MAYBE
922.43/297.04	MAYBE
922.43/297.04	
922.43/297.04	We are left with following problem, upon which TcT provides the
922.43/297.04	certificate MAYBE.
922.43/297.04	
922.43/297.04	Strict Trs:
922.43/297.04	  { first(X1, X2) -> n__first(X1, X2)
922.43/297.04	  , first(0(), X) -> nil()
922.43/297.04	  , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
922.43/297.04	  , s(X) -> n__s(X)
922.43/297.04	  , activate(X) -> X
922.43/297.04	  , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
922.43/297.04	  , activate(n__from(X)) -> from(activate(X))
922.43/297.04	  , activate(n__s(X)) -> s(activate(X))
922.43/297.04	  , from(X) -> cons(X, n__from(n__s(X)))
922.43/297.04	  , from(X) -> n__from(X) }
922.43/297.04	Obligation:
922.43/297.04	  runtime complexity
922.43/297.04	Answer:
922.43/297.04	  MAYBE
922.43/297.04	
922.43/297.04	None of the processors succeeded.
922.43/297.04	
922.43/297.04	Details of failed attempt(s):
922.43/297.04	-----------------------------
922.43/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
922.43/297.04	   following reason:
922.43/297.04	   
922.43/297.04	   Computation stopped due to timeout after 297.0 seconds.
922.43/297.04	
922.43/297.04	2) 'Best' failed due to the following reason:
922.43/297.04	   
922.43/297.04	   None of the processors succeeded.
922.43/297.04	   
922.43/297.04	   Details of failed attempt(s):
922.43/297.04	   -----------------------------
922.43/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
922.43/297.04	      seconds)' failed due to the following reason:
922.43/297.04	      
922.43/297.04	      None of the processors succeeded.
922.43/297.04	      
922.43/297.04	      Details of failed attempt(s):
922.43/297.04	      -----------------------------
922.43/297.04	      1) 'empty' failed due to the following reason:
922.43/297.04	         
922.43/297.04	         Empty strict component of the problem is NOT empty.
922.43/297.04	      
922.43/297.04	      2) 'With Problem ...' failed due to the following reason:
922.43/297.04	         
922.43/297.04	         None of the processors succeeded.
922.43/297.04	         
922.43/297.04	         Details of failed attempt(s):
922.43/297.04	         -----------------------------
922.43/297.04	         1) 'empty' failed due to the following reason:
922.43/297.04	            
922.43/297.04	            Empty strict component of the problem is NOT empty.
922.43/297.04	         
922.43/297.04	         2) 'Fastest' failed due to the following reason:
922.43/297.04	            
922.43/297.04	            None of the processors succeeded.
922.43/297.04	            
922.43/297.04	            Details of failed attempt(s):
922.43/297.04	            -----------------------------
922.43/297.04	            1) 'With Problem ...' failed due to the following reason:
922.43/297.04	               
922.43/297.04	               None of the processors succeeded.
922.43/297.04	               
922.43/297.04	               Details of failed attempt(s):
922.43/297.04	               -----------------------------
922.43/297.04	               1) 'empty' failed due to the following reason:
922.43/297.04	                  
922.43/297.04	                  Empty strict component of the problem is NOT empty.
922.43/297.04	               
922.43/297.04	               2) 'With Problem ...' failed due to the following reason:
922.43/297.04	                  
922.43/297.04	                  None of the processors succeeded.
922.43/297.04	                  
922.43/297.04	                  Details of failed attempt(s):
922.43/297.04	                  -----------------------------
922.43/297.04	                  1) 'empty' failed due to the following reason:
922.43/297.04	                     
922.43/297.04	                     Empty strict component of the problem is NOT empty.
922.43/297.04	                  
922.43/297.04	                  2) 'With Problem ...' failed due to the following reason:
922.43/297.04	                     
922.43/297.04	                     None of the processors succeeded.
922.43/297.04	                     
922.43/297.04	                     Details of failed attempt(s):
922.43/297.04	                     -----------------------------
922.43/297.04	                     1) 'empty' failed due to the following reason:
922.43/297.04	                        
922.43/297.04	                        Empty strict component of the problem is NOT empty.
922.43/297.04	                     
922.43/297.04	                     2) 'With Problem ...' failed due to the following reason:
922.43/297.04	                        
922.43/297.04	                        Empty strict component of the problem is NOT empty.
922.43/297.04	                     
922.43/297.04	                  
922.43/297.04	               
922.43/297.04	            
922.43/297.04	            2) 'With Problem ...' failed due to the following reason:
922.43/297.04	               
922.43/297.04	               None of the processors succeeded.
922.43/297.04	               
922.43/297.04	               Details of failed attempt(s):
922.43/297.04	               -----------------------------
922.43/297.04	               1) 'empty' failed due to the following reason:
922.43/297.04	                  
922.43/297.04	                  Empty strict component of the problem is NOT empty.
922.43/297.04	               
922.43/297.04	               2) 'With Problem ...' failed due to the following reason:
922.43/297.04	                  
922.43/297.04	                  Empty strict component of the problem is NOT empty.
922.43/297.04	               
922.43/297.04	            
922.43/297.04	         
922.43/297.04	      
922.43/297.04	   
922.43/297.04	   2) 'Best' failed due to the following reason:
922.43/297.04	      
922.43/297.04	      None of the processors succeeded.
922.43/297.04	      
922.43/297.04	      Details of failed attempt(s):
922.43/297.04	      -----------------------------
922.43/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
922.43/297.04	         following reason:
922.43/297.04	         
922.43/297.04	         The processor is inapplicable, reason:
922.43/297.04	           Processor only applicable for innermost runtime complexity analysis
922.43/297.04	      
922.43/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
922.43/297.04	         to the following reason:
922.43/297.04	         
922.43/297.04	         The processor is inapplicable, reason:
922.43/297.04	           Processor only applicable for innermost runtime complexity analysis
922.43/297.04	      
922.43/297.04	   
922.43/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
922.43/297.04	      failed due to the following reason:
922.43/297.04	      
922.43/297.04	      None of the processors succeeded.
922.43/297.04	      
922.43/297.04	      Details of failed attempt(s):
922.43/297.04	      -----------------------------
922.43/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
922.43/297.04	         failed due to the following reason:
922.43/297.04	         
922.43/297.04	         match-boundness of the problem could not be verified.
922.43/297.04	      
922.43/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
922.43/297.04	         failed due to the following reason:
922.43/297.04	         
922.43/297.04	         match-boundness of the problem could not be verified.
922.43/297.04	      
922.43/297.04	   
922.43/297.04	
922.43/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
922.43/297.04	   the following reason:
922.43/297.04	   
922.43/297.04	   We add the following weak dependency pairs:
922.43/297.04	   
922.43/297.04	   Strict DPs:
922.43/297.04	     { first^#(X1, X2) -> c_1(X1, X2)
922.43/297.04	     , first^#(0(), X) -> c_2()
922.43/297.04	     , first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z))
922.43/297.04	     , activate^#(X) -> c_5(X)
922.43/297.04	     , activate^#(n__first(X1, X2)) ->
922.43/297.04	       c_6(first^#(activate(X1), activate(X2)))
922.43/297.04	     , activate^#(n__from(X)) -> c_7(from^#(activate(X)))
922.43/297.04	     , activate^#(n__s(X)) -> c_8(s^#(activate(X)))
922.43/297.04	     , s^#(X) -> c_4(X)
922.43/297.04	     , from^#(X) -> c_9(X, X)
922.43/297.04	     , from^#(X) -> c_10(X) }
922.43/297.04	   
922.43/297.04	   and mark the set of starting terms.
922.43/297.04	   
922.43/297.04	   We are left with following problem, upon which TcT provides the
922.43/297.04	   certificate MAYBE.
922.43/297.04	   
922.43/297.04	   Strict DPs:
922.43/297.04	     { first^#(X1, X2) -> c_1(X1, X2)
922.43/297.04	     , first^#(0(), X) -> c_2()
922.43/297.04	     , first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z))
922.43/297.04	     , activate^#(X) -> c_5(X)
922.43/297.04	     , activate^#(n__first(X1, X2)) ->
922.43/297.04	       c_6(first^#(activate(X1), activate(X2)))
922.43/297.04	     , activate^#(n__from(X)) -> c_7(from^#(activate(X)))
922.43/297.04	     , activate^#(n__s(X)) -> c_8(s^#(activate(X)))
922.43/297.04	     , s^#(X) -> c_4(X)
922.43/297.04	     , from^#(X) -> c_9(X, X)
922.43/297.04	     , from^#(X) -> c_10(X) }
922.43/297.04	   Strict Trs:
922.43/297.04	     { first(X1, X2) -> n__first(X1, X2)
922.43/297.04	     , first(0(), X) -> nil()
922.43/297.04	     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
922.43/297.04	     , s(X) -> n__s(X)
922.43/297.04	     , activate(X) -> X
922.43/297.04	     , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
922.43/297.04	     , activate(n__from(X)) -> from(activate(X))
922.43/297.04	     , activate(n__s(X)) -> s(activate(X))
922.43/297.04	     , from(X) -> cons(X, n__from(n__s(X)))
922.43/297.04	     , from(X) -> n__from(X) }
922.43/297.04	   Obligation:
922.43/297.04	     runtime complexity
922.43/297.04	   Answer:
922.43/297.04	     MAYBE
922.43/297.04	   
922.43/297.04	   We estimate the number of application of {2} by applications of
922.43/297.04	   Pre({2}) = {1,3,4,5,8,9,10}. Here rules are labeled as follows:
922.43/297.04	   
922.43/297.04	     DPs:
922.43/297.04	       { 1: first^#(X1, X2) -> c_1(X1, X2)
922.43/297.04	       , 2: first^#(0(), X) -> c_2()
922.43/297.04	       , 3: first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z))
922.43/297.04	       , 4: activate^#(X) -> c_5(X)
922.43/297.04	       , 5: activate^#(n__first(X1, X2)) ->
922.43/297.04	            c_6(first^#(activate(X1), activate(X2)))
922.43/297.04	       , 6: activate^#(n__from(X)) -> c_7(from^#(activate(X)))
922.43/297.04	       , 7: activate^#(n__s(X)) -> c_8(s^#(activate(X)))
922.43/297.04	       , 8: s^#(X) -> c_4(X)
922.43/297.04	       , 9: from^#(X) -> c_9(X, X)
922.43/297.04	       , 10: from^#(X) -> c_10(X) }
922.43/297.04	   
922.43/297.04	   We are left with following problem, upon which TcT provides the
922.43/297.04	   certificate MAYBE.
922.43/297.04	   
922.43/297.04	   Strict DPs:
922.43/297.04	     { first^#(X1, X2) -> c_1(X1, X2)
922.43/297.04	     , first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z))
922.43/297.04	     , activate^#(X) -> c_5(X)
922.43/297.04	     , activate^#(n__first(X1, X2)) ->
922.43/297.04	       c_6(first^#(activate(X1), activate(X2)))
922.43/297.04	     , activate^#(n__from(X)) -> c_7(from^#(activate(X)))
922.43/297.04	     , activate^#(n__s(X)) -> c_8(s^#(activate(X)))
922.43/297.04	     , s^#(X) -> c_4(X)
922.43/297.04	     , from^#(X) -> c_9(X, X)
922.43/297.04	     , from^#(X) -> c_10(X) }
922.43/297.04	   Strict Trs:
922.43/297.04	     { first(X1, X2) -> n__first(X1, X2)
922.43/297.04	     , first(0(), X) -> nil()
922.43/297.04	     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
922.43/297.04	     , s(X) -> n__s(X)
922.43/297.04	     , activate(X) -> X
922.43/297.04	     , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
922.43/297.04	     , activate(n__from(X)) -> from(activate(X))
922.43/297.04	     , activate(n__s(X)) -> s(activate(X))
922.43/297.04	     , from(X) -> cons(X, n__from(n__s(X)))
922.43/297.04	     , from(X) -> n__from(X) }
922.43/297.04	   Weak DPs: { first^#(0(), X) -> c_2() }
922.43/297.04	   Obligation:
922.43/297.04	     runtime complexity
922.43/297.04	   Answer:
922.43/297.04	     MAYBE
922.43/297.04	   
922.43/297.04	   Empty strict component of the problem is NOT empty.
922.43/297.04	
922.43/297.04	
922.43/297.04	Arrrr..
923.11/297.62	EOF