MAYBE
830.07/297.02	MAYBE
830.07/297.02	
830.07/297.02	We are left with following problem, upon which TcT provides the
830.07/297.02	certificate MAYBE.
830.07/297.02	
830.07/297.02	Strict Trs:
830.07/297.02	  { f(x) -> s(x)
830.07/297.02	  , f(s(s(x))) -> s(f(f(x))) }
830.07/297.02	Obligation:
830.07/297.02	  runtime complexity
830.07/297.02	Answer:
830.07/297.02	  MAYBE
830.07/297.02	
830.07/297.02	The input is overlay and right-linear. Switching to innermost
830.07/297.02	rewriting.
830.07/297.02	
830.07/297.02	We are left with following problem, upon which TcT provides the
830.07/297.02	certificate MAYBE.
830.07/297.02	
830.07/297.02	Strict Trs:
830.07/297.02	  { f(x) -> s(x)
830.07/297.02	  , f(s(s(x))) -> s(f(f(x))) }
830.07/297.02	Obligation:
830.07/297.02	  innermost runtime complexity
830.07/297.02	Answer:
830.07/297.02	  MAYBE
830.07/297.02	
830.07/297.02	None of the processors succeeded.
830.07/297.02	
830.07/297.02	Details of failed attempt(s):
830.07/297.02	-----------------------------
830.07/297.02	1) 'empty' failed due to the following reason:
830.07/297.02	   
830.07/297.02	   Empty strict component of the problem is NOT empty.
830.07/297.02	
830.07/297.02	2) 'Best' failed due to the following reason:
830.07/297.02	   
830.07/297.02	   None of the processors succeeded.
830.07/297.02	   
830.07/297.02	   Details of failed attempt(s):
830.07/297.02	   -----------------------------
830.07/297.02	   1) 'With Problem ... (timeout of 297 seconds)' failed due to the
830.07/297.02	      following reason:
830.07/297.02	      
830.07/297.02	      Computation stopped due to timeout after 297.0 seconds.
830.07/297.02	   
830.07/297.02	   2) 'Best' failed due to the following reason:
830.07/297.02	      
830.07/297.02	      None of the processors succeeded.
830.07/297.02	      
830.07/297.02	      Details of failed attempt(s):
830.07/297.02	      -----------------------------
830.07/297.02	      1) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
830.07/297.02	         failed due to the following reason:
830.07/297.02	         
830.07/297.02	         Computation stopped due to timeout after 24.0 seconds.
830.07/297.02	      
830.07/297.02	      2) 'With Problem ... (timeout of 148 seconds) (timeout of 297
830.07/297.02	         seconds)' failed due to the following reason:
830.07/297.02	         
830.07/297.02	         The weightgap principle applies (using the following nonconstant
830.07/297.02	         growth matrix-interpretation)
830.07/297.02	         
830.07/297.02	         TcT has computed the following matrix interpretation satisfying
830.07/297.02	         not(EDA) and not(IDA(1)).
830.07/297.02	         
830.07/297.02	           [f](x1) = [1] x1 + [0]
830.07/297.02	                                 
830.07/297.02	           [s](x1) = [1] x1 + [4]
830.07/297.02	         
830.07/297.02	         The order satisfies the following ordering constraints:
830.07/297.02	         
830.07/297.02	                 [f(x)] = [1] x + [0] 
830.07/297.02	                        ? [1] x + [4] 
830.07/297.02	                        = [s(x)]      
830.07/297.02	                                      
830.07/297.02	           [f(s(s(x)))] = [1] x + [8] 
830.07/297.02	                        > [1] x + [4] 
830.07/297.02	                        = [s(f(f(x)))]
830.07/297.02	                                      
830.07/297.02	         
830.07/297.02	         Further, it can be verified that all rules not oriented are covered by the weightgap condition.
830.07/297.02	         
830.07/297.02	         We are left with following problem, upon which TcT provides the
830.07/297.02	         certificate MAYBE.
830.07/297.02	         
830.07/297.02	         Strict Trs: { f(x) -> s(x) }
830.07/297.02	         Weak Trs: { f(s(s(x))) -> s(f(f(x))) }
830.07/297.02	         Obligation:
830.07/297.02	           innermost runtime complexity
830.07/297.02	         Answer:
830.07/297.02	           MAYBE
830.07/297.02	         
830.07/297.02	         None of the processors succeeded.
830.07/297.02	         
830.07/297.02	         Details of failed attempt(s):
830.07/297.02	         -----------------------------
830.07/297.02	         1) 'empty' failed due to the following reason:
830.07/297.02	            
830.07/297.02	            Empty strict component of the problem is NOT empty.
830.07/297.02	         
830.07/297.02	         2) 'With Problem ...' failed due to the following reason:
830.07/297.02	            
830.07/297.02	            None of the processors succeeded.
830.07/297.02	            
830.07/297.02	            Details of failed attempt(s):
830.07/297.02	            -----------------------------
830.07/297.02	            1) 'empty' failed due to the following reason:
830.07/297.02	               
830.07/297.02	               Empty strict component of the problem is NOT empty.
830.07/297.02	            
830.07/297.02	            2) 'Fastest' failed due to the following reason:
830.07/297.02	               
830.07/297.02	               None of the processors succeeded.
830.07/297.02	               
830.07/297.02	               Details of failed attempt(s):
830.07/297.02	               -----------------------------
830.07/297.02	               1) 'With Problem ...' failed due to the following reason:
830.07/297.02	                  
830.07/297.02	                  None of the processors succeeded.
830.07/297.02	                  
830.07/297.02	                  Details of failed attempt(s):
830.07/297.02	                  -----------------------------
830.07/297.02	                  1) 'empty' failed due to the following reason:
830.07/297.02	                     
830.07/297.02	                     Empty strict component of the problem is NOT empty.
830.07/297.02	                  
830.07/297.02	                  2) 'With Problem ...' failed due to the following reason:
830.07/297.02	                     
830.07/297.02	                     None of the processors succeeded.
830.07/297.02	                     
830.07/297.02	                     Details of failed attempt(s):
830.07/297.02	                     -----------------------------
830.07/297.02	                     1) 'empty' failed due to the following reason:
830.07/297.02	                        
830.07/297.02	                        Empty strict component of the problem is NOT empty.
830.07/297.02	                     
830.07/297.02	                     2) 'With Problem ...' failed due to the following reason:
830.07/297.02	                        
830.07/297.02	                        None of the processors succeeded.
830.07/297.02	                        
830.07/297.02	                        Details of failed attempt(s):
830.07/297.02	                        -----------------------------
830.07/297.02	                        1) 'empty' failed due to the following reason:
830.07/297.02	                           
830.07/297.02	                           Empty strict component of the problem is NOT empty.
830.07/297.02	                        
830.07/297.02	                        2) 'With Problem ...' failed due to the following reason:
830.07/297.02	                           
830.07/297.02	                           Empty strict component of the problem is NOT empty.
830.07/297.02	                        
830.07/297.02	                     
830.07/297.02	                  
830.07/297.02	               
830.07/297.02	               2) 'With Problem ...' failed due to the following reason:
830.07/297.02	                  
830.07/297.02	                  None of the processors succeeded.
830.07/297.02	                  
830.07/297.02	                  Details of failed attempt(s):
830.07/297.02	                  -----------------------------
830.07/297.02	                  1) 'empty' failed due to the following reason:
830.07/297.02	                     
830.07/297.02	                     Empty strict component of the problem is NOT empty.
830.07/297.02	                  
830.07/297.02	                  2) 'With Problem ...' failed due to the following reason:
830.07/297.02	                     
830.07/297.02	                     Empty strict component of the problem is NOT empty.
830.07/297.02	                  
830.07/297.02	               
830.07/297.02	            
830.07/297.02	         
830.07/297.02	      
830.07/297.02	      3) 'Best' failed due to the following reason:
830.07/297.02	         
830.07/297.02	         None of the processors succeeded.
830.07/297.02	         
830.07/297.02	         Details of failed attempt(s):
830.07/297.02	         -----------------------------
830.07/297.02	         1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
830.07/297.02	            following reason:
830.07/297.02	            
830.07/297.02	            The input cannot be shown compatible
830.07/297.02	         
830.07/297.02	         2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
830.07/297.02	            to the following reason:
830.07/297.02	            
830.07/297.02	            The input cannot be shown compatible
830.07/297.02	         
830.07/297.02	      
830.07/297.02	   
830.07/297.02	
830.07/297.02	
830.07/297.02	Arrrr..
830.28/297.25	EOF