MAYBE

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

Strict Trs:
  { top(free(x)) -> top(check(new(x)))
  , check(free(x)) -> free(check(x))
  , check(new(x)) -> new(check(x))
  , check(old(x)) -> old(x)
  , check(old(x)) -> old(check(x))
  , new(free(x)) -> free(new(x))
  , new(serve()) -> free(serve())
  , old(free(x)) -> free(old(x))
  , old(serve()) -> free(serve()) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) '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
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { top^#(free(x)) -> c_1(top^#(check(new(x))))
     , check^#(free(x)) -> c_2(check^#(x))
     , check^#(new(x)) -> c_3(new^#(check(x)))
     , check^#(old(x)) -> c_4(old^#(x))
     , check^#(old(x)) -> c_5(old^#(check(x)))
     , new^#(free(x)) -> c_6(new^#(x))
     , new^#(serve()) -> c_7()
     , old^#(free(x)) -> c_8(old^#(x))
     , old^#(serve()) -> c_9() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { top^#(free(x)) -> c_1(top^#(check(new(x))))
     , check^#(free(x)) -> c_2(check^#(x))
     , check^#(new(x)) -> c_3(new^#(check(x)))
     , check^#(old(x)) -> c_4(old^#(x))
     , check^#(old(x)) -> c_5(old^#(check(x)))
     , new^#(free(x)) -> c_6(new^#(x))
     , new^#(serve()) -> c_7()
     , old^#(free(x)) -> c_8(old^#(x))
     , old^#(serve()) -> c_9() }
   Strict Trs:
     { top(free(x)) -> top(check(new(x)))
     , check(free(x)) -> free(check(x))
     , check(new(x)) -> new(check(x))
     , check(old(x)) -> old(x)
     , check(old(x)) -> old(check(x))
     , new(free(x)) -> free(new(x))
     , new(serve()) -> free(serve())
     , old(free(x)) -> free(old(x))
     , old(serve()) -> free(serve()) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {7,9} by applications of
   Pre({7,9}) = {4,6,8}. Here rules are labeled as follows:
   
     DPs:
       { 1: top^#(free(x)) -> c_1(top^#(check(new(x))))
       , 2: check^#(free(x)) -> c_2(check^#(x))
       , 3: check^#(new(x)) -> c_3(new^#(check(x)))
       , 4: check^#(old(x)) -> c_4(old^#(x))
       , 5: check^#(old(x)) -> c_5(old^#(check(x)))
       , 6: new^#(free(x)) -> c_6(new^#(x))
       , 7: new^#(serve()) -> c_7()
       , 8: old^#(free(x)) -> c_8(old^#(x))
       , 9: old^#(serve()) -> c_9() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { top^#(free(x)) -> c_1(top^#(check(new(x))))
     , check^#(free(x)) -> c_2(check^#(x))
     , check^#(new(x)) -> c_3(new^#(check(x)))
     , check^#(old(x)) -> c_4(old^#(x))
     , check^#(old(x)) -> c_5(old^#(check(x)))
     , new^#(free(x)) -> c_6(new^#(x))
     , old^#(free(x)) -> c_8(old^#(x)) }
   Strict Trs:
     { top(free(x)) -> top(check(new(x)))
     , check(free(x)) -> free(check(x))
     , check(new(x)) -> new(check(x))
     , check(old(x)) -> old(x)
     , check(old(x)) -> old(check(x))
     , new(free(x)) -> free(new(x))
     , new(serve()) -> free(serve())
     , old(free(x)) -> free(old(x))
     , old(serve()) -> free(serve()) }
   Weak DPs:
     { new^#(serve()) -> c_7()
     , old^#(serve()) -> c_9() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..