MAYBE
199.58/60.06	MAYBE
199.58/60.06	
199.58/60.06	We are left with following problem, upon which TcT provides the
199.58/60.06	certificate MAYBE.
199.58/60.06	
199.58/60.06	Strict Trs:
199.58/60.06	  { a(x1) -> x1
199.58/60.06	  , a(x1) -> b(x1)
199.58/60.06	  , a(c(b(x1))) -> c(c(a(a(x1))))
199.58/60.06	  , c(x1) -> b(x1) }
199.58/60.06	Obligation:
199.58/60.06	  derivational complexity
199.58/60.06	Answer:
199.58/60.06	  MAYBE
199.58/60.06	
199.58/60.06	None of the processors succeeded.
199.58/60.06	
199.58/60.06	Details of failed attempt(s):
199.58/60.06	-----------------------------
199.58/60.06	1) 'Fastest (timeout of 60 seconds)' failed due to the following
199.58/60.06	   reason:
199.58/60.06	   
199.58/60.06	   Computation stopped due to timeout after 60.0 seconds.
199.58/60.06	
199.58/60.06	2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to
199.58/60.06	   the following reason:
199.58/60.06	   
199.58/60.06	   The weightgap principle applies (using the following nonconstant
199.58/60.06	   growth matrix-interpretation)
199.58/60.06	   
199.58/60.06	   TcT has computed the following triangular matrix interpretation.
199.58/60.06	   Note that the diagonal of the component-wise maxima of
199.58/60.06	   interpretation-entries contains no more than 1 non-zero entries.
199.58/60.06	   
199.58/60.06	     [a](x1) = [1] x1 + [2]
199.58/60.06	                           
199.58/60.06	     [b](x1) = [1] x1 + [2]
199.58/60.06	                           
199.58/60.06	     [c](x1) = [1] x1 + [0]
199.58/60.06	   
199.58/60.06	   The order satisfies the following ordering constraints:
199.58/60.06	   
199.58/60.06	           [a(x1)] =  [1] x1 + [2]    
199.58/60.06	                   >  [1] x1 + [0]    
199.58/60.06	                   =  [x1]            
199.58/60.06	                                      
199.58/60.06	           [a(x1)] =  [1] x1 + [2]    
199.58/60.06	                   >= [1] x1 + [2]    
199.58/60.06	                   =  [b(x1)]         
199.58/60.06	                                      
199.58/60.06	     [a(c(b(x1)))] =  [1] x1 + [4]    
199.58/60.06	                   >= [1] x1 + [4]    
199.58/60.06	                   =  [c(c(a(a(x1))))]
199.58/60.06	                                      
199.58/60.06	           [c(x1)] =  [1] x1 + [0]    
199.58/60.06	                   ?  [1] x1 + [2]    
199.58/60.06	                   =  [b(x1)]         
199.58/60.06	                                      
199.58/60.06	   
199.58/60.06	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
199.58/60.06	   
199.58/60.06	   We are left with following problem, upon which TcT provides the
199.58/60.06	   certificate MAYBE.
199.58/60.06	   
199.58/60.06	   Strict Trs:
199.58/60.06	     { a(x1) -> b(x1)
199.58/60.06	     , a(c(b(x1))) -> c(c(a(a(x1))))
199.58/60.06	     , c(x1) -> b(x1) }
199.58/60.06	   Weak Trs: { a(x1) -> x1 }
199.58/60.06	   Obligation:
199.58/60.06	     derivational complexity
199.58/60.06	   Answer:
199.58/60.06	     MAYBE
199.58/60.06	   
199.58/60.06	   The weightgap principle applies (using the following nonconstant
199.58/60.06	   growth matrix-interpretation)
199.58/60.06	   
199.58/60.06	   TcT has computed the following triangular matrix interpretation.
199.58/60.06	   Note that the diagonal of the component-wise maxima of
199.58/60.06	   interpretation-entries contains no more than 1 non-zero entries.
199.58/60.06	   
199.58/60.06	     [a](x1) = [1] x1 + [0]
199.58/60.06	                           
199.58/60.06	     [b](x1) = [1] x1 + [1]
199.58/60.06	                           
199.58/60.06	     [c](x1) = [1] x1 + [0]
199.58/60.06	   
199.58/60.06	   The order satisfies the following ordering constraints:
199.58/60.06	   
199.58/60.06	           [a(x1)] =  [1] x1 + [0]    
199.58/60.06	                   >= [1] x1 + [0]    
199.58/60.06	                   =  [x1]            
199.58/60.06	                                      
199.58/60.06	           [a(x1)] =  [1] x1 + [0]    
199.58/60.06	                   ?  [1] x1 + [1]    
199.58/60.06	                   =  [b(x1)]         
199.58/60.06	                                      
199.58/60.06	     [a(c(b(x1)))] =  [1] x1 + [1]    
199.58/60.06	                   >  [1] x1 + [0]    
199.58/60.06	                   =  [c(c(a(a(x1))))]
199.58/60.06	                                      
199.58/60.06	           [c(x1)] =  [1] x1 + [0]    
199.58/60.06	                   ?  [1] x1 + [1]    
199.58/60.06	                   =  [b(x1)]         
199.58/60.06	                                      
199.58/60.06	   
199.58/60.06	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
199.58/60.06	   
199.58/60.06	   We are left with following problem, upon which TcT provides the
199.58/60.06	   certificate MAYBE.
199.58/60.06	   
199.58/60.06	   Strict Trs:
199.58/60.06	     { a(x1) -> b(x1)
199.58/60.06	     , c(x1) -> b(x1) }
199.58/60.06	   Weak Trs:
199.58/60.06	     { a(x1) -> x1
199.58/60.06	     , a(c(b(x1))) -> c(c(a(a(x1)))) }
199.58/60.06	   Obligation:
199.58/60.06	     derivational complexity
199.58/60.06	   Answer:
199.58/60.06	     MAYBE
199.58/60.06	   
199.58/60.06	   None of the processors succeeded.
199.58/60.06	   
199.58/60.06	   Details of failed attempt(s):
199.58/60.06	   -----------------------------
199.58/60.06	   1) 'empty' failed due to the following reason:
199.58/60.06	      
199.58/60.06	      Empty strict component of the problem is NOT empty.
199.58/60.06	   
199.58/60.06	   2) 'Fastest' failed due to the following reason:
199.58/60.06	      
199.58/60.06	      None of the processors succeeded.
199.58/60.06	      
199.58/60.06	      Details of failed attempt(s):
199.58/60.06	      -----------------------------
199.58/60.06	      1) 'Fastest (timeout of 30 seconds)' failed due to the following
199.58/60.06	         reason:
199.58/60.06	         
199.58/60.06	         Computation stopped due to timeout after 30.0 seconds.
199.58/60.06	      
199.58/60.06	      2) 'Fastest' failed due to the following reason:
199.58/60.06	         
199.58/60.06	         None of the processors succeeded.
199.58/60.06	         
199.58/60.06	         Details of failed attempt(s):
199.58/60.06	         -----------------------------
199.58/60.06	         1) 'matrix interpretation of dimension 6' failed due to the
199.58/60.06	            following reason:
199.58/60.06	            
199.58/60.06	            The input cannot be shown compatible
199.58/60.06	         
199.58/60.06	         2) 'matrix interpretation of dimension 5' failed due to the
199.58/60.06	            following reason:
199.58/60.06	            
199.58/60.06	            The input cannot be shown compatible
199.58/60.06	         
199.58/60.06	         3) 'matrix interpretation of dimension 4' failed due to the
199.58/60.06	            following reason:
199.58/60.06	            
199.58/60.06	            The input cannot be shown compatible
199.58/60.06	         
199.58/60.06	         4) 'matrix interpretation of dimension 3' failed due to the
199.58/60.06	            following reason:
199.58/60.06	            
199.58/60.06	            The input cannot be shown compatible
199.58/60.06	         
199.58/60.06	         5) 'matrix interpretation of dimension 2' failed due to the
199.58/60.06	            following reason:
199.58/60.06	            
199.58/60.06	            The input cannot be shown compatible
199.58/60.06	         
199.58/60.06	         6) 'matrix interpretation of dimension 1' failed due to the
199.58/60.06	            following reason:
199.58/60.06	            
199.58/60.06	            The input cannot be shown compatible
199.58/60.06	         
199.58/60.06	      
199.58/60.06	      3) 'iteProgress' failed due to the following reason:
199.58/60.06	         
199.58/60.06	         Fail
199.58/60.06	      
199.58/60.06	      4) 'bsearch-matrix' failed due to the following reason:
199.58/60.06	         
199.58/60.06	         The input cannot be shown compatible
199.58/60.06	      
199.58/60.06	   
199.58/60.06	
199.58/60.06	3) 'iteProgress (timeout of 297 seconds)' failed due to the
199.58/60.06	   following reason:
199.58/60.06	   
199.58/60.06	   Fail
199.58/60.06	
199.58/60.06	4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the
199.58/60.06	   following reason:
199.58/60.06	   
199.58/60.06	   The input cannot be shown compatible
199.58/60.06	
199.58/60.06	
199.58/60.06	Arrrr..
199.58/60.06	EOF