MAYBE
675.76/297.06	MAYBE
675.76/297.06	
675.76/297.06	We are left with following problem, upon which TcT provides the
675.76/297.06	certificate MAYBE.
675.76/297.06	
675.76/297.06	Strict Trs:
675.76/297.06	  { f(x, f(y, z)) -> f(f(x, y), z)
675.76/297.06	  , f(f(a(), b()), x) -> f(a(), f(a(), x))
675.76/297.06	  , f(f(b(), a()), x) -> f(b(), f(b(), x)) }
675.76/297.06	Obligation:
675.76/297.06	  derivational complexity
675.76/297.06	Answer:
675.76/297.06	  MAYBE
675.76/297.06	
675.76/297.06	None of the processors succeeded.
675.76/297.06	
675.76/297.06	Details of failed attempt(s):
675.76/297.06	-----------------------------
675.76/297.06	1) 'iteProgress (timeout of 297 seconds)' failed due to the
675.76/297.06	   following reason:
675.76/297.06	   
675.76/297.06	   Computation stopped due to timeout after 297.0 seconds.
675.76/297.06	
675.76/297.06	2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to
675.76/297.06	   the following reason:
675.76/297.06	   
675.76/297.06	   The weightgap principle applies (using the following nonconstant
675.76/297.06	   growth matrix-interpretation)
675.76/297.06	   
675.76/297.06	   TcT has computed the following triangular matrix interpretation.
675.76/297.06	   Note that the diagonal of the component-wise maxima of
675.76/297.06	   interpretation-entries contains no more than 1 non-zero entries.
675.76/297.06	   
675.76/297.06	     [f](x1, x2) = [1] x1 + [1] x2 + [0]
675.76/297.06	                                        
675.76/297.06	             [a] = [0]                  
675.76/297.06	                                        
675.76/297.06	             [b] = [1]                  
675.76/297.06	   
675.76/297.06	   The order satisfies the following ordering constraints:
675.76/297.06	   
675.76/297.06	         [f(x, f(y, z))] =  [1] x + [1] y + [1] z + [0]
675.76/297.06	                         >= [1] x + [1] y + [1] z + [0]
675.76/297.06	                         =  [f(f(x, y), z)]            
675.76/297.06	                                                       
675.76/297.06	     [f(f(a(), b()), x)] =  [1] x + [1]                
675.76/297.06	                         >  [1] x + [0]                
675.76/297.06	                         =  [f(a(), f(a(), x))]        
675.76/297.06	                                                       
675.76/297.06	     [f(f(b(), a()), x)] =  [1] x + [1]                
675.76/297.06	                         ?  [1] x + [2]                
675.76/297.06	                         =  [f(b(), f(b(), x))]        
675.76/297.06	                                                       
675.76/297.06	   
675.76/297.06	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
675.76/297.06	   
675.76/297.06	   We are left with following problem, upon which TcT provides the
675.76/297.06	   certificate MAYBE.
675.76/297.06	   
675.76/297.06	   Strict Trs:
675.76/297.06	     { f(x, f(y, z)) -> f(f(x, y), z)
675.76/297.06	     , f(f(b(), a()), x) -> f(b(), f(b(), x)) }
675.76/297.06	   Weak Trs: { f(f(a(), b()), x) -> f(a(), f(a(), x)) }
675.76/297.06	   Obligation:
675.76/297.06	     derivational complexity
675.76/297.06	   Answer:
675.76/297.06	     MAYBE
675.76/297.06	   
675.76/297.06	   The weightgap principle applies (using the following nonconstant
675.76/297.06	   growth matrix-interpretation)
675.76/297.06	   
675.76/297.06	   TcT has computed the following triangular matrix interpretation.
675.76/297.06	   Note that the diagonal of the component-wise maxima of
675.76/297.06	   interpretation-entries contains no more than 1 non-zero entries.
675.76/297.06	   
675.76/297.06	     [f](x1, x2) = [1 2] x1 + [1 0] x2 + [0]
675.76/297.06	                   [0 0]      [0 0]      [2]
675.76/297.06	                                            
675.76/297.06	             [a] = [0]                      
675.76/297.06	                   [0]                      
675.76/297.06	                                            
675.76/297.06	             [b] = [0]                      
675.76/297.06	                   [0]                      
675.76/297.06	   
675.76/297.06	   The order satisfies the following ordering constraints:
675.76/297.06	   
675.76/297.06	         [f(x, f(y, z))] = [1 2] x + [1 2] y + [1 0] z + [0]
675.76/297.06	                           [0 0]     [0 0]     [0 0]     [2]
675.76/297.06	                         ? [1 2] x + [1 0] y + [1 0] z + [4]
675.76/297.06	                           [0 0]     [0 0]     [0 0]     [2]
675.76/297.06	                         = [f(f(x, y), z)]                  
675.76/297.06	                                                            
675.76/297.06	     [f(f(a(), b()), x)] = [1 0] x + [4]                    
675.76/297.06	                           [0 0]     [2]                    
675.76/297.06	                         > [1 0] x + [0]                    
675.76/297.06	                           [0 0]     [2]                    
675.76/297.06	                         = [f(a(), f(a(), x))]              
675.76/297.06	                                                            
675.76/297.06	     [f(f(b(), a()), x)] = [1 0] x + [4]                    
675.76/297.06	                           [0 0]     [2]                    
675.76/297.06	                         > [1 0] x + [0]                    
675.76/297.06	                           [0 0]     [2]                    
675.76/297.06	                         = [f(b(), f(b(), x))]              
675.76/297.06	                                                            
675.76/297.06	   
675.76/297.06	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
675.76/297.06	   
675.76/297.06	   We are left with following problem, upon which TcT provides the
675.76/297.06	   certificate MAYBE.
675.76/297.06	   
675.76/297.06	   Strict Trs: { f(x, f(y, z)) -> f(f(x, y), z) }
675.76/297.06	   Weak Trs:
675.76/297.06	     { f(f(a(), b()), x) -> f(a(), f(a(), x))
675.76/297.06	     , f(f(b(), a()), x) -> f(b(), f(b(), x)) }
675.76/297.06	   Obligation:
675.76/297.06	     derivational complexity
675.76/297.06	   Answer:
675.76/297.06	     MAYBE
675.76/297.06	   
675.76/297.06	   None of the processors succeeded.
675.76/297.06	   
675.76/297.06	   Details of failed attempt(s):
675.76/297.06	   -----------------------------
675.76/297.06	   1) 'empty' failed due to the following reason:
675.76/297.06	      
675.76/297.06	      Empty strict component of the problem is NOT empty.
675.76/297.06	   
675.76/297.06	   2) 'Fastest' failed due to the following reason:
675.76/297.06	      
675.76/297.06	      None of the processors succeeded.
675.76/297.06	      
675.76/297.06	      Details of failed attempt(s):
675.76/297.06	      -----------------------------
675.76/297.06	      1) 'Fastest' failed due to the following reason:
675.76/297.06	         
675.76/297.06	         None of the processors succeeded.
675.76/297.06	         
675.76/297.06	         Details of failed attempt(s):
675.76/297.06	         -----------------------------
675.76/297.06	         1) 'matrix interpretation of dimension 6' failed due to the
675.76/297.06	            following reason:
675.76/297.06	            
675.76/297.06	            The input cannot be shown compatible
675.76/297.06	         
675.76/297.06	         2) 'matrix interpretation of dimension 5' failed due to the
675.76/297.06	            following reason:
675.76/297.06	            
675.76/297.06	            The input cannot be shown compatible
675.76/297.06	         
675.76/297.06	         3) 'matrix interpretation of dimension 4' failed due to the
675.76/297.06	            following reason:
675.76/297.06	            
675.76/297.06	            The input cannot be shown compatible
675.76/297.06	         
675.76/297.06	         4) 'matrix interpretation of dimension 3' failed due to the
675.76/297.06	            following reason:
675.76/297.06	            
675.76/297.06	            The input cannot be shown compatible
675.76/297.06	         
675.76/297.06	         5) 'matrix interpretation of dimension 2' failed due to the
675.76/297.06	            following reason:
675.76/297.06	            
675.76/297.06	            The input cannot be shown compatible
675.76/297.06	         
675.76/297.06	         6) 'matrix interpretation of dimension 1' failed due to the
675.76/297.06	            following reason:
675.76/297.06	            
675.76/297.06	            The input cannot be shown compatible
675.76/297.06	         
675.76/297.06	      
675.76/297.06	      2) 'Fastest (timeout of 30 seconds)' failed due to the following
675.76/297.06	         reason:
675.76/297.06	         
675.76/297.06	         Computation stopped due to timeout after 30.0 seconds.
675.76/297.06	      
675.76/297.06	      3) 'iteProgress' failed due to the following reason:
675.76/297.06	         
675.76/297.06	         Fail
675.76/297.06	      
675.76/297.06	      4) 'bsearch-matrix' failed due to the following reason:
675.76/297.06	         
675.76/297.06	         The input cannot be shown compatible
675.76/297.06	      
675.76/297.06	   
675.76/297.06	
675.76/297.06	3) 'Fastest (timeout of 60 seconds)' failed due to the following
675.76/297.06	   reason:
675.76/297.06	   
675.76/297.06	   Computation stopped due to timeout after 60.0 seconds.
675.76/297.06	
675.76/297.06	4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the
675.76/297.06	   following reason:
675.76/297.06	   
675.76/297.06	   The input cannot be shown compatible
675.76/297.06	
675.76/297.06	
675.76/297.06	Arrrr..
675.76/297.06	EOF