MAYBE

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

Strict Trs:
  { app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
  , from(X) -> cons(X, from(s(X)))
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, nil())), zWadr(XS, YS))
  , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

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

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

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { app^#(nil(), YS) -> c_1(YS)
     , app^#(cons(X, XS), YS) -> c_2(X, app^#(XS, YS))
     , from^#(X) -> c_3(X, from^#(s(X)))
     , zWadr^#(XS, nil()) -> c_4()
     , zWadr^#(nil(), YS) -> c_5()
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
     , prefix^#(L) -> c_7(zWadr^#(L, prefix(L))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { app^#(nil(), YS) -> c_1(YS)
     , app^#(cons(X, XS), YS) -> c_2(X, app^#(XS, YS))
     , from^#(X) -> c_3(X, from^#(s(X)))
     , zWadr^#(XS, nil()) -> c_4()
     , zWadr^#(nil(), YS) -> c_5()
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
     , prefix^#(L) -> c_7(zWadr^#(L, prefix(L))) }
   Strict Trs:
     { app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
     , from(X) -> cons(X, from(s(X)))
     , zWadr(XS, nil()) -> nil()
     , zWadr(nil(), YS) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, nil())), zWadr(XS, YS))
     , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,5} by applications of
   Pre({4,5}) = {1,2,3,6,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: app^#(nil(), YS) -> c_1(YS)
       , 2: app^#(cons(X, XS), YS) -> c_2(X, app^#(XS, YS))
       , 3: from^#(X) -> c_3(X, from^#(s(X)))
       , 4: zWadr^#(XS, nil()) -> c_4()
       , 5: zWadr^#(nil(), YS) -> c_5()
       , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
            c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
       , 7: prefix^#(L) -> c_7(zWadr^#(L, prefix(L))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { app^#(nil(), YS) -> c_1(YS)
     , app^#(cons(X, XS), YS) -> c_2(X, app^#(XS, YS))
     , from^#(X) -> c_3(X, from^#(s(X)))
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
     , prefix^#(L) -> c_7(zWadr^#(L, prefix(L))) }
   Strict Trs:
     { app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
     , from(X) -> cons(X, from(s(X)))
     , zWadr(XS, nil()) -> nil()
     , zWadr(nil(), YS) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, nil())), zWadr(XS, YS))
     , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
   Weak DPs:
     { zWadr^#(XS, nil()) -> c_4()
     , zWadr^#(nil(), YS) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..