MAYBE
219.25/60.04	MAYBE
219.25/60.04	
219.25/60.04	We are left with following problem, upon which TcT provides the
219.25/60.04	certificate MAYBE.
219.25/60.04	
219.25/60.04	Strict Trs:
219.25/60.04	  { f(0(x1)) -> s(0(x1))
219.25/60.04	  , f(s(x1)) -> d(f(p(s(x1))))
219.25/60.04	  , d(0(x1)) -> 0(x1)
219.25/60.04	  , d(s(x1)) -> s(s(d(p(s(x1)))))
219.25/60.04	  , p(s(x1)) -> x1 }
219.25/60.04	Obligation:
219.25/60.04	  derivational complexity
219.25/60.04	Answer:
219.25/60.04	  MAYBE
219.25/60.04	
219.25/60.04	None of the processors succeeded.
219.25/60.04	
219.25/60.04	Details of failed attempt(s):
219.25/60.04	-----------------------------
219.25/60.04	1) 'Fastest (timeout of 60 seconds)' failed due to the following
219.25/60.04	   reason:
219.25/60.04	   
219.25/60.04	   Computation stopped due to timeout after 60.0 seconds.
219.25/60.04	
219.25/60.04	2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to
219.25/60.04	   the following reason:
219.25/60.04	   
219.25/60.04	   We use the processor 'matrix interpretation of dimension 1' to
219.25/60.04	   orient following rules strictly.
219.25/60.04	   
219.25/60.04	   Trs: { f(0(x1)) -> s(0(x1)) }
219.25/60.04	   
219.25/60.04	   The induced complexity on above rules (modulo remaining rules) is
219.25/60.04	   YES(?,O(n^1)) . These rules are moved into the corresponding weak
219.25/60.04	   component(s).
219.25/60.04	   
219.25/60.04	   Sub-proof:
219.25/60.04	   ----------
219.25/60.04	     TcT has computed the following triangular matrix interpretation.
219.25/60.04	     
219.25/60.04	       [f](x1) = [1] x1 + [32]
219.25/60.04	                              
219.25/60.04	       [0](x1) = [1] x1 + [0] 
219.25/60.04	                              
219.25/60.04	       [s](x1) = [1] x1 + [0] 
219.25/60.04	                              
219.25/60.04	       [d](x1) = [1] x1 + [0] 
219.25/60.04	                              
219.25/60.04	       [p](x1) = [1] x1 + [0] 
219.25/60.04	     
219.25/60.04	     The order satisfies the following ordering constraints:
219.25/60.04	     
219.25/60.04	       [f(0(x1))] =  [1] x1 + [32]      
219.25/60.04	                  >  [1] x1 + [0]       
219.25/60.04	                  =  [s(0(x1))]         
219.25/60.04	                                        
219.25/60.04	       [f(s(x1))] =  [1] x1 + [32]      
219.25/60.04	                  >= [1] x1 + [32]      
219.25/60.04	                  =  [d(f(p(s(x1))))]   
219.25/60.04	                                        
219.25/60.04	       [d(0(x1))] =  [1] x1 + [0]       
219.25/60.04	                  >= [1] x1 + [0]       
219.25/60.04	                  =  [0(x1)]            
219.25/60.04	                                        
219.25/60.04	       [d(s(x1))] =  [1] x1 + [0]       
219.25/60.04	                  >= [1] x1 + [0]       
219.25/60.04	                  =  [s(s(d(p(s(x1)))))]
219.25/60.04	                                        
219.25/60.04	       [p(s(x1))] =  [1] x1 + [0]       
219.25/60.04	                  >= [1] x1 + [0]       
219.25/60.04	                  =  [x1]               
219.25/60.04	                                        
219.25/60.04	   
219.25/60.04	   We return to the main proof.
219.25/60.04	   
219.25/60.04	   We are left with following problem, upon which TcT provides the
219.25/60.04	   certificate MAYBE.
219.25/60.04	   
219.25/60.04	   Strict Trs:
219.25/60.04	     { f(s(x1)) -> d(f(p(s(x1))))
219.25/60.04	     , d(0(x1)) -> 0(x1)
219.25/60.04	     , d(s(x1)) -> s(s(d(p(s(x1)))))
219.25/60.04	     , p(s(x1)) -> x1 }
219.25/60.04	   Weak Trs: { f(0(x1)) -> s(0(x1)) }
219.25/60.04	   Obligation:
219.25/60.04	     derivational complexity
219.25/60.04	   Answer:
219.25/60.04	     MAYBE
219.25/60.04	   
219.25/60.04	   The weightgap principle applies (using the following nonconstant
219.25/60.04	   growth matrix-interpretation)
219.25/60.04	   
219.25/60.04	   TcT has computed the following triangular matrix interpretation.
219.25/60.04	   Note that the diagonal of the component-wise maxima of
219.25/60.04	   interpretation-entries contains no more than 1 non-zero entries.
219.25/60.04	   
219.25/60.04	     [f](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [0](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [s](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [d](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [p](x1) = [1] x1 + [1]
219.25/60.04	   
219.25/60.04	   The order satisfies the following ordering constraints:
219.25/60.04	   
219.25/60.04	     [f(0(x1))] =  [1] x1 + [0]       
219.25/60.04	                >= [1] x1 + [0]       
219.25/60.04	                =  [s(0(x1))]         
219.25/60.04	                                      
219.25/60.04	     [f(s(x1))] =  [1] x1 + [0]       
219.25/60.04	                ?  [1] x1 + [1]       
219.25/60.04	                =  [d(f(p(s(x1))))]   
219.25/60.04	                                      
219.25/60.04	     [d(0(x1))] =  [1] x1 + [0]       
219.25/60.04	                >= [1] x1 + [0]       
219.25/60.04	                =  [0(x1)]            
219.25/60.04	                                      
219.25/60.04	     [d(s(x1))] =  [1] x1 + [0]       
219.25/60.04	                ?  [1] x1 + [1]       
219.25/60.04	                =  [s(s(d(p(s(x1)))))]
219.25/60.04	                                      
219.25/60.04	     [p(s(x1))] =  [1] x1 + [1]       
219.25/60.04	                >  [1] x1 + [0]       
219.25/60.04	                =  [x1]               
219.25/60.04	                                      
219.25/60.04	   
219.25/60.04	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
219.25/60.04	   
219.25/60.04	   We are left with following problem, upon which TcT provides the
219.25/60.04	   certificate MAYBE.
219.25/60.04	   
219.25/60.04	   Strict Trs:
219.25/60.04	     { f(s(x1)) -> d(f(p(s(x1))))
219.25/60.04	     , d(0(x1)) -> 0(x1)
219.25/60.04	     , d(s(x1)) -> s(s(d(p(s(x1))))) }
219.25/60.04	   Weak Trs:
219.25/60.04	     { f(0(x1)) -> s(0(x1))
219.25/60.04	     , p(s(x1)) -> x1 }
219.25/60.04	   Obligation:
219.25/60.04	     derivational complexity
219.25/60.04	   Answer:
219.25/60.04	     MAYBE
219.25/60.04	   
219.25/60.04	   The weightgap principle applies (using the following nonconstant
219.25/60.04	   growth matrix-interpretation)
219.25/60.04	   
219.25/60.04	   TcT has computed the following triangular matrix interpretation.
219.25/60.04	   Note that the diagonal of the component-wise maxima of
219.25/60.04	   interpretation-entries contains no more than 1 non-zero entries.
219.25/60.04	   
219.25/60.04	     [f](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [0](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [s](x1) = [1] x1 + [0]
219.25/60.04	                           
219.25/60.04	     [d](x1) = [1] x1 + [1]
219.25/60.04	                           
219.25/60.04	     [p](x1) = [1] x1 + [0]
219.25/60.04	   
219.25/60.04	   The order satisfies the following ordering constraints:
219.25/60.04	   
219.25/60.04	     [f(0(x1))] =  [1] x1 + [0]       
219.25/60.04	                >= [1] x1 + [0]       
219.25/60.04	                =  [s(0(x1))]         
219.25/60.04	                                      
219.25/60.04	     [f(s(x1))] =  [1] x1 + [0]       
219.25/60.04	                ?  [1] x1 + [1]       
219.25/60.04	                =  [d(f(p(s(x1))))]   
219.25/60.04	                                      
219.25/60.04	     [d(0(x1))] =  [1] x1 + [1]       
219.25/60.04	                >  [1] x1 + [0]       
219.25/60.04	                =  [0(x1)]            
219.25/60.04	                                      
219.25/60.04	     [d(s(x1))] =  [1] x1 + [1]       
219.25/60.04	                >= [1] x1 + [1]       
219.25/60.04	                =  [s(s(d(p(s(x1)))))]
219.25/60.04	                                      
219.25/60.04	     [p(s(x1))] =  [1] x1 + [0]       
219.25/60.04	                >= [1] x1 + [0]       
219.25/60.04	                =  [x1]               
219.25/60.04	                                      
219.25/60.04	   
219.25/60.04	   Further, it can be verified that all rules not oriented are covered by the weightgap condition.
219.25/60.04	   
219.25/60.04	   We are left with following problem, upon which TcT provides the
219.25/60.04	   certificate MAYBE.
219.25/60.04	   
219.25/60.04	   Strict Trs:
219.25/60.04	     { f(s(x1)) -> d(f(p(s(x1))))
219.25/60.04	     , d(s(x1)) -> s(s(d(p(s(x1))))) }
219.25/60.04	   Weak Trs:
219.25/60.04	     { f(0(x1)) -> s(0(x1))
219.25/60.04	     , d(0(x1)) -> 0(x1)
219.25/60.04	     , p(s(x1)) -> x1 }
219.25/60.04	   Obligation:
219.25/60.04	     derivational complexity
219.25/60.04	   Answer:
219.25/60.04	     MAYBE
219.25/60.04	   
219.25/60.04	   None of the processors succeeded.
219.25/60.04	   
219.25/60.04	   Details of failed attempt(s):
219.25/60.04	   -----------------------------
219.25/60.04	   1) 'empty' failed due to the following reason:
219.25/60.04	      
219.25/60.04	      Empty strict component of the problem is NOT empty.
219.25/60.04	   
219.25/60.04	   2) 'Fastest' failed due to the following reason:
219.25/60.04	      
219.25/60.04	      None of the processors succeeded.
219.25/60.04	      
219.25/60.04	      Details of failed attempt(s):
219.25/60.04	      -----------------------------
219.25/60.04	      1) 'bsearch-matrix' failed due to the following reason:
219.25/60.04	         
219.25/60.04	         The input cannot be shown compatible
219.25/60.04	      
219.25/60.04	      2) 'iteProgress' failed due to the following reason:
219.25/60.04	         
219.25/60.04	         Fail
219.25/60.04	      
219.25/60.04	      3) 'Fastest (timeout of 30 seconds)' failed due to the following
219.25/60.04	         reason:
219.25/60.04	         
219.25/60.04	         Computation stopped due to timeout after 30.0 seconds.
219.25/60.04	      
219.25/60.04	      4) 'Fastest' failed due to the following reason:
219.25/60.04	         
219.25/60.04	         None of the processors succeeded.
219.25/60.04	         
219.25/60.04	         Details of failed attempt(s):
219.25/60.04	         -----------------------------
219.25/60.04	         1) 'matrix interpretation of dimension 5' failed due to the
219.25/60.04	            following reason:
219.25/60.04	            
219.25/60.04	            The input cannot be shown compatible
219.25/60.04	         
219.25/60.04	         2) 'matrix interpretation of dimension 6' failed due to the
219.25/60.04	            following reason:
219.25/60.04	            
219.25/60.04	            The input cannot be shown compatible
219.25/60.04	         
219.25/60.04	         3) 'matrix interpretation of dimension 4' failed due to the
219.25/60.04	            following reason:
219.25/60.04	            
219.25/60.04	            The input cannot be shown compatible
219.25/60.04	         
219.25/60.04	         4) 'matrix interpretation of dimension 3' failed due to the
219.25/60.04	            following reason:
219.25/60.04	            
219.25/60.04	            The input cannot be shown compatible
219.25/60.04	         
219.25/60.04	         5) 'matrix interpretation of dimension 2' failed due to the
219.25/60.04	            following reason:
219.25/60.04	            
219.25/60.04	            The input cannot be shown compatible
219.25/60.04	         
219.25/60.04	         6) 'matrix interpretation of dimension 1' failed due to the
219.25/60.04	            following reason:
219.25/60.04	            
219.25/60.04	            The input cannot be shown compatible
219.25/60.04	         
219.25/60.04	      
219.25/60.04	   
219.25/60.04	
219.25/60.04	3) 'iteProgress (timeout of 297 seconds)' failed due to the
219.25/60.04	   following reason:
219.25/60.04	   
219.25/60.04	   Fail
219.25/60.04	
219.25/60.04	4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the
219.25/60.04	   following reason:
219.25/60.04	   
219.25/60.04	   The input cannot be shown compatible
219.25/60.04	
219.25/60.04	
219.25/60.04	Arrrr..
219.25/60.04	EOF