MAYBE

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

Strict Trs:
  { f(x, c(x), c(y)) -> f(y, y, f(y, x, y))
  , f(c(x), x, y) -> c(y)
  , f(s(x), y, z) -> f(x, s(c(y)), c(z))
  , g(x, y) -> x
  , g(x, y) -> y }
Obligation:
  innermost 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) 'Best' failed due to the following reason:
   
   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:
         
         The weightgap principle applies (using the following nonconstant
         growth matrix-interpretation)
         
         The following argument positions are usable:
           Uargs(f) = {3}
         
         TcT has computed the following matrix interpretation satisfying
         not(EDA) and not(IDA(1)).
         
           [f](x1, x2, x3) = [1] x3 + [7]         
                                                  
                   [c](x1) = [1] x1 + [7]         
                                                  
                   [s](x1) = [1] x1 + [7]         
                                                  
               [g](x1, x2) = [1] x1 + [1] x2 + [7]
         
         The following symbols are considered usable
         
           {f, g}
         
         The order satisfies the following ordering constraints:
         
           [f(x, c(x), c(y))] =  [1] y + [14]         
                              >= [1] y + [14]         
                              =  [f(y, y, f(y, x, y))]
                                                      
              [f(c(x), x, y)] =  [1] y + [7]          
                              >= [1] y + [7]          
                              =  [c(y)]               
                                                      
              [f(s(x), y, z)] =  [1] z + [7]          
                              ?  [1] z + [14]         
                              =  [f(x, s(c(y)), c(z))]
                                                      
                    [g(x, y)] =  [1] x + [1] y + [7]  
                              >  [1] x + [0]          
                              =  [x]                  
                                                      
                    [g(x, y)] =  [1] x + [1] y + [7]  
                              >  [1] y + [0]          
                              =  [y]                  
                                                      
         
         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, c(x), c(y)) -> f(y, y, f(y, x, y))
           , f(c(x), x, y) -> c(y)
           , f(s(x), y, z) -> f(x, s(c(y)), c(z)) }
         Weak Trs:
           { g(x, y) -> x
           , g(x, y) -> y }
         Obligation:
           innermost runtime complexity
         Answer:
           MAYBE
         
         The weightgap principle applies (using the following nonconstant
         growth matrix-interpretation)
         
         The following argument positions are usable:
           Uargs(f) = {3}
         
         TcT has computed the following matrix interpretation satisfying
         not(EDA) and not(IDA(1)).
         
           [f](x1, x2, x3) = [1] x3 + [7]         
                                                  
                   [c](x1) = [1] x1 + [3]         
                                                  
                   [s](x1) = [1] x1 + [7]         
                                                  
               [g](x1, x2) = [1] x1 + [1] x2 + [0]
         
         The following symbols are considered usable
         
           {f, g}
         
         The order satisfies the following ordering constraints:
         
           [f(x, c(x), c(y))] =  [1] y + [10]         
                              ?  [1] y + [14]         
                              =  [f(y, y, f(y, x, y))]
                                                      
              [f(c(x), x, y)] =  [1] y + [7]          
                              >  [1] y + [3]          
                              =  [c(y)]               
                                                      
              [f(s(x), y, z)] =  [1] z + [7]          
                              ?  [1] z + [10]         
                              =  [f(x, s(c(y)), c(z))]
                                                      
                    [g(x, y)] =  [1] x + [1] y + [0]  
                              >= [1] x + [0]          
                              =  [x]                  
                                                      
                    [g(x, y)] =  [1] x + [1] y + [0]  
                              >= [1] y + [0]          
                              =  [y]                  
                                                      
         
         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, c(x), c(y)) -> f(y, y, f(y, x, y))
           , f(s(x), y, z) -> f(x, s(c(y)), c(z)) }
         Weak Trs:
           { f(c(x), x, y) -> c(y)
           , g(x, y) -> x
           , g(x, y) -> y }
         Obligation:
           innermost 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:
                     
                     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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
         2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
            following reason:
            
            The input cannot be shown compatible
         
      
      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.
         
      
   


Arrrr..