MAYBE

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

Strict Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
  , last(x, l) -> if(empty(l), x, l)
  , if(true(), x, l) -> x
  , if(false(), x, l) -> last(head(l), tail(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:
     { empty^#(nil()) -> c_1()
     , empty^#(cons(x, l)) -> c_2()
     , head^#(cons(x, l)) -> c_3(x)
     , tail^#(nil()) -> c_4()
     , tail^#(cons(x, l)) -> c_5(l)
     , rev^#(nil()) -> c_6()
     , rev^#(cons(x, l)) -> c_7(x, l, rev2^#(x, l))
     , rev2^#(x, nil()) -> c_8()
     , rev2^#(x, cons(y, l)) -> c_9(rev^#(cons(x, rev2(y, l))))
     , last^#(x, l) -> c_10(if^#(empty(l), x, l))
     , if^#(true(), x, l) -> c_11(x)
     , if^#(false(), x, l) -> c_12(last^#(head(l), tail(l))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { empty^#(nil()) -> c_1()
     , empty^#(cons(x, l)) -> c_2()
     , head^#(cons(x, l)) -> c_3(x)
     , tail^#(nil()) -> c_4()
     , tail^#(cons(x, l)) -> c_5(l)
     , rev^#(nil()) -> c_6()
     , rev^#(cons(x, l)) -> c_7(x, l, rev2^#(x, l))
     , rev2^#(x, nil()) -> c_8()
     , rev2^#(x, cons(y, l)) -> c_9(rev^#(cons(x, rev2(y, l))))
     , last^#(x, l) -> c_10(if^#(empty(l), x, l))
     , if^#(true(), x, l) -> c_11(x)
     , if^#(false(), x, l) -> c_12(last^#(head(l), tail(l))) }
   Strict Trs:
     { empty(nil()) -> true()
     , empty(cons(x, l)) -> false()
     , head(cons(x, l)) -> x
     , tail(nil()) -> nil()
     , tail(cons(x, l)) -> l
     , rev(nil()) -> nil()
     , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
     , rev2(x, nil()) -> nil()
     , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
     , last(x, l) -> if(empty(l), x, l)
     , if(true(), x, l) -> x
     , if(false(), x, l) -> last(head(l), tail(l)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,4,6,8} by
   applications of Pre({1,2,4,6,8}) = {3,5,7,11}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: empty^#(nil()) -> c_1()
       , 2: empty^#(cons(x, l)) -> c_2()
       , 3: head^#(cons(x, l)) -> c_3(x)
       , 4: tail^#(nil()) -> c_4()
       , 5: tail^#(cons(x, l)) -> c_5(l)
       , 6: rev^#(nil()) -> c_6()
       , 7: rev^#(cons(x, l)) -> c_7(x, l, rev2^#(x, l))
       , 8: rev2^#(x, nil()) -> c_8()
       , 9: rev2^#(x, cons(y, l)) -> c_9(rev^#(cons(x, rev2(y, l))))
       , 10: last^#(x, l) -> c_10(if^#(empty(l), x, l))
       , 11: if^#(true(), x, l) -> c_11(x)
       , 12: if^#(false(), x, l) -> c_12(last^#(head(l), tail(l))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { head^#(cons(x, l)) -> c_3(x)
     , tail^#(cons(x, l)) -> c_5(l)
     , rev^#(cons(x, l)) -> c_7(x, l, rev2^#(x, l))
     , rev2^#(x, cons(y, l)) -> c_9(rev^#(cons(x, rev2(y, l))))
     , last^#(x, l) -> c_10(if^#(empty(l), x, l))
     , if^#(true(), x, l) -> c_11(x)
     , if^#(false(), x, l) -> c_12(last^#(head(l), tail(l))) }
   Strict Trs:
     { empty(nil()) -> true()
     , empty(cons(x, l)) -> false()
     , head(cons(x, l)) -> x
     , tail(nil()) -> nil()
     , tail(cons(x, l)) -> l
     , rev(nil()) -> nil()
     , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
     , rev2(x, nil()) -> nil()
     , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
     , last(x, l) -> if(empty(l), x, l)
     , if(true(), x, l) -> x
     , if(false(), x, l) -> last(head(l), tail(l)) }
   Weak DPs:
     { empty^#(nil()) -> c_1()
     , empty^#(cons(x, l)) -> c_2()
     , tail^#(nil()) -> c_4()
     , rev^#(nil()) -> c_6()
     , rev2^#(x, nil()) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..