MAYBE

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

Strict Trs:
  { top1(free(x), y) -> top2(x, check(new(y)))
  , top1(free(x), y) -> top2(check(x), new(y))
  , top1(free(x), y) -> top2(check(new(x)), y)
  , top1(free(x), y) -> top2(new(x), check(y))
  , top2(x, free(y)) -> top1(x, check(new(y)))
  , top2(x, free(y)) -> top1(check(x), new(y))
  , top2(x, free(y)) -> top1(check(new(x)), y)
  , top2(x, free(y)) -> top1(new(x), check(y))
  , 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:
     { top1^#(free(x), y) -> c_1(top2^#(x, check(new(y))))
     , top1^#(free(x), y) -> c_2(top2^#(check(x), new(y)))
     , top1^#(free(x), y) -> c_3(top2^#(check(new(x)), y))
     , top1^#(free(x), y) -> c_4(top2^#(new(x), check(y)))
     , top2^#(x, free(y)) -> c_5(top1^#(x, check(new(y))))
     , top2^#(x, free(y)) -> c_6(top1^#(check(x), new(y)))
     , top2^#(x, free(y)) -> c_7(top1^#(check(new(x)), y))
     , top2^#(x, free(y)) -> c_8(top1^#(new(x), check(y)))
     , check^#(free(x)) -> c_9(check^#(x))
     , check^#(new(x)) -> c_10(new^#(check(x)))
     , check^#(old(x)) -> c_11(old^#(x))
     , check^#(old(x)) -> c_12(old^#(check(x)))
     , new^#(free(x)) -> c_13(new^#(x))
     , new^#(serve()) -> c_14()
     , old^#(free(x)) -> c_15(old^#(x))
     , old^#(serve()) -> c_16() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { top1^#(free(x), y) -> c_1(top2^#(x, check(new(y))))
     , top1^#(free(x), y) -> c_2(top2^#(check(x), new(y)))
     , top1^#(free(x), y) -> c_3(top2^#(check(new(x)), y))
     , top1^#(free(x), y) -> c_4(top2^#(new(x), check(y)))
     , top2^#(x, free(y)) -> c_5(top1^#(x, check(new(y))))
     , top2^#(x, free(y)) -> c_6(top1^#(check(x), new(y)))
     , top2^#(x, free(y)) -> c_7(top1^#(check(new(x)), y))
     , top2^#(x, free(y)) -> c_8(top1^#(new(x), check(y)))
     , check^#(free(x)) -> c_9(check^#(x))
     , check^#(new(x)) -> c_10(new^#(check(x)))
     , check^#(old(x)) -> c_11(old^#(x))
     , check^#(old(x)) -> c_12(old^#(check(x)))
     , new^#(free(x)) -> c_13(new^#(x))
     , new^#(serve()) -> c_14()
     , old^#(free(x)) -> c_15(old^#(x))
     , old^#(serve()) -> c_16() }
   Strict Trs:
     { top1(free(x), y) -> top2(x, check(new(y)))
     , top1(free(x), y) -> top2(check(x), new(y))
     , top1(free(x), y) -> top2(check(new(x)), y)
     , top1(free(x), y) -> top2(new(x), check(y))
     , top2(x, free(y)) -> top1(x, check(new(y)))
     , top2(x, free(y)) -> top1(check(x), new(y))
     , top2(x, free(y)) -> top1(check(new(x)), y)
     , top2(x, free(y)) -> top1(new(x), check(y))
     , 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 {14,16} by applications of
   Pre({14,16}) = {11,13,15}. Here rules are labeled as follows:
   
     DPs:
       { 1: top1^#(free(x), y) -> c_1(top2^#(x, check(new(y))))
       , 2: top1^#(free(x), y) -> c_2(top2^#(check(x), new(y)))
       , 3: top1^#(free(x), y) -> c_3(top2^#(check(new(x)), y))
       , 4: top1^#(free(x), y) -> c_4(top2^#(new(x), check(y)))
       , 5: top2^#(x, free(y)) -> c_5(top1^#(x, check(new(y))))
       , 6: top2^#(x, free(y)) -> c_6(top1^#(check(x), new(y)))
       , 7: top2^#(x, free(y)) -> c_7(top1^#(check(new(x)), y))
       , 8: top2^#(x, free(y)) -> c_8(top1^#(new(x), check(y)))
       , 9: check^#(free(x)) -> c_9(check^#(x))
       , 10: check^#(new(x)) -> c_10(new^#(check(x)))
       , 11: check^#(old(x)) -> c_11(old^#(x))
       , 12: check^#(old(x)) -> c_12(old^#(check(x)))
       , 13: new^#(free(x)) -> c_13(new^#(x))
       , 14: new^#(serve()) -> c_14()
       , 15: old^#(free(x)) -> c_15(old^#(x))
       , 16: old^#(serve()) -> c_16() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { top1^#(free(x), y) -> c_1(top2^#(x, check(new(y))))
     , top1^#(free(x), y) -> c_2(top2^#(check(x), new(y)))
     , top1^#(free(x), y) -> c_3(top2^#(check(new(x)), y))
     , top1^#(free(x), y) -> c_4(top2^#(new(x), check(y)))
     , top2^#(x, free(y)) -> c_5(top1^#(x, check(new(y))))
     , top2^#(x, free(y)) -> c_6(top1^#(check(x), new(y)))
     , top2^#(x, free(y)) -> c_7(top1^#(check(new(x)), y))
     , top2^#(x, free(y)) -> c_8(top1^#(new(x), check(y)))
     , check^#(free(x)) -> c_9(check^#(x))
     , check^#(new(x)) -> c_10(new^#(check(x)))
     , check^#(old(x)) -> c_11(old^#(x))
     , check^#(old(x)) -> c_12(old^#(check(x)))
     , new^#(free(x)) -> c_13(new^#(x))
     , old^#(free(x)) -> c_15(old^#(x)) }
   Strict Trs:
     { top1(free(x), y) -> top2(x, check(new(y)))
     , top1(free(x), y) -> top2(check(x), new(y))
     , top1(free(x), y) -> top2(check(new(x)), y)
     , top1(free(x), y) -> top2(new(x), check(y))
     , top2(x, free(y)) -> top1(x, check(new(y)))
     , top2(x, free(y)) -> top1(check(x), new(y))
     , top2(x, free(y)) -> top1(check(new(x)), y)
     , top2(x, free(y)) -> top1(new(x), check(y))
     , 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_14()
     , old^#(serve()) -> c_16() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..