MAYBE
204.41/60.05	MAYBE
204.41/60.05	
204.41/60.05	We are left with following problem, upon which TcT provides the
204.41/60.05	certificate MAYBE.
204.41/60.05	
204.41/60.05	Strict Trs:
204.41/60.05	  { a(x1) -> x1
204.41/60.05	  , a(a(x1)) -> b(x1)
204.41/60.05	  , b(x1) -> a(x1)
204.41/60.05	  , b(c(x1)) -> c(c(b(a(x1)))) }
204.41/60.05	Obligation:
204.41/60.05	  derivational complexity
204.41/60.05	Answer:
204.41/60.05	  MAYBE
204.41/60.05	
204.41/60.05	None of the processors succeeded.
204.41/60.05	
204.41/60.05	Details of failed attempt(s):
204.41/60.05	-----------------------------
204.41/60.05	1) 'Fastest (timeout of 60 seconds)' failed due to the following
204.41/60.05	   reason:
204.41/60.05	   
204.41/60.05	   Computation stopped due to timeout after 60.0 seconds.
204.41/60.05	
204.41/60.05	2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to
204.41/60.05	   the following reason:
204.41/60.05	   
204.41/60.05	   The weightgap principle applies (using the following nonconstant
204.41/60.05	   growth matrix-interpretation)
204.41/60.05	   
204.41/60.05	   TcT has computed the following triangular matrix interpretation.
204.41/60.05	   Note that the diagonal of the component-wise maxima of
204.41/60.05	   interpretation-entries contains no more than 1 non-zero entries.
204.41/60.05	   
204.41/60.05	     [a](x1) = [1] x1 + [2]
204.41/60.05	                           
204.41/60.05	     [b](x1) = [1] x1 + [1]
204.41/60.05	                           
204.41/60.05	     [c](x1) = [1] x1 + [0]
204.41/60.05	   
204.41/60.05	   The order satisfies the following ordering constraints:
204.41/60.05	   
204.41/60.05	        [a(x1)] = [1] x1 + [2]    
204.41/60.05	                > [1] x1 + [0]    
204.41/60.05	                = [x1]            
204.41/60.05	                                  
204.41/60.05	     [a(a(x1))] = [1] x1 + [4]    
204.41/60.05	                > [1] x1 + [1]    
204.41/60.05	                = [b(x1)]         
204.41/60.05	                                  
204.41/60.05	        [b(x1)] = [1] x1 + [1]    
204.41/60.05	                ? [1] x1 + [2]    
204.41/60.05	                = [a(x1)]         
204.41/60.05	                                  
204.41/60.05	     [b(c(x1))] = [1] x1 + [1]    
204.41/60.05	                ? [1] x1 + [3]    
204.41/60.05	                = [c(c(b(a(x1))))]
204.41/60.05	                                  
204.41/60.05	   
204.41/60.05	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
204.41/60.05	   
204.41/60.05	   We are left with following problem, upon which TcT provides the
204.41/60.05	   certificate MAYBE.
204.41/60.05	   
204.41/60.05	   Strict Trs:
204.41/60.05	     { b(x1) -> a(x1)
204.41/60.05	     , b(c(x1)) -> c(c(b(a(x1)))) }
204.41/60.05	   Weak Trs:
204.41/60.05	     { a(x1) -> x1
204.41/60.05	     , a(a(x1)) -> b(x1) }
204.41/60.05	   Obligation:
204.41/60.05	     derivational complexity
204.41/60.05	   Answer:
204.41/60.05	     MAYBE
204.41/60.05	   
204.41/60.05	   The weightgap principle applies (using the following nonconstant
204.41/60.05	   growth matrix-interpretation)
204.41/60.05	   
204.41/60.05	   TcT has computed the following triangular matrix interpretation.
204.41/60.05	   Note that the diagonal of the component-wise maxima of
204.41/60.05	   interpretation-entries contains no more than 1 non-zero entries.
204.41/60.05	   
204.41/60.05	     [a](x1) = [1] x1 + [1]
204.41/60.05	                           
204.41/60.05	     [b](x1) = [1] x1 + [2]
204.41/60.05	                           
204.41/60.05	     [c](x1) = [1] x1 + [1]
204.41/60.05	   
204.41/60.05	   The order satisfies the following ordering constraints:
204.41/60.05	   
204.41/60.05	        [a(x1)] =  [1] x1 + [1]    
204.41/60.05	                >  [1] x1 + [0]    
204.41/60.05	                =  [x1]            
204.41/60.05	                                   
204.41/60.05	     [a(a(x1))] =  [1] x1 + [2]    
204.41/60.05	                >= [1] x1 + [2]    
204.41/60.05	                =  [b(x1)]         
204.41/60.05	                                   
204.41/60.05	        [b(x1)] =  [1] x1 + [2]    
204.41/60.05	                >  [1] x1 + [1]    
204.41/60.05	                =  [a(x1)]         
204.41/60.05	                                   
204.41/60.05	     [b(c(x1))] =  [1] x1 + [3]    
204.41/60.05	                ?  [1] x1 + [5]    
204.41/60.05	                =  [c(c(b(a(x1))))]
204.41/60.05	                                   
204.41/60.05	   
204.41/60.05	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
204.41/60.05	   
204.41/60.05	   We are left with following problem, upon which TcT provides the
204.41/60.05	   certificate MAYBE.
204.41/60.05	   
204.41/60.05	   Strict Trs: { b(c(x1)) -> c(c(b(a(x1)))) }
204.41/60.05	   Weak Trs:
204.41/60.05	     { a(x1) -> x1
204.41/60.05	     , a(a(x1)) -> b(x1)
204.41/60.05	     , b(x1) -> a(x1) }
204.41/60.05	   Obligation:
204.41/60.05	     derivational complexity
204.41/60.05	   Answer:
204.41/60.05	     MAYBE
204.41/60.05	   
204.41/60.05	   None of the processors succeeded.
204.41/60.05	   
204.41/60.05	   Details of failed attempt(s):
204.41/60.05	   -----------------------------
204.41/60.05	   1) 'empty' failed due to the following reason:
204.41/60.05	      
204.41/60.05	      Empty strict component of the problem is NOT empty.
204.41/60.05	   
204.41/60.05	   2) 'Fastest' failed due to the following reason:
204.41/60.05	      
204.41/60.05	      None of the processors succeeded.
204.41/60.05	      
204.41/60.05	      Details of failed attempt(s):
204.41/60.05	      -----------------------------
204.41/60.05	      1) 'Fastest (timeout of 30 seconds)' failed due to the following
204.41/60.05	         reason:
204.41/60.05	         
204.41/60.05	         Computation stopped due to timeout after 30.0 seconds.
204.41/60.05	      
204.41/60.05	      2) 'Fastest' failed due to the following reason:
204.41/60.05	         
204.41/60.05	         None of the processors succeeded.
204.41/60.05	         
204.41/60.05	         Details of failed attempt(s):
204.41/60.05	         -----------------------------
204.41/60.05	         1) 'matrix interpretation of dimension 6' failed due to the
204.41/60.05	            following reason:
204.41/60.05	            
204.41/60.05	            The input cannot be shown compatible
204.41/60.05	         
204.41/60.05	         2) 'matrix interpretation of dimension 5' failed due to the
204.41/60.05	            following reason:
204.41/60.05	            
204.41/60.05	            The input cannot be shown compatible
204.41/60.05	         
204.41/60.05	         3) 'matrix interpretation of dimension 4' failed due to the
204.41/60.05	            following reason:
204.41/60.05	            
204.41/60.05	            The input cannot be shown compatible
204.41/60.05	         
204.41/60.05	         4) 'matrix interpretation of dimension 3' failed due to the
204.41/60.05	            following reason:
204.41/60.05	            
204.41/60.05	            The input cannot be shown compatible
204.41/60.05	         
204.41/60.05	         5) 'matrix interpretation of dimension 2' failed due to the
204.41/60.05	            following reason:
204.41/60.05	            
204.41/60.05	            The input cannot be shown compatible
204.41/60.05	         
204.41/60.05	         6) 'matrix interpretation of dimension 1' failed due to the
204.41/60.05	            following reason:
204.41/60.05	            
204.41/60.05	            The input cannot be shown compatible
204.41/60.05	         
204.41/60.05	      
204.41/60.05	      3) 'iteProgress' failed due to the following reason:
204.41/60.05	         
204.41/60.05	         Fail
204.41/60.05	      
204.41/60.05	      4) 'bsearch-matrix' failed due to the following reason:
204.41/60.05	         
204.41/60.05	         The input cannot be shown compatible
204.41/60.05	      
204.41/60.05	   
204.41/60.05	
204.41/60.05	3) 'iteProgress (timeout of 297 seconds)' failed due to the
204.41/60.05	   following reason:
204.41/60.05	   
204.41/60.05	   Fail
204.41/60.05	
204.41/60.05	4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the
204.41/60.05	   following reason:
204.41/60.05	   
204.41/60.05	   The input cannot be shown compatible
204.41/60.05	
204.41/60.05	
204.41/60.05	Arrrr..
204.41/60.05	EOF