MAYBE

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

Strict Trs:
  { ack(0(), y) -> s(y)
  , ack(s(x), y) -> f(x, x)
  , ack(s(x), 0()) -> ack(x, s(0()))
  , ack(s(x), s(y)) -> ack(x, ack(s(x), y))
  , f(x, y) -> ack(x, y)
  , f(x, s(y)) -> f(y, x)
  , f(s(x), y) -> f(x, s(x)) }
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:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'empty' failed due to the following reason:
         
         Empty strict component of the problem is NOT empty.
      
      2) 'WithProblem' failed due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'empty' failed due to the following reason:
            
            Empty strict component of the problem is NOT empty.
         
         2) 'Fastest' failed due to the following reason:
            
            None of the processors succeeded.
            
            Details of failed attempt(s):
            -----------------------------
            1) 'WithProblem' failed due to the following reason:
               
               None of the processors succeeded.
               
               Details of failed attempt(s):
               -----------------------------
               1) 'empty' failed due to the following reason:
                  
                  Empty strict component of the problem is NOT empty.
               
               2) 'WithProblem' failed due to the following reason:
                  
                  Empty strict component of the problem is NOT empty.
               
            
            2) 'WithProblem' failed due to the following reason:
               
               None of the processors succeeded.
               
               Details of failed attempt(s):
               -----------------------------
               1) 'empty' failed due to the following reason:
                  
                  Empty strict component of the problem is NOT empty.
               
               2) 'WithProblem' failed due to the following reason:
                  
                  None of the processors succeeded.
                  
                  Details of failed attempt(s):
                  -----------------------------
                  1) 'empty' failed due to the following reason:
                     
                     Empty strict component of the problem is NOT empty.
                  
                  2) 'WithProblem' failed due to the following reason:
                     
                     None of the processors succeeded.
                     
                     Details of failed attempt(s):
                     -----------------------------
                     1) 'empty' failed due to the following reason:
                        
                        Empty strict component of the problem is NOT empty.
                     
                     2) 'WithProblem' failed due to the following reason:
                        
                        Empty strict component of the problem is NOT empty.
                     
                  
               
            
         
      
   
   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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-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:
     { ack^#(0(), y) -> c_1(y)
     , ack^#(s(x), y) -> c_2(f^#(x, x))
     , ack^#(s(x), 0()) -> c_3(ack^#(x, s(0())))
     , ack^#(s(x), s(y)) -> c_4(ack^#(x, ack(s(x), y)))
     , f^#(x, y) -> c_5(ack^#(x, y))
     , f^#(x, s(y)) -> c_6(f^#(y, x))
     , f^#(s(x), y) -> c_7(f^#(x, s(x))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { ack^#(0(), y) -> c_1(y)
     , ack^#(s(x), y) -> c_2(f^#(x, x))
     , ack^#(s(x), 0()) -> c_3(ack^#(x, s(0())))
     , ack^#(s(x), s(y)) -> c_4(ack^#(x, ack(s(x), y)))
     , f^#(x, y) -> c_5(ack^#(x, y))
     , f^#(x, s(y)) -> c_6(f^#(y, x))
     , f^#(s(x), y) -> c_7(f^#(x, s(x))) }
   Strict Trs:
     { ack(0(), y) -> s(y)
     , ack(s(x), y) -> f(x, x)
     , ack(s(x), 0()) -> ack(x, s(0()))
     , ack(s(x), s(y)) -> ack(x, ack(s(x), y))
     , f(x, y) -> ack(x, y)
     , f(x, s(y)) -> f(y, x)
     , f(s(x), y) -> f(x, s(x)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..