MAYBE

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

Strict Trs:
  { from(X) -> cons(X, n__from(n__s(X)))
  , from(X) -> n__from(X)
  , sel(0(), cons(X, XS)) -> X
  , sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
  , s(X) -> n__s(X)
  , activate(X) -> X
  , activate(n__from(X)) -> from(activate(X))
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2))
  , minus(X, 0()) -> 0()
  , minus(s(X), s(Y)) -> minus(X, Y)
  , quot(0(), s(Y)) -> 0()
  , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
  , zWquot(X1, X2) -> n__zWquot(X1, X2)
  , zWquot(XS, nil()) -> nil()
  , zWquot(cons(X, XS), cons(Y, YS)) ->
    cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
  , zWquot(nil(), XS) -> nil() }
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 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:
     { from^#(X) -> c_1(X, X)
     , from^#(X) -> c_2(X)
     , sel^#(0(), cons(X, XS)) -> c_3(X)
     , sel^#(s(N), cons(X, XS)) -> c_4(sel^#(N, activate(XS)))
     , s^#(X) -> c_5(X)
     , activate^#(X) -> c_6(X)
     , activate^#(n__from(X)) -> c_7(from^#(activate(X)))
     , activate^#(n__s(X)) -> c_8(s^#(activate(X)))
     , activate^#(n__zWquot(X1, X2)) ->
       c_9(zWquot^#(activate(X1), activate(X2)))
     , zWquot^#(X1, X2) -> c_14(X1, X2)
     , zWquot^#(XS, nil()) -> c_15()
     , zWquot^#(cons(X, XS), cons(Y, YS)) ->
       c_16(quot^#(X, Y), activate^#(XS), activate^#(YS))
     , zWquot^#(nil(), XS) -> c_17()
     , minus^#(X, 0()) -> c_10()
     , minus^#(s(X), s(Y)) -> c_11(minus^#(X, Y))
     , quot^#(0(), s(Y)) -> c_12()
     , quot^#(s(X), s(Y)) -> c_13(s^#(quot(minus(X, Y), s(Y)))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(X, X)
     , from^#(X) -> c_2(X)
     , sel^#(0(), cons(X, XS)) -> c_3(X)
     , sel^#(s(N), cons(X, XS)) -> c_4(sel^#(N, activate(XS)))
     , s^#(X) -> c_5(X)
     , activate^#(X) -> c_6(X)
     , activate^#(n__from(X)) -> c_7(from^#(activate(X)))
     , activate^#(n__s(X)) -> c_8(s^#(activate(X)))
     , activate^#(n__zWquot(X1, X2)) ->
       c_9(zWquot^#(activate(X1), activate(X2)))
     , zWquot^#(X1, X2) -> c_14(X1, X2)
     , zWquot^#(XS, nil()) -> c_15()
     , zWquot^#(cons(X, XS), cons(Y, YS)) ->
       c_16(quot^#(X, Y), activate^#(XS), activate^#(YS))
     , zWquot^#(nil(), XS) -> c_17()
     , minus^#(X, 0()) -> c_10()
     , minus^#(s(X), s(Y)) -> c_11(minus^#(X, Y))
     , quot^#(0(), s(Y)) -> c_12()
     , quot^#(s(X), s(Y)) -> c_13(s^#(quot(minus(X, Y), s(Y)))) }
   Strict Trs:
     { from(X) -> cons(X, n__from(n__s(X)))
     , from(X) -> n__from(X)
     , sel(0(), cons(X, XS)) -> X
     , sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
     , s(X) -> n__s(X)
     , activate(X) -> X
     , activate(n__from(X)) -> from(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2))
     , minus(X, 0()) -> 0()
     , minus(s(X), s(Y)) -> minus(X, Y)
     , quot(0(), s(Y)) -> 0()
     , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
     , zWquot(X1, X2) -> n__zWquot(X1, X2)
     , zWquot(XS, nil()) -> nil()
     , zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
     , zWquot(nil(), XS) -> nil() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {11,13,14,16} by
   applications of Pre({11,13,14,16}) = {1,2,3,5,6,9,10,12,15}. Here
   rules are labeled as follows:
   
     DPs:
       { 1: from^#(X) -> c_1(X, X)
       , 2: from^#(X) -> c_2(X)
       , 3: sel^#(0(), cons(X, XS)) -> c_3(X)
       , 4: sel^#(s(N), cons(X, XS)) -> c_4(sel^#(N, activate(XS)))
       , 5: s^#(X) -> c_5(X)
       , 6: activate^#(X) -> c_6(X)
       , 7: activate^#(n__from(X)) -> c_7(from^#(activate(X)))
       , 8: activate^#(n__s(X)) -> c_8(s^#(activate(X)))
       , 9: activate^#(n__zWquot(X1, X2)) ->
            c_9(zWquot^#(activate(X1), activate(X2)))
       , 10: zWquot^#(X1, X2) -> c_14(X1, X2)
       , 11: zWquot^#(XS, nil()) -> c_15()
       , 12: zWquot^#(cons(X, XS), cons(Y, YS)) ->
             c_16(quot^#(X, Y), activate^#(XS), activate^#(YS))
       , 13: zWquot^#(nil(), XS) -> c_17()
       , 14: minus^#(X, 0()) -> c_10()
       , 15: minus^#(s(X), s(Y)) -> c_11(minus^#(X, Y))
       , 16: quot^#(0(), s(Y)) -> c_12()
       , 17: quot^#(s(X), s(Y)) -> c_13(s^#(quot(minus(X, Y), s(Y)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(X, X)
     , from^#(X) -> c_2(X)
     , sel^#(0(), cons(X, XS)) -> c_3(X)
     , sel^#(s(N), cons(X, XS)) -> c_4(sel^#(N, activate(XS)))
     , s^#(X) -> c_5(X)
     , activate^#(X) -> c_6(X)
     , activate^#(n__from(X)) -> c_7(from^#(activate(X)))
     , activate^#(n__s(X)) -> c_8(s^#(activate(X)))
     , activate^#(n__zWquot(X1, X2)) ->
       c_9(zWquot^#(activate(X1), activate(X2)))
     , zWquot^#(X1, X2) -> c_14(X1, X2)
     , zWquot^#(cons(X, XS), cons(Y, YS)) ->
       c_16(quot^#(X, Y), activate^#(XS), activate^#(YS))
     , minus^#(s(X), s(Y)) -> c_11(minus^#(X, Y))
     , quot^#(s(X), s(Y)) -> c_13(s^#(quot(minus(X, Y), s(Y)))) }
   Strict Trs:
     { from(X) -> cons(X, n__from(n__s(X)))
     , from(X) -> n__from(X)
     , sel(0(), cons(X, XS)) -> X
     , sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
     , s(X) -> n__s(X)
     , activate(X) -> X
     , activate(n__from(X)) -> from(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2))
     , minus(X, 0()) -> 0()
     , minus(s(X), s(Y)) -> minus(X, Y)
     , quot(0(), s(Y)) -> 0()
     , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
     , zWquot(X1, X2) -> n__zWquot(X1, X2)
     , zWquot(XS, nil()) -> nil()
     , zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
     , zWquot(nil(), XS) -> nil() }
   Weak DPs:
     { zWquot^#(XS, nil()) -> c_15()
     , zWquot^#(nil(), XS) -> c_17()
     , minus^#(X, 0()) -> c_10()
     , quot^#(0(), s(Y)) -> c_12() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..