MAYBE

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

Strict Trs:
  { f(x) -> g(f(x))
  , g(x) -> a()
  , g(f(x)) -> 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) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      Computation stopped due to timeout after 5.0 seconds.
   
   2) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      The weightgap principle applies (using the following nonconstant
      growth matrix-interpretation)
      
      The following argument positions are usable:
        Uargs(g) = {1}
      
      TcT has computed the following matrix interpretation satisfying
      not(EDA) and not(IDA(1)).
      
        [f](x1) = [1] x1 + [7]
                              
        [g](x1) = [1] x1 + [7]
                              
            [a] = [6]         
      
      The following symbols are considered usable
      
        {f, g}
      
      The order satisfies the following ordering constraints:
      
           [f(x)] = [1] x + [7] 
                  ? [1] x + [14]
                  = [g(f(x))]   
                                
           [g(x)] = [1] x + [7] 
                  > [6]         
                  = [a()]       
                                
        [g(f(x))] = [1] x + [14]
                  > [1] x + [0] 
                  = [x]         
                                
      
      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
      
      We are left with following problem, upon which TcT provides the
      certificate MAYBE.
      
      Strict Trs: { f(x) -> g(f(x)) }
      Weak Trs:
        { g(x) -> a()
        , g(f(x)) -> x }
      Obligation:
        runtime complexity
      Answer:
        MAYBE
      
      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.
               
            
         
      
   
   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
      
   

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


Arrrr..