MAYBE
416.53/142.14	MAYBE
416.53/142.14	
416.53/142.14	We are left with following problem, upon which TcT provides the
416.53/142.14	certificate MAYBE.
416.53/142.14	
416.53/142.14	Strict Trs:
416.53/142.14	  { a(x1) -> x1
416.53/142.14	  , a(b(x1)) -> b(b(c(a(c(a(x1))))))
416.53/142.14	  , b(x1) -> x1
416.53/142.14	  , c(c(x1)) -> x1 }
416.53/142.14	Obligation:
416.53/142.14	  derivational complexity
416.53/142.14	Answer:
416.53/142.14	  MAYBE
416.53/142.14	
416.53/142.14	None of the processors succeeded.
416.53/142.14	
416.53/142.14	Details of failed attempt(s):
416.53/142.14	-----------------------------
416.53/142.14	1) 'Inspecting Problem... (timeout of 297 seconds)' failed due to
416.53/142.14	   the following reason:
416.53/142.14	   
416.53/142.14	   The weightgap principle applies (using the following nonconstant
416.53/142.14	   growth matrix-interpretation)
416.53/142.14	   
416.53/142.14	   TcT has computed the following triangular matrix interpretation.
416.53/142.14	   Note that the diagonal of the component-wise maxima of
416.53/142.14	   interpretation-entries contains no more than 1 non-zero entries.
416.53/142.14	   
416.53/142.14	     [a](x1) = [1] x1 + [0]
416.53/142.14	                           
416.53/142.14	     [b](x1) = [1] x1 + [0]
416.53/142.14	                           
416.53/142.14	     [c](x1) = [1] x1 + [2]
416.53/142.14	   
416.53/142.14	   The order satisfies the following ordering constraints:
416.53/142.14	   
416.53/142.14	        [a(x1)] =  [1] x1 + [0]          
416.53/142.14	                >= [1] x1 + [0]          
416.53/142.14	                =  [x1]                  
416.53/142.14	                                         
416.53/142.14	     [a(b(x1))] =  [1] x1 + [0]          
416.53/142.14	                ?  [1] x1 + [4]          
416.53/142.14	                =  [b(b(c(a(c(a(x1))))))]
416.53/142.14	                                         
416.53/142.14	        [b(x1)] =  [1] x1 + [0]          
416.53/142.14	                >= [1] x1 + [0]          
416.53/142.14	                =  [x1]                  
416.53/142.14	                                         
416.53/142.14	     [c(c(x1))] =  [1] x1 + [4]          
416.53/142.14	                >  [1] x1 + [0]          
416.53/142.14	                =  [x1]                  
416.53/142.14	                                         
416.53/142.14	   
416.53/142.14	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
416.53/142.14	   
416.53/142.14	   We are left with following problem, upon which TcT provides the
416.53/142.14	   certificate MAYBE.
416.53/142.14	   
416.53/142.14	   Strict Trs:
416.53/142.14	     { a(x1) -> x1
416.53/142.14	     , a(b(x1)) -> b(b(c(a(c(a(x1))))))
416.53/142.14	     , b(x1) -> x1 }
416.53/142.14	   Weak Trs: { c(c(x1)) -> x1 }
416.53/142.14	   Obligation:
416.53/142.14	     derivational complexity
416.53/142.14	   Answer:
416.53/142.14	     MAYBE
416.53/142.14	   
416.53/142.14	   The weightgap principle applies (using the following nonconstant
416.53/142.14	   growth matrix-interpretation)
416.53/142.14	   
416.53/142.14	   TcT has computed the following triangular matrix interpretation.
416.53/142.14	   Note that the diagonal of the component-wise maxima of
416.53/142.14	   interpretation-entries contains no more than 1 non-zero entries.
416.53/142.14	   
416.53/142.14	     [a](x1) = [1] x1 + [1]
416.53/142.14	                           
416.53/142.14	     [b](x1) = [1] x1 + [0]
416.53/142.14	                           
416.53/142.14	     [c](x1) = [1] x1 + [1]
416.53/142.14	   
416.53/142.14	   The order satisfies the following ordering constraints:
416.53/142.14	   
416.53/142.14	        [a(x1)] =  [1] x1 + [1]          
416.53/142.14	                >  [1] x1 + [0]          
416.53/142.14	                =  [x1]                  
416.53/142.14	                                         
416.53/142.14	     [a(b(x1))] =  [1] x1 + [1]          
416.53/142.14	                ?  [1] x1 + [4]          
416.53/142.14	                =  [b(b(c(a(c(a(x1))))))]
416.53/142.14	                                         
416.53/142.14	        [b(x1)] =  [1] x1 + [0]          
416.53/142.14	                >= [1] x1 + [0]          
416.53/142.14	                =  [x1]                  
416.53/142.14	                                         
416.53/142.14	     [c(c(x1))] =  [1] x1 + [2]          
416.53/142.15	                >  [1] x1 + [0]          
416.53/142.15	                =  [x1]                  
416.53/142.15	                                         
416.53/142.15	   
416.53/142.15	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
416.53/142.15	   
416.53/142.15	   We are left with following problem, upon which TcT provides the
416.53/142.15	   certificate MAYBE.
416.53/142.15	   
416.53/142.15	   Strict Trs:
416.53/142.15	     { a(b(x1)) -> b(b(c(a(c(a(x1))))))
416.53/142.15	     , b(x1) -> x1 }
416.53/142.15	   Weak Trs:
416.53/142.15	     { a(x1) -> x1
416.53/142.15	     , c(c(x1)) -> x1 }
416.53/142.15	   Obligation:
416.53/142.15	     derivational complexity
416.53/142.15	   Answer:
416.53/142.15	     MAYBE
416.53/142.15	   
416.53/142.15	   The weightgap principle applies (using the following nonconstant
416.53/142.15	   growth matrix-interpretation)
416.53/142.15	   
416.53/142.15	   TcT has computed the following triangular matrix interpretation.
416.53/142.15	   Note that the diagonal of the component-wise maxima of
416.53/142.15	   interpretation-entries contains no more than 1 non-zero entries.
416.53/142.15	   
416.53/142.15	     [a](x1) = [1] x1 + [0]
416.53/142.15	                           
416.53/142.15	     [b](x1) = [1] x1 + [1]
416.53/142.15	                           
416.53/142.15	     [c](x1) = [1] x1 + [0]
416.53/142.15	   
416.53/142.15	   The order satisfies the following ordering constraints:
416.53/142.15	   
416.53/142.15	        [a(x1)] =  [1] x1 + [0]          
416.53/142.15	                >= [1] x1 + [0]          
416.53/142.15	                =  [x1]                  
416.53/142.15	                                         
416.53/142.15	     [a(b(x1))] =  [1] x1 + [1]          
416.53/142.15	                ?  [1] x1 + [2]          
416.53/142.15	                =  [b(b(c(a(c(a(x1))))))]
416.53/142.15	                                         
416.53/142.15	        [b(x1)] =  [1] x1 + [1]          
416.53/142.15	                >  [1] x1 + [0]          
416.53/142.15	                =  [x1]                  
416.53/142.15	                                         
416.53/142.15	     [c(c(x1))] =  [1] x1 + [0]          
416.53/142.15	                >= [1] x1 + [0]          
416.53/142.15	                =  [x1]                  
416.53/142.15	                                         
416.53/142.15	   
416.53/142.15	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
416.53/142.15	   
416.53/142.15	   We are left with following problem, upon which TcT provides the
416.53/142.15	   certificate MAYBE.
416.53/142.15	   
416.53/142.15	   Strict Trs: { a(b(x1)) -> b(b(c(a(c(a(x1)))))) }
416.53/142.15	   Weak Trs:
416.53/142.15	     { a(x1) -> x1
416.53/142.15	     , b(x1) -> x1
416.53/142.15	     , c(c(x1)) -> x1 }
416.53/142.15	   Obligation:
416.53/142.15	     derivational complexity
416.53/142.15	   Answer:
416.53/142.15	     MAYBE
416.53/142.15	   
416.53/142.15	   None of the processors succeeded.
416.53/142.15	   
416.53/142.15	   Details of failed attempt(s):
416.53/142.15	   -----------------------------
416.53/142.15	   1) 'empty' failed due to the following reason:
416.53/142.15	      
416.53/142.15	      Empty strict component of the problem is NOT empty.
416.53/142.15	   
416.53/142.15	   2) 'Fastest' failed due to the following reason:
416.53/142.15	      
416.53/142.15	      None of the processors succeeded.
416.53/142.15	      
416.53/142.15	      Details of failed attempt(s):
416.53/142.15	      -----------------------------
416.53/142.15	      1) 'bsearch-matrix' failed due to the following reason:
416.53/142.15	         
416.53/142.15	         The input cannot be shown compatible
416.53/142.15	      
416.53/142.15	      2) 'iteProgress' failed due to the following reason:
416.53/142.15	         
416.53/142.15	         Fail
416.53/142.15	      
416.53/142.15	      3) 'Fastest' failed due to the following reason:
416.53/142.15	         
416.53/142.15	         None of the processors succeeded.
416.53/142.15	         
416.53/142.15	         Details of failed attempt(s):
416.53/142.15	         -----------------------------
416.53/142.15	         1) 'matrix interpretation of dimension 6' failed due to the
416.53/142.15	            following reason:
416.53/142.15	            
416.53/142.15	            The input cannot be shown compatible
416.53/142.15	         
416.53/142.15	         2) 'matrix interpretation of dimension 5' failed due to the
416.53/142.15	            following reason:
416.53/142.15	            
416.53/142.15	            The input cannot be shown compatible
416.53/142.15	         
416.53/142.15	         3) 'matrix interpretation of dimension 4' failed due to the
416.53/142.15	            following reason:
416.53/142.15	            
416.53/142.15	            The input cannot be shown compatible
416.53/142.15	         
416.53/142.15	         4) 'matrix interpretation of dimension 3' failed due to the
416.53/142.15	            following reason:
416.53/142.15	            
416.53/142.15	            The input cannot be shown compatible
416.53/142.15	         
416.53/142.15	         5) 'matrix interpretation of dimension 2' failed due to the
416.53/142.15	            following reason:
416.53/142.15	            
416.53/142.15	            The input cannot be shown compatible
416.53/142.15	         
416.53/142.15	         6) 'matrix interpretation of dimension 1' failed due to the
416.53/142.15	            following reason:
416.53/142.15	            
416.53/142.15	            The input cannot be shown compatible
416.53/142.15	         
416.53/142.15	      
416.53/142.15	      4) 'Fastest (timeout of 30 seconds)' failed due to the following
416.53/142.15	         reason:
416.53/142.15	         
416.53/142.15	         Computation stopped due to timeout after 30.0 seconds.
416.53/142.15	      
416.53/142.15	   
416.53/142.15	
416.53/142.15	2) 'bsearch-matrix (timeout of 297 seconds)' failed due to the
416.53/142.15	   following reason:
416.53/142.15	   
416.53/142.15	   The input cannot be shown compatible
416.53/142.15	
416.53/142.15	3) 'Fastest (timeout of 60 seconds)' failed due to the following
416.53/142.15	   reason:
416.53/142.15	   
416.53/142.15	   Computation stopped due to timeout after 60.0 seconds.
416.53/142.15	
416.53/142.15	4) 'iteProgress (timeout of 297 seconds)' failed due to the
416.53/142.15	   following reason:
416.53/142.15	   
416.53/142.15	   Fail
416.53/142.15	
416.53/142.15	
416.53/142.15	Arrrr..
416.78/142.25	EOF