MAYBE

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

Strict Trs:
  { app(X1, X2) -> n__app(X1, X2)
  , app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
  , nil() -> n__nil()
  , activate(X) -> X
  , activate(n__app(X1, X2)) -> app(X1, X2)
  , activate(n__from(X)) -> from(X)
  , activate(n__nil()) -> nil()
  , activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
  , from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , zWadr(X1, X2) -> n__zWadr(X1, X2)
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, n__nil())),
         n__zWadr(activate(XS), activate(YS)))
  , prefix(L) -> cons(nil(), n__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) '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:
     { app^#(X1, X2) -> c_1(X1, X2)
     , app^#(nil(), YS) -> c_2(YS)
     , app^#(cons(X, XS), YS) -> c_3(X, activate^#(XS), YS)
     , activate^#(X) -> c_5(X)
     , activate^#(n__app(X1, X2)) -> c_6(app^#(X1, X2))
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__nil()) -> c_8(nil^#())
     , activate^#(n__zWadr(X1, X2)) -> c_9(zWadr^#(X1, X2))
     , nil^#() -> c_4()
     , from^#(X) -> c_10(X, X)
     , from^#(X) -> c_11(X)
     , zWadr^#(X1, X2) -> c_12(X1, X2)
     , zWadr^#(XS, nil()) -> c_13(nil^#())
     , zWadr^#(nil(), YS) -> c_14(nil^#())
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_15(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
     , prefix^#(L) -> c_16(nil^#(), 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^#(X1, X2) -> c_1(X1, X2)
     , app^#(nil(), YS) -> c_2(YS)
     , app^#(cons(X, XS), YS) -> c_3(X, activate^#(XS), YS)
     , activate^#(X) -> c_5(X)
     , activate^#(n__app(X1, X2)) -> c_6(app^#(X1, X2))
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__nil()) -> c_8(nil^#())
     , activate^#(n__zWadr(X1, X2)) -> c_9(zWadr^#(X1, X2))
     , nil^#() -> c_4()
     , from^#(X) -> c_10(X, X)
     , from^#(X) -> c_11(X)
     , zWadr^#(X1, X2) -> c_12(X1, X2)
     , zWadr^#(XS, nil()) -> c_13(nil^#())
     , zWadr^#(nil(), YS) -> c_14(nil^#())
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_15(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
     , prefix^#(L) -> c_16(nil^#(), L, prefix^#(L)) }
   Strict Trs:
     { app(X1, X2) -> n__app(X1, X2)
     , app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
     , nil() -> n__nil()
     , activate(X) -> X
     , activate(n__app(X1, X2)) -> app(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(n__nil()) -> nil()
     , activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
     , from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , zWadr(X1, X2) -> n__zWadr(X1, X2)
     , zWadr(XS, nil()) -> nil()
     , zWadr(nil(), YS) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, n__nil())),
            n__zWadr(activate(XS), activate(YS)))
     , prefix(L) -> cons(nil(), n__zWadr(L, prefix(L))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {9} by applications of
   Pre({9}) = {1,2,3,4,7,10,11,12,13,14,16}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: app^#(X1, X2) -> c_1(X1, X2)
       , 2: app^#(nil(), YS) -> c_2(YS)
       , 3: app^#(cons(X, XS), YS) -> c_3(X, activate^#(XS), YS)
       , 4: activate^#(X) -> c_5(X)
       , 5: activate^#(n__app(X1, X2)) -> c_6(app^#(X1, X2))
       , 6: activate^#(n__from(X)) -> c_7(from^#(X))
       , 7: activate^#(n__nil()) -> c_8(nil^#())
       , 8: activate^#(n__zWadr(X1, X2)) -> c_9(zWadr^#(X1, X2))
       , 9: nil^#() -> c_4()
       , 10: from^#(X) -> c_10(X, X)
       , 11: from^#(X) -> c_11(X)
       , 12: zWadr^#(X1, X2) -> c_12(X1, X2)
       , 13: zWadr^#(XS, nil()) -> c_13(nil^#())
       , 14: zWadr^#(nil(), YS) -> c_14(nil^#())
       , 15: zWadr^#(cons(X, XS), cons(Y, YS)) ->
             c_15(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
       , 16: prefix^#(L) -> c_16(nil^#(), L, prefix^#(L)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { app^#(X1, X2) -> c_1(X1, X2)
     , app^#(nil(), YS) -> c_2(YS)
     , app^#(cons(X, XS), YS) -> c_3(X, activate^#(XS), YS)
     , activate^#(X) -> c_5(X)
     , activate^#(n__app(X1, X2)) -> c_6(app^#(X1, X2))
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__nil()) -> c_8(nil^#())
     , activate^#(n__zWadr(X1, X2)) -> c_9(zWadr^#(X1, X2))
     , from^#(X) -> c_10(X, X)
     , from^#(X) -> c_11(X)
     , zWadr^#(X1, X2) -> c_12(X1, X2)
     , zWadr^#(XS, nil()) -> c_13(nil^#())
     , zWadr^#(nil(), YS) -> c_14(nil^#())
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_15(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
     , prefix^#(L) -> c_16(nil^#(), L, prefix^#(L)) }
   Strict Trs:
     { app(X1, X2) -> n__app(X1, X2)
     , app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
     , nil() -> n__nil()
     , activate(X) -> X
     , activate(n__app(X1, X2)) -> app(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(n__nil()) -> nil()
     , activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
     , from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , zWadr(X1, X2) -> n__zWadr(X1, X2)
     , zWadr(XS, nil()) -> nil()
     , zWadr(nil(), YS) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, n__nil())),
            n__zWadr(activate(XS), activate(YS)))
     , prefix(L) -> cons(nil(), n__zWadr(L, prefix(L))) }
   Weak DPs: { nil^#() -> c_4() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {7,12,13} by applications
   of Pre({7,12,13}) = {1,2,3,4,8,9,10,11,14,15}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: app^#(X1, X2) -> c_1(X1, X2)
       , 2: app^#(nil(), YS) -> c_2(YS)
       , 3: app^#(cons(X, XS), YS) -> c_3(X, activate^#(XS), YS)
       , 4: activate^#(X) -> c_5(X)
       , 5: activate^#(n__app(X1, X2)) -> c_6(app^#(X1, X2))
       , 6: activate^#(n__from(X)) -> c_7(from^#(X))
       , 7: activate^#(n__nil()) -> c_8(nil^#())
       , 8: activate^#(n__zWadr(X1, X2)) -> c_9(zWadr^#(X1, X2))
       , 9: from^#(X) -> c_10(X, X)
       , 10: from^#(X) -> c_11(X)
       , 11: zWadr^#(X1, X2) -> c_12(X1, X2)
       , 12: zWadr^#(XS, nil()) -> c_13(nil^#())
       , 13: zWadr^#(nil(), YS) -> c_14(nil^#())
       , 14: zWadr^#(cons(X, XS), cons(Y, YS)) ->
             c_15(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
       , 15: prefix^#(L) -> c_16(nil^#(), L, prefix^#(L))
       , 16: nil^#() -> c_4() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { app^#(X1, X2) -> c_1(X1, X2)
     , app^#(nil(), YS) -> c_2(YS)
     , app^#(cons(X, XS), YS) -> c_3(X, activate^#(XS), YS)
     , activate^#(X) -> c_5(X)
     , activate^#(n__app(X1, X2)) -> c_6(app^#(X1, X2))
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__zWadr(X1, X2)) -> c_9(zWadr^#(X1, X2))
     , from^#(X) -> c_10(X, X)
     , from^#(X) -> c_11(X)
     , zWadr^#(X1, X2) -> c_12(X1, X2)
     , zWadr^#(cons(X, XS), cons(Y, YS)) ->
       c_15(app^#(Y, cons(X, n__nil())), activate^#(XS), activate^#(YS))
     , prefix^#(L) -> c_16(nil^#(), L, prefix^#(L)) }
   Strict Trs:
     { app(X1, X2) -> n__app(X1, X2)
     , app(nil(), YS) -> YS
     , app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
     , nil() -> n__nil()
     , activate(X) -> X
     , activate(n__app(X1, X2)) -> app(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(n__nil()) -> nil()
     , activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
     , from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , zWadr(X1, X2) -> n__zWadr(X1, X2)
     , zWadr(XS, nil()) -> nil()
     , zWadr(nil(), YS) -> nil()
     , zWadr(cons(X, XS), cons(Y, YS)) ->
       cons(app(Y, cons(X, n__nil())),
            n__zWadr(activate(XS), activate(YS)))
     , prefix(L) -> cons(nil(), n__zWadr(L, prefix(L))) }
   Weak DPs:
     { activate^#(n__nil()) -> c_8(nil^#())
     , nil^#() -> c_4()
     , zWadr^#(XS, nil()) -> c_13(nil^#())
     , zWadr^#(nil(), YS) -> c_14(nil^#()) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..