MAYBE
198.52/60.01	MAYBE
198.52/60.01	
198.52/60.01	We are left with following problem, upon which TcT provides the
198.52/60.01	certificate MAYBE.
198.52/60.01	
198.52/60.01	Strict Trs:
198.52/60.01	  { a(x1) -> x1
198.52/60.01	  , a(b(x1)) -> b(a(c(b(a(x1)))))
198.52/60.01	  , b(x1) -> x1
198.52/60.01	  , c(c(c(x1))) -> x1 }
198.52/60.01	Obligation:
198.52/60.01	  derivational complexity
198.52/60.01	Answer:
198.52/60.01	  MAYBE
198.52/60.01	
198.52/60.01	None of the processors succeeded.
198.52/60.01	
198.52/60.01	Details of failed attempt(s):
198.52/60.01	-----------------------------
198.52/60.01	1) 'Fastest (timeout of 60 seconds)' failed due to the following
198.52/60.01	   reason:
198.52/60.01	   
198.52/60.01	   Computation stopped due to timeout after 60.0 seconds.
198.52/60.01	
198.52/60.01	2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to
198.52/60.01	   the following reason:
198.52/60.01	   
198.52/60.01	   The weightgap principle applies (using the following nonconstant
198.52/60.01	   growth matrix-interpretation)
198.52/60.01	   
198.52/60.01	   TcT has computed the following triangular matrix interpretation.
198.52/60.01	   Note that the diagonal of the component-wise maxima of
198.52/60.01	   interpretation-entries contains no more than 1 non-zero entries.
198.52/60.01	   
198.52/60.01	     [a](x1) = [1] x1 + [0]
198.52/60.01	                           
198.52/60.01	     [b](x1) = [1] x1 + [1]
198.52/60.01	                           
198.52/60.01	     [c](x1) = [1] x1 + [2]
198.52/60.01	   
198.52/60.01	   The order satisfies the following ordering constraints:
198.52/60.01	   
198.52/60.01	           [a(x1)] =  [1] x1 + [0]       
198.52/60.01	                   >= [1] x1 + [0]       
198.52/60.01	                   =  [x1]               
198.52/60.01	                                         
198.52/60.01	        [a(b(x1))] =  [1] x1 + [1]       
198.52/60.01	                   ?  [1] x1 + [4]       
198.52/60.01	                   =  [b(a(c(b(a(x1)))))]
198.52/60.01	                                         
198.52/60.01	           [b(x1)] =  [1] x1 + [1]       
198.52/60.01	                   >  [1] x1 + [0]       
198.52/60.01	                   =  [x1]               
198.52/60.01	                                         
198.52/60.01	     [c(c(c(x1)))] =  [1] x1 + [6]       
198.52/60.01	                   >  [1] x1 + [0]       
198.52/60.01	                   =  [x1]               
198.52/60.01	                                         
198.52/60.01	   
198.52/60.01	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
198.52/60.01	   
198.52/60.01	   We are left with following problem, upon which TcT provides the
198.52/60.01	   certificate MAYBE.
198.52/60.01	   
198.52/60.01	   Strict Trs:
198.52/60.01	     { a(x1) -> x1
198.52/60.01	     , a(b(x1)) -> b(a(c(b(a(x1))))) }
198.52/60.01	   Weak Trs:
198.52/60.01	     { b(x1) -> x1
198.52/60.01	     , c(c(c(x1))) -> x1 }
198.52/60.01	   Obligation:
198.52/60.01	     derivational complexity
198.52/60.01	   Answer:
198.52/60.01	     MAYBE
198.52/60.01	   
198.52/60.01	   The weightgap principle applies (using the following nonconstant
198.52/60.01	   growth matrix-interpretation)
198.52/60.01	   
198.52/60.01	   TcT has computed the following triangular matrix interpretation.
198.52/60.01	   Note that the diagonal of the component-wise maxima of
198.52/60.01	   interpretation-entries contains no more than 1 non-zero entries.
198.52/60.01	   
198.52/60.01	     [a](x1) = [1] x1 + [1]
198.52/60.01	                           
198.52/60.01	     [b](x1) = [1] x1 + [0]
198.52/60.01	                           
198.52/60.01	     [c](x1) = [1] x1 + [2]
198.52/60.01	   
198.52/60.01	   The order satisfies the following ordering constraints:
198.52/60.01	   
198.52/60.01	           [a(x1)] =  [1] x1 + [1]       
198.52/60.01	                   >  [1] x1 + [0]       
198.52/60.01	                   =  [x1]               
198.52/60.01	                                         
198.52/60.01	        [a(b(x1))] =  [1] x1 + [1]       
198.52/60.01	                   ?  [1] x1 + [4]       
198.52/60.01	                   =  [b(a(c(b(a(x1)))))]
198.52/60.01	                                         
198.52/60.01	           [b(x1)] =  [1] x1 + [0]       
198.52/60.01	                   >= [1] x1 + [0]       
198.52/60.01	                   =  [x1]               
198.52/60.01	                                         
198.52/60.01	     [c(c(c(x1)))] =  [1] x1 + [6]       
198.52/60.01	                   >  [1] x1 + [0]       
198.52/60.01	                   =  [x1]               
198.52/60.01	                                         
198.52/60.01	   
198.52/60.01	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
198.52/60.01	   
198.52/60.01	   We are left with following problem, upon which TcT provides the
198.52/60.01	   certificate MAYBE.
198.52/60.01	   
198.52/60.01	   Strict Trs: { a(b(x1)) -> b(a(c(b(a(x1))))) }
198.52/60.01	   Weak Trs:
198.52/60.01	     { a(x1) -> x1
198.52/60.01	     , b(x1) -> x1
198.52/60.01	     , c(c(c(x1))) -> x1 }
198.52/60.01	   Obligation:
198.52/60.01	     derivational complexity
198.52/60.01	   Answer:
198.52/60.01	     MAYBE
198.52/60.01	   
198.52/60.01	   None of the processors succeeded.
198.52/60.01	   
198.52/60.01	   Details of failed attempt(s):
198.52/60.01	   -----------------------------
198.52/60.01	   1) 'empty' failed due to the following reason:
198.52/60.01	      
198.52/60.01	      Empty strict component of the problem is NOT empty.
198.52/60.01	   
198.52/60.01	   2) 'Fastest' failed due to the following reason:
198.52/60.01	      
198.52/60.01	      None of the processors succeeded.
198.52/60.01	      
198.52/60.01	      Details of failed attempt(s):
198.52/60.02	      -----------------------------
198.52/60.02	      1) 'Fastest (timeout of 30 seconds)' failed due to the following
198.52/60.02	         reason:
198.52/60.02	         
198.52/60.02	         Computation stopped due to timeout after 30.0 seconds.
198.52/60.02	      
198.52/60.02	      2) 'Fastest' failed due to the following reason:
198.52/60.02	         
198.52/60.02	         None of the processors succeeded.
198.52/60.02	         
198.52/60.02	         Details of failed attempt(s):
198.52/60.02	         -----------------------------
198.52/60.02	         1) 'matrix interpretation of dimension 6' failed due to the
198.52/60.02	            following reason:
198.52/60.02	            
198.52/60.02	            The input cannot be shown compatible
198.52/60.02	         
198.52/60.02	         2) 'matrix interpretation of dimension 5' failed due to the
198.52/60.02	            following reason:
198.52/60.02	            
198.52/60.02	            The input cannot be shown compatible
198.52/60.02	         
198.52/60.02	         3) 'matrix interpretation of dimension 4' failed due to the
198.52/60.02	            following reason:
198.52/60.02	            
198.52/60.02	            The input cannot be shown compatible
198.52/60.02	         
198.52/60.02	         4) 'matrix interpretation of dimension 3' failed due to the
198.52/60.02	            following reason:
198.52/60.02	            
198.52/60.02	            The input cannot be shown compatible
198.52/60.02	         
198.52/60.02	         5) 'matrix interpretation of dimension 2' failed due to the
198.52/60.02	            following reason:
198.52/60.02	            
198.52/60.02	            The input cannot be shown compatible
198.52/60.02	         
198.52/60.02	         6) 'matrix interpretation of dimension 1' failed due to the
198.52/60.02	            following reason:
198.52/60.02	            
198.52/60.02	            The input cannot be shown compatible
198.52/60.02	         
198.52/60.02	      
198.52/60.02	      3) 'iteProgress' failed due to the following reason:
198.52/60.02	         
198.52/60.02	         Fail
198.52/60.02	      
198.52/60.02	      4) 'bsearch-matrix' failed due to the following reason:
198.52/60.02	         
198.52/60.02	         The input cannot be shown compatible
198.52/60.02	      
198.52/60.02	   
198.52/60.02	
198.52/60.02	3) 'iteProgress (timeout of 297 seconds)' failed due to the
198.52/60.02	   following reason:
198.52/60.02	   
198.52/60.02	   Fail
198.52/60.02	
198.52/60.02	4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the
198.52/60.02	   following reason:
198.52/60.02	   
198.52/60.02	   The input cannot be shown compatible
198.52/60.02	
198.52/60.02	
198.52/60.02	Arrrr..
198.52/60.02	EOF