MAYBE

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

Strict Trs:
  { msort(nil()) -> nil()
  , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
  , min(x, nil()) -> x
  , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
  , del(x, nil()) -> nil()
  , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
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) '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) '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:
     { msort^#(nil()) -> c_1()
     , msort^#(.(x, y)) ->
       c_2(min^#(x, y), msort^#(del(min(x, y), .(x, y))))
     , min^#(x, nil()) -> c_3(x)
     , min^#(x, .(y, z)) -> c_4(x, y, min^#(x, z), min^#(y, z))
     , del^#(x, nil()) -> c_5()
     , del^#(x, .(y, z)) -> c_6(x, y, z, y, del^#(x, z)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { msort^#(nil()) -> c_1()
     , msort^#(.(x, y)) ->
       c_2(min^#(x, y), msort^#(del(min(x, y), .(x, y))))
     , min^#(x, nil()) -> c_3(x)
     , min^#(x, .(y, z)) -> c_4(x, y, min^#(x, z), min^#(y, z))
     , del^#(x, nil()) -> c_5()
     , del^#(x, .(y, z)) -> c_6(x, y, z, y, del^#(x, z)) }
   Strict Trs:
     { msort(nil()) -> nil()
     , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
     , min(x, nil()) -> x
     , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
     , del(x, nil()) -> nil()
     , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,5} by applications of
   Pre({1,5}) = {2,3,4,6}. Here rules are labeled as follows:
   
     DPs:
       { 1: msort^#(nil()) -> c_1()
       , 2: msort^#(.(x, y)) ->
            c_2(min^#(x, y), msort^#(del(min(x, y), .(x, y))))
       , 3: min^#(x, nil()) -> c_3(x)
       , 4: min^#(x, .(y, z)) -> c_4(x, y, min^#(x, z), min^#(y, z))
       , 5: del^#(x, nil()) -> c_5()
       , 6: del^#(x, .(y, z)) -> c_6(x, y, z, y, del^#(x, z)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { msort^#(.(x, y)) ->
       c_2(min^#(x, y), msort^#(del(min(x, y), .(x, y))))
     , min^#(x, nil()) -> c_3(x)
     , min^#(x, .(y, z)) -> c_4(x, y, min^#(x, z), min^#(y, z))
     , del^#(x, .(y, z)) -> c_6(x, y, z, y, del^#(x, z)) }
   Strict Trs:
     { msort(nil()) -> nil()
     , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
     , min(x, nil()) -> x
     , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
     , del(x, nil()) -> nil()
     , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
   Weak DPs:
     { msort^#(nil()) -> c_1()
     , del^#(x, nil()) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..