MAYBE

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

Strict Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(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:
                  
                  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) '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 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:
     { f^#(0()) -> c_1()
     , f^#(s(x)) -> c_2(g^#(f(x)))
     , f^#(s(x)) -> c_3(f^#(x), f^#(x))
     , g^#(x) -> c_4(x, x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { f^#(0()) -> c_1()
     , f^#(s(x)) -> c_2(g^#(f(x)))
     , f^#(s(x)) -> c_3(f^#(x), f^#(x))
     , g^#(x) -> c_4(x, x) }
   Strict Trs:
     { f(0()) -> 1()
     , f(s(x)) -> g(f(x))
     , f(s(x)) -> +(f(x), s(f(x)))
     , g(x) -> +(x, s(x)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1} by applications of
   Pre({1}) = {3,4}. Here rules are labeled as follows:
   
     DPs:
       { 1: f^#(0()) -> c_1()
       , 2: f^#(s(x)) -> c_2(g^#(f(x)))
       , 3: f^#(s(x)) -> c_3(f^#(x), f^#(x))
       , 4: g^#(x) -> c_4(x, x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { f^#(s(x)) -> c_2(g^#(f(x)))
     , f^#(s(x)) -> c_3(f^#(x), f^#(x))
     , g^#(x) -> c_4(x, x) }
   Strict Trs:
     { f(0()) -> 1()
     , f(s(x)) -> g(f(x))
     , f(s(x)) -> +(f(x), s(f(x)))
     , g(x) -> +(x, s(x)) }
   Weak DPs: { f^#(0()) -> c_1() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..