MAYBE

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

Strict Trs:
  { top(sent(x)) -> top(check(rest(x)))
  , check(sent(x)) -> sent(check(x))
  , check(rest(x)) -> rest(check(x))
  , check(cons(x, y)) -> cons(x, y)
  , check(cons(x, y)) -> cons(x, check(y))
  , check(cons(x, y)) -> cons(check(x), y)
  , rest(nil()) -> sent(nil())
  , rest(cons(x, y)) -> sent(y) }
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:
      
      Computation stopped due to timeout after 5.0 seconds.
   
   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:
     { top^#(sent(x)) -> c_1(top^#(check(rest(x))))
     , check^#(sent(x)) -> c_2(check^#(x))
     , check^#(rest(x)) -> c_3(rest^#(check(x)))
     , check^#(cons(x, y)) -> c_4(x, y)
     , check^#(cons(x, y)) -> c_5(x, check^#(y))
     , check^#(cons(x, y)) -> c_6(check^#(x), y)
     , rest^#(nil()) -> c_7()
     , rest^#(cons(x, y)) -> c_8(y) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { top^#(sent(x)) -> c_1(top^#(check(rest(x))))
     , check^#(sent(x)) -> c_2(check^#(x))
     , check^#(rest(x)) -> c_3(rest^#(check(x)))
     , check^#(cons(x, y)) -> c_4(x, y)
     , check^#(cons(x, y)) -> c_5(x, check^#(y))
     , check^#(cons(x, y)) -> c_6(check^#(x), y)
     , rest^#(nil()) -> c_7()
     , rest^#(cons(x, y)) -> c_8(y) }
   Strict Trs:
     { top(sent(x)) -> top(check(rest(x)))
     , check(sent(x)) -> sent(check(x))
     , check(rest(x)) -> rest(check(x))
     , check(cons(x, y)) -> cons(x, y)
     , check(cons(x, y)) -> cons(x, check(y))
     , check(cons(x, y)) -> cons(check(x), y)
     , rest(nil()) -> sent(nil())
     , rest(cons(x, y)) -> sent(y) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {7} by applications of
   Pre({7}) = {4,5,6,8}. Here rules are labeled as follows:
   
     DPs:
       { 1: top^#(sent(x)) -> c_1(top^#(check(rest(x))))
       , 2: check^#(sent(x)) -> c_2(check^#(x))
       , 3: check^#(rest(x)) -> c_3(rest^#(check(x)))
       , 4: check^#(cons(x, y)) -> c_4(x, y)
       , 5: check^#(cons(x, y)) -> c_5(x, check^#(y))
       , 6: check^#(cons(x, y)) -> c_6(check^#(x), y)
       , 7: rest^#(nil()) -> c_7()
       , 8: rest^#(cons(x, y)) -> c_8(y) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { top^#(sent(x)) -> c_1(top^#(check(rest(x))))
     , check^#(sent(x)) -> c_2(check^#(x))
     , check^#(rest(x)) -> c_3(rest^#(check(x)))
     , check^#(cons(x, y)) -> c_4(x, y)
     , check^#(cons(x, y)) -> c_5(x, check^#(y))
     , check^#(cons(x, y)) -> c_6(check^#(x), y)
     , rest^#(cons(x, y)) -> c_8(y) }
   Strict Trs:
     { top(sent(x)) -> top(check(rest(x)))
     , check(sent(x)) -> sent(check(x))
     , check(rest(x)) -> rest(check(x))
     , check(cons(x, y)) -> cons(x, y)
     , check(cons(x, y)) -> cons(x, check(y))
     , check(cons(x, y)) -> cons(check(x), y)
     , rest(nil()) -> sent(nil())
     , rest(cons(x, y)) -> sent(y) }
   Weak DPs: { rest^#(nil()) -> c_7() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..