ok(X)) -> c_27(s^#(X)) :27
        -->_1 s^#(mark(X)) -> c_26(s^#(X)) :26
     
     27: s^#(ok(X)) -> c_27(s^#(X))
        -->_1 s^#(ok(X)) -> c_27(s^#(X)) :27
        -->_1 s^#(mark(X)) -> c_26(s^#(X)) :26
     
     28: sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     29: sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     30: sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     31: minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     32: minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     33: minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     34: quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2))
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
     
     35: quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2))
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
     
     36: quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2))
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
     
     37: zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2))
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
     
     38: zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2))
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
     
     39: zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2))
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
     
     40: proper^#(from(X)) -> c_40(from^#(proper(X)))
        -->_1 from^#(ok(X)) -> c_23(from^#(X)) :23
        -->_1 from^#(mark(X)) -> c_22(from^#(X)) :22
     
     41: proper^#(cons(X1, X2)) -> c_41(cons^#(proper(X1), proper(X2)))
        -->_1 cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2)) :25
        -->_1 cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2)) :24
     
     42: proper^#(s(X)) -> c_42(s^#(proper(X)))
        -->_1 s^#(ok(X)) -> c_27(s^#(X)) :27
        -->_1 s^#(mark(X)) -> c_26(s^#(X)) :26
     
     43: proper^#(sel(X1, X2)) -> c_43(sel^#(proper(X1), proper(X2)))
        -->_1 sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2)) :30
        -->_1 sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2)) :29
        -->_1 sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2)) :28
     
     44: proper^#(0()) -> c_44()
     
     45: proper^#(minus(X1, X2)) ->
         c_45(minus^#(proper(X1), proper(X2)))
        -->_1 minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2)) :33
        -->_1 minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2)) :32
        -->_1 minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2)) :31
     
     46: proper^#(quot(X1, X2)) -> c_46(quot^#(proper(X1), proper(X2)))
        -->_1 quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2)) :36
        -->_1 quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2)) :35
        -->_1 quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2)) :34
     
     47: proper^#(zWquot(X1, X2)) ->
         c_47(zWquot^#(proper(X1), proper(X2)))
        -->_1 zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2)) :39
        -->_1 zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2)) :38
        -->_1 zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2)) :37
     
     48: proper^#(nil()) -> c_48()
     
     49: top^#(mark(X)) -> c_49(top^#(proper(X)))
        -->_1 top^#(ok(X)) -> c_50(top^#(active(X))) :50
        -->_1 top^#(mark(X)) -> c_49(top^#(proper(X))) :49
     
     50: top^#(ok(X)) -> c_50(top^#(active(X)))
        -->_1 top^#(ok(X)) -> c_50(top^#(active(X))) :50
        -->_1 top^#(mark(X)) -> c_49(top^#(proper(X))) :49
     
   
   Only the nodes
   {22,23,24,25,26,27,28,30,29,31,33,32,34,36,35,37,39,38,44,48,49,50}
   are reachable from nodes
   {22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,44,48,49,50}
   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_22(from^#(X))
     , from^#(ok(X)) -> c_23(from^#(X))
     , cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2))
     , s^#(mark(X)) -> c_26(s^#(X))
     , s^#(ok(X)) -> c_27(s^#(X))
     , sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2))
     , minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2))
     , minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2))
     , minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2))
     , quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2))
     , quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2))
     , quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2))
     , zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2))
     , zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2))
     , zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2))
     , proper^#(0()) -> c_44()
     , proper^#(nil()) -> c_48()
     , top^#(mark(X)) -> c_49(top^#(proper(X)))
     , top^#(ok(X)) -> c_50(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(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , active(minus(X1, X2)) -> minus(X1, active(X2))
     , active(minus(X1, X2)) -> minus(active(X1), X2)
     , active(minus(X, 0())) -> mark(0())
     , active(minus(s(X), s(Y))) -> mark(minus(X, Y))
     , active(quot(X1, X2)) -> quot(X1, active(X2))
     , active(quot(X1, X2)) -> quot(active(X1), X2)
     , active(quot(s(X), s(Y))) -> mark(s(quot(minus(X, Y), s(Y))))
     , active(quot(0(), s(Y))) -> mark(0())
     , active(zWquot(X1, X2)) -> zWquot(X1, active(X2))
     , active(zWquot(X1, X2)) -> zWquot(active(X1), X2)
     , active(zWquot(XS, nil())) -> mark(nil())
     , active(zWquot(cons(X, XS), cons(Y, YS))) ->
       mark(cons(quot(X, Y), zWquot(XS, YS)))
     , active(zWquot(nil(), XS)) -> mark(nil())
     , 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))
     , 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))
     , minus(X1, mark(X2)) -> mark(minus(X1, X2))
     , minus(mark(X1), X2) -> mark(minus(X1, X2))
     , minus(ok(X1), ok(X2)) -> ok(minus(X1, X2))
     , quot(X1, mark(X2)) -> mark(quot(X1, X2))
     , quot(mark(X1), X2) -> mark(quot(X1, X2))
     , quot(ok(X1), ok(X2)) -> ok(quot(X1, X2))
     , zWquot(X1, mark(X2)) -> mark(zWquot(X1, X2))
     , zWquot(mark(X1), X2) -> mark(zWquot(X1, X2))
     , zWquot(ok(X1), ok(X2)) -> ok(zWquot(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(minus(X1, X2)) -> minus(proper(X1), proper(X2))
     , proper(quot(X1, X2)) -> quot(proper(X1), proper(X2))
     , proper(zWquot(X1, X2)) -> zWquot(proper(X1), proper(X2))
     , 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 {19,20} by applications of
   Pre({19,20}) = {}. Here rules are labeled as follows:
   
     DPs:
       { 1: from^#(mark(X)) -> c_22(from^#(X))
       , 2: from^#(ok(X)) -> c_23(from^#(X))
       , 3: cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2))
       , 4: cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2))
       , 5: s^#(mark(X)) -> c_26(s^#(X))
       , 6: s^#(ok(X)) -> c_27(s^#(X))
       , 7: sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2))
       , 8: sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2))
       , 9: sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2))
       , 10: minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2))
       , 11: minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2))
       , 12: minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2))
       , 13: quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2))
       , 14: quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2))
       , 15: quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2))
       , 16: zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2))
       , 17: zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2))
       , 18: zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2))
       , 19: proper^#(0()) -> c_44()
       , 20: proper^#(nil()) -> c_48()
       , 21: top^#(mark(X)) -> c_49(top^#(proper(X)))
       , 22: top^#(ok(X)) -> c_50(top^#(active(X))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(mark(X)) -> c_22(from^#(X))
     , from^#(ok(X)) -> c_23(from^#(X))
     , cons^#(mark(X1), X2) -> c_24(cons^#(X1, X2))
     , cons^#(ok(X1), ok(X2)) -> c_25(cons^#(X1, X2))
     , s^#(mark(X)) -> c_26(s^#(X))
     , s^#(ok(X)) -> c_27(s^#(X))
     , sel^#(X1, mark(X2)) -> c_28(sel^#(X1, X2))
     , sel^#(mark(X1), X2) -> c_29(sel^#(X1, X2))
     , sel^#(ok(X1), ok(X2)) -> c_30(sel^#(X1, X2))
     , minus^#(X1, mark(X2)) -> c_31(minus^#(X1, X2))
     , minus^#(mark(X1), X2) -> c_32(minus^#(X1, X2))
     , minus^#(ok(X1), ok(X2)) -> c_33(minus^#(X1, X2))
     , quot^#(X1, mark(X2)) -> c_34(quot^#(X1, X2))
     , quot^#(mark(X1), X2) -> c_35(quot^#(X1, X2))
     , quot^#(ok(X1), ok(X2)) -> c_36(quot^#(X1, X2))
     , zWquot^#(X1, mark(X2)) -> c_37(zWquot^#(X1, X2))
     , zWquot^#(mark(X1), X2) -> c_38(zWquot^#(X1, X2))
     , zWquot^#(ok(X1), ok(X2)) -> c_39(zWquot^#(X1, X2))
     , top^#(mark(X)) -> c_49(top^#(proper(X)))
     , top^#(ok(X)) -> c_50(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(sel(X1, X2)) -> sel(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , active(minus(X1, X2)) -> minus(X1, active(X2))
     , active(minus(X1, X2)) -> minus(active(X1), X2)
     , active(minus(X, 0())) -> mark(0())
     , active(minus(s(X), s(Y))) -> mark(minus(X, Y))
     , active(quot(X1, X2)) -> quot(X1, active(X2))
     , active(quot(X1, X2)) -> quot(active(X1), X2)
     , active(quot(s(X), s(Y))) -> mark(s(quot(minus(X, Y), s(Y))))
     , active(quot(0(), s(Y))) -> mark(0())
     , active(zWquot(X1, X2)) -> zWquot(X1, active(X2))
     , active(zWquot(X1, X2)) -> zWquot(active(X1), X2)
     , active(zWquot(XS, nil())) -> mark(nil())
     , active(zWquot(cons(X, XS), cons(Y, YS))) ->
       mark(cons(quot(X, Y), zWquot(XS, YS)))
     , active(zWquot(nil(), XS)) -> mark(nil())
     , 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))
     , 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))
     , minus(X1, mark(X2)) -> mark(minus(X1, X2))
     , minus(mark(X1), X2) -> mark(minus(X1, X2))
     , minus(ok(X1), ok(X2)) -> ok(minus(X1, X2))
     , quot(X1, mark(X2)) -> mark(quot(X1, X2))
     , quot(mark(X1), X2) -> mark(quot(X1, X2))
     , quot(ok(X1), ok(X2)) -> ok(quot(X1, X2))
     , zWquot(X1, mark(X2)) -> mark(zWquot(X1, X2))
     , zWquot(mark(X1), X2) -> mark(zWquot(X1, X2))
     , zWquot(ok(X1), ok(X2)) -> ok(zWquot(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(minus(X1, X2)) -> minus(proper(X1), proper(X2))
     , proper(quot(X1, X2)) -> quot(proper(X1), proper(X2))
     , proper(zWquot(X1, X2)) -> zWquot(proper(X1), proper(X2))
     , proper(nil()) -> ok(nil())
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X)) }
   Weak DPs:
     { proper^#(0()) -> c_44()
     , proper^#(nil()) -> c_48() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..