MAYBE
1112.03/297.02	MAYBE
1112.03/297.02	
1112.03/297.02	We are left with following problem, upon which TcT provides the
1112.03/297.02	certificate MAYBE.
1112.03/297.02	
1112.03/297.02	Strict Trs:
1112.03/297.02	  { and(true(), X) -> activate(X)
1112.03/297.02	  , and(false(), Y) -> false()
1112.03/297.02	  , activate(X) -> X
1112.03/297.02	  , activate(n__add(X1, X2)) -> add(activate(X1), X2)
1112.03/297.02	  , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
1112.03/297.02	  , activate(n__from(X)) -> from(X)
1112.03/297.02	  , activate(n__s(X)) -> s(X)
1112.03/297.02	  , if(true(), X, Y) -> activate(X)
1112.03/297.02	  , if(false(), X, Y) -> activate(Y)
1112.03/297.02	  , add(X1, X2) -> n__add(X1, X2)
1112.03/297.02	  , add(0(), X) -> activate(X)
1112.03/297.02	  , add(s(X), Y) -> s(n__add(activate(X), activate(Y)))
1112.03/297.02	  , s(X) -> n__s(X)
1112.03/297.02	  , first(X1, X2) -> n__first(X1, X2)
1112.03/297.02	  , first(0(), X) -> nil()
1112.03/297.02	  , first(s(X), cons(Y, Z)) ->
1112.03/297.02	    cons(activate(Y), n__first(activate(X), activate(Z)))
1112.03/297.02	  , from(X) -> cons(activate(X), n__from(n__s(activate(X))))
1112.03/297.02	  , from(X) -> n__from(X) }
1112.03/297.02	Obligation:
1112.03/297.02	  runtime complexity
1112.03/297.02	Answer:
1112.03/297.02	  MAYBE
1112.03/297.02	
1112.03/297.02	None of the processors succeeded.
1112.03/297.02	
1112.03/297.02	Details of failed attempt(s):
1112.03/297.02	-----------------------------
1112.03/297.02	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1112.03/297.02	   following reason:
1112.03/297.02	   
1112.03/297.02	   Computation stopped due to timeout after 297.0 seconds.
1112.03/297.02	
1112.03/297.02	2) 'Best' failed due to the following reason:
1112.03/297.02	   
1112.03/297.02	   None of the processors succeeded.
1112.03/297.02	   
1112.03/297.02	   Details of failed attempt(s):
1112.03/297.02	   -----------------------------
1112.03/297.02	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1112.03/297.02	      seconds)' failed due to the following reason:
1112.03/297.02	      
1112.03/297.02	      None of the processors succeeded.
1112.03/297.02	      
1112.03/297.02	      Details of failed attempt(s):
1112.03/297.02	      -----------------------------
1112.03/297.02	      1) 'empty' failed due to the following reason:
1112.03/297.02	         
1112.03/297.02	         Empty strict component of the problem is NOT empty.
1112.03/297.02	      
1112.03/297.02	      2) 'With Problem ...' failed due to the following reason:
1112.03/297.02	         
1112.03/297.02	         None of the processors succeeded.
1112.03/297.02	         
1112.03/297.02	         Details of failed attempt(s):
1112.03/297.02	         -----------------------------
1112.03/297.02	         1) 'empty' failed due to the following reason:
1112.03/297.02	            
1112.03/297.02	            Empty strict component of the problem is NOT empty.
1112.03/297.02	         
1112.03/297.02	         2) 'Fastest' failed due to the following reason:
1112.03/297.02	            
1112.03/297.02	            None of the processors succeeded.
1112.03/297.02	            
1112.03/297.02	            Details of failed attempt(s):
1112.03/297.02	            -----------------------------
1112.03/297.02	            1) 'With Problem ...' failed due to the following reason:
1112.03/297.02	               
1112.03/297.02	               None of the processors succeeded.
1112.03/297.02	               
1112.03/297.02	               Details of failed attempt(s):
1112.03/297.02	               -----------------------------
1112.03/297.02	               1) 'empty' failed due to the following reason:
1112.03/297.02	                  
1112.03/297.02	                  Empty strict component of the problem is NOT empty.
1112.03/297.02	               
1112.03/297.02	               2) 'With Problem ...' failed due to the following reason:
1112.03/297.02	                  
1112.03/297.02	                  None of the processors succeeded.
1112.03/297.02	                  
1112.03/297.02	                  Details of failed attempt(s):
1112.03/297.02	                  -----------------------------
1112.03/297.02	                  1) 'empty' failed due to the following reason:
1112.03/297.02	                     
1112.03/297.02	                     Empty strict component of the problem is NOT empty.
1112.03/297.02	                  
1112.03/297.02	                  2) 'With Problem ...' failed due to the following reason:
1112.03/297.02	                     
1112.03/297.02	                     None of the processors succeeded.
1112.03/297.02	                     
1112.03/297.02	                     Details of failed attempt(s):
1112.03/297.02	                     -----------------------------
1112.03/297.02	                     1) 'empty' failed due to the following reason:
1112.03/297.02	                        
1112.03/297.02	                        Empty strict component of the problem is NOT empty.
1112.03/297.02	                     
1112.03/297.02	                     2) 'With Problem ...' failed due to the following reason:
1112.03/297.02	                        
1112.03/297.02	                        Empty strict component of the problem is NOT empty.
1112.03/297.02	                     
1112.03/297.02	                  
1112.03/297.02	               
1112.03/297.02	            
1112.03/297.02	            2) 'With Problem ...' failed due to the following reason:
1112.03/297.02	               
1112.03/297.02	               None of the processors succeeded.
1112.03/297.02	               
1112.03/297.02	               Details of failed attempt(s):
1112.03/297.02	               -----------------------------
1112.03/297.02	               1) 'empty' failed due to the following reason:
1112.03/297.02	                  
1112.03/297.02	                  Empty strict component of the problem is NOT empty.
1112.03/297.02	               
1112.03/297.02	               2) 'With Problem ...' failed due to the following reason:
1112.03/297.02	                  
1112.03/297.02	                  Empty strict component of the problem is NOT empty.
1112.03/297.02	               
1112.03/297.02	            
1112.03/297.02	         
1112.03/297.02	      
1112.03/297.02	   
1112.03/297.02	   2) 'Best' failed due to the following reason:
1112.03/297.02	      
1112.03/297.02	      None of the processors succeeded.
1112.03/297.02	      
1112.03/297.02	      Details of failed attempt(s):
1112.03/297.02	      -----------------------------
1112.03/297.02	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1112.03/297.02	         to the following reason:
1112.03/297.02	         
1112.03/297.02	         The processor is inapplicable, reason:
1112.03/297.02	           Processor only applicable for innermost runtime complexity analysis
1112.03/297.02	      
1112.03/297.02	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1112.03/297.02	         following reason:
1112.03/297.02	         
1112.03/297.02	         The processor is inapplicable, reason:
1112.03/297.02	           Processor only applicable for innermost runtime complexity analysis
1112.03/297.02	      
1112.03/297.02	   
1112.03/297.02	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1112.03/297.02	      failed due to the following reason:
1112.03/297.02	      
1112.03/297.02	      None of the processors succeeded.
1112.03/297.02	      
1112.03/297.02	      Details of failed attempt(s):
1112.03/297.02	      -----------------------------
1112.03/297.02	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1112.03/297.02	         failed due to the following reason:
1112.03/297.02	         
1112.03/297.02	         match-boundness of the problem could not be verified.
1112.03/297.02	      
1112.03/297.02	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1112.03/297.02	         failed due to the following reason:
1112.03/297.02	         
1112.03/297.02	         match-boundness of the problem could not be verified.
1112.03/297.02	      
1112.03/297.02	   
1112.03/297.02	
1112.03/297.02	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1112.03/297.02	   the following reason:
1112.03/297.02	   
1112.03/297.02	   We add the following weak dependency pairs:
1112.03/297.02	   
1112.03/297.02	   Strict DPs:
1112.03/297.02	     { and^#(true(), X) -> c_1(activate^#(X))
1112.03/297.02	     , and^#(false(), Y) -> c_2()
1112.03/297.02	     , activate^#(X) -> c_3(X)
1112.03/297.02	     , activate^#(n__add(X1, X2)) -> c_4(add^#(activate(X1), X2))
1112.03/297.02	     , activate^#(n__first(X1, X2)) ->
1112.03/297.02	       c_5(first^#(activate(X1), activate(X2)))
1112.03/297.02	     , activate^#(n__from(X)) -> c_6(from^#(X))
1112.03/297.02	     , activate^#(n__s(X)) -> c_7(s^#(X))
1112.03/297.02	     , add^#(X1, X2) -> c_10(X1, X2)
1112.03/297.02	     , add^#(0(), X) -> c_11(activate^#(X))
1112.03/297.02	     , add^#(s(X), Y) -> c_12(s^#(n__add(activate(X), activate(Y))))
1112.03/297.02	     , first^#(X1, X2) -> c_14(X1, X2)
1112.03/297.02	     , first^#(0(), X) -> c_15()
1112.03/297.02	     , first^#(s(X), cons(Y, Z)) ->
1112.03/297.02	       c_16(activate^#(Y), activate^#(X), activate^#(Z))
1112.03/297.02	     , from^#(X) -> c_17(activate^#(X), activate^#(X))
1112.03/297.02	     , from^#(X) -> c_18(X)
1112.03/297.02	     , s^#(X) -> c_13(X)
1112.03/297.02	     , if^#(true(), X, Y) -> c_8(activate^#(X))
1112.03/297.02	     , if^#(false(), X, Y) -> c_9(activate^#(Y)) }
1112.03/297.02	   
1112.03/297.02	   and mark the set of starting terms.
1112.03/297.02	   
1112.03/297.02	   We are left with following problem, upon which TcT provides the
1112.03/297.02	   certificate MAYBE.
1112.03/297.02	   
1112.03/297.02	   Strict DPs:
1112.03/297.02	     { and^#(true(), X) -> c_1(activate^#(X))
1112.03/297.02	     , and^#(false(), Y) -> c_2()
1112.03/297.02	     , activate^#(X) -> c_3(X)
1112.03/297.02	     , activate^#(n__add(X1, X2)) -> c_4(add^#(activate(X1), X2))
1112.03/297.02	     , activate^#(n__first(X1, X2)) ->
1112.03/297.02	       c_5(first^#(activate(X1), activate(X2)))
1112.03/297.02	     , activate^#(n__from(X)) -> c_6(from^#(X))
1112.03/297.02	     , activate^#(n__s(X)) -> c_7(s^#(X))
1112.03/297.02	     , add^#(X1, X2) -> c_10(X1, X2)
1112.03/297.02	     , add^#(0(), X) -> c_11(activate^#(X))
1112.03/297.02	     , add^#(s(X), Y) -> c_12(s^#(n__add(activate(X), activate(Y))))
1112.03/297.02	     , first^#(X1, X2) -> c_14(X1, X2)
1112.03/297.02	     , first^#(0(), X) -> c_15()
1112.03/297.02	     , first^#(s(X), cons(Y, Z)) ->
1112.03/297.02	       c_16(activate^#(Y), activate^#(X), activate^#(Z))
1112.03/297.02	     , from^#(X) -> c_17(activate^#(X), activate^#(X))
1112.03/297.02	     , from^#(X) -> c_18(X)
1112.03/297.02	     , s^#(X) -> c_13(X)
1112.03/297.02	     , if^#(true(), X, Y) -> c_8(activate^#(X))
1112.03/297.02	     , if^#(false(), X, Y) -> c_9(activate^#(Y)) }
1112.03/297.02	   Strict Trs:
1112.03/297.02	     { and(true(), X) -> activate(X)
1112.03/297.02	     , and(false(), Y) -> false()
1112.03/297.02	     , activate(X) -> X
1112.03/297.02	     , activate(n__add(X1, X2)) -> add(activate(X1), X2)
1112.03/297.02	     , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
1112.03/297.02	     , activate(n__from(X)) -> from(X)
1112.03/297.02	     , activate(n__s(X)) -> s(X)
1112.03/297.02	     , if(true(), X, Y) -> activate(X)
1112.03/297.02	     , if(false(), X, Y) -> activate(Y)
1112.03/297.02	     , add(X1, X2) -> n__add(X1, X2)
1112.03/297.02	     , add(0(), X) -> activate(X)
1112.03/297.02	     , add(s(X), Y) -> s(n__add(activate(X), activate(Y)))
1112.03/297.02	     , s(X) -> n__s(X)
1112.03/297.02	     , first(X1, X2) -> n__first(X1, X2)
1112.03/297.02	     , first(0(), X) -> nil()
1112.03/297.02	     , first(s(X), cons(Y, Z)) ->
1112.03/297.02	       cons(activate(Y), n__first(activate(X), activate(Z)))
1112.03/297.02	     , from(X) -> cons(activate(X), n__from(n__s(activate(X))))
1112.03/297.02	     , from(X) -> n__from(X) }
1112.03/297.02	   Obligation:
1112.03/297.02	     runtime complexity
1112.03/297.02	   Answer:
1112.03/297.02	     MAYBE
1112.03/297.02	   
1112.03/297.02	   We estimate the number of application of {2,12} by applications of
1112.03/297.02	   Pre({2,12}) = {3,5,8,11,15,16}. Here rules are labeled as follows:
1112.03/297.02	   
1112.03/297.02	     DPs:
1112.03/297.02	       { 1: and^#(true(), X) -> c_1(activate^#(X))
1112.03/297.02	       , 2: and^#(false(), Y) -> c_2()
1112.03/297.02	       , 3: activate^#(X) -> c_3(X)
1112.03/297.02	       , 4: activate^#(n__add(X1, X2)) -> c_4(add^#(activate(X1), X2))
1112.03/297.02	       , 5: activate^#(n__first(X1, X2)) ->
1112.03/297.02	            c_5(first^#(activate(X1), activate(X2)))
1112.03/297.02	       , 6: activate^#(n__from(X)) -> c_6(from^#(X))
1112.03/297.02	       , 7: activate^#(n__s(X)) -> c_7(s^#(X))
1112.03/297.02	       , 8: add^#(X1, X2) -> c_10(X1, X2)
1112.03/297.02	       , 9: add^#(0(), X) -> c_11(activate^#(X))
1112.03/297.02	       , 10: add^#(s(X), Y) -> c_12(s^#(n__add(activate(X), activate(Y))))
1112.03/297.02	       , 11: first^#(X1, X2) -> c_14(X1, X2)
1112.03/297.02	       , 12: first^#(0(), X) -> c_15()
1112.03/297.02	       , 13: first^#(s(X), cons(Y, Z)) ->
1112.03/297.02	             c_16(activate^#(Y), activate^#(X), activate^#(Z))
1112.03/297.02	       , 14: from^#(X) -> c_17(activate^#(X), activate^#(X))
1112.03/297.02	       , 15: from^#(X) -> c_18(X)
1112.03/297.02	       , 16: s^#(X) -> c_13(X)
1112.03/297.02	       , 17: if^#(true(), X, Y) -> c_8(activate^#(X))
1112.03/297.02	       , 18: if^#(false(), X, Y) -> c_9(activate^#(Y)) }
1112.03/297.02	   
1112.03/297.02	   We are left with following problem, upon which TcT provides the
1112.03/297.02	   certificate MAYBE.
1112.03/297.02	   
1112.03/297.02	   Strict DPs:
1112.03/297.02	     { and^#(true(), X) -> c_1(activate^#(X))
1112.03/297.02	     , activate^#(X) -> c_3(X)
1112.03/297.02	     , activate^#(n__add(X1, X2)) -> c_4(add^#(activate(X1), X2))
1112.03/297.02	     , activate^#(n__first(X1, X2)) ->
1112.03/297.02	       c_5(first^#(activate(X1), activate(X2)))
1112.03/297.02	     , activate^#(n__from(X)) -> c_6(from^#(X))
1112.03/297.02	     , activate^#(n__s(X)) -> c_7(s^#(X))
1112.03/297.02	     , add^#(X1, X2) -> c_10(X1, X2)
1112.03/297.02	     , add^#(0(), X) -> c_11(activate^#(X))
1112.03/297.02	     , add^#(s(X), Y) -> c_12(s^#(n__add(activate(X), activate(Y))))
1112.03/297.02	     , first^#(X1, X2) -> c_14(X1, X2)
1112.03/297.02	     , first^#(s(X), cons(Y, Z)) ->
1112.03/297.02	       c_16(activate^#(Y), activate^#(X), activate^#(Z))
1112.03/297.02	     , from^#(X) -> c_17(activate^#(X), activate^#(X))
1112.03/297.02	     , from^#(X) -> c_18(X)
1112.03/297.02	     , s^#(X) -> c_13(X)
1112.03/297.02	     , if^#(true(), X, Y) -> c_8(activate^#(X))
1112.03/297.02	     , if^#(false(), X, Y) -> c_9(activate^#(Y)) }
1112.03/297.02	   Strict Trs:
1112.03/297.02	     { and(true(), X) -> activate(X)
1112.03/297.02	     , and(false(), Y) -> false()
1112.03/297.02	     , activate(X) -> X
1112.03/297.02	     , activate(n__add(X1, X2)) -> add(activate(X1), X2)
1112.03/297.02	     , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
1112.03/297.02	     , activate(n__from(X)) -> from(X)
1112.03/297.02	     , activate(n__s(X)) -> s(X)
1112.03/297.02	     , if(true(), X, Y) -> activate(X)
1112.03/297.02	     , if(false(), X, Y) -> activate(Y)
1112.03/297.02	     , add(X1, X2) -> n__add(X1, X2)
1112.03/297.02	     , add(0(), X) -> activate(X)
1112.03/297.02	     , add(s(X), Y) -> s(n__add(activate(X), activate(Y)))
1112.03/297.02	     , s(X) -> n__s(X)
1112.03/297.02	     , first(X1, X2) -> n__first(X1, X2)
1112.03/297.02	     , first(0(), X) -> nil()
1112.03/297.02	     , first(s(X), cons(Y, Z)) ->
1112.03/297.02	       cons(activate(Y), n__first(activate(X), activate(Z)))
1112.03/297.02	     , from(X) -> cons(activate(X), n__from(n__s(activate(X))))
1112.03/297.02	     , from(X) -> n__from(X) }
1112.03/297.02	   Weak DPs:
1112.03/297.02	     { and^#(false(), Y) -> c_2()
1112.03/297.02	     , first^#(0(), X) -> c_15() }
1112.03/297.02	   Obligation:
1112.03/297.02	     runtime complexity
1112.03/297.02	   Answer:
1112.03/297.02	     MAYBE
1112.03/297.02	   
1112.03/297.02	   Empty strict component of the problem is NOT empty.
1112.03/297.02	
1112.03/297.02	
1112.03/297.02	Arrrr..
1112.25/297.27	EOF