MAYBE
1180.37/297.03	MAYBE
1180.37/297.03	
1180.37/297.03	We are left with following problem, upon which TcT provides the
1180.37/297.03	certificate MAYBE.
1180.37/297.03	
1180.37/297.03	Strict Trs:
1180.37/297.03	  { a__from(X) -> cons(mark(X), from(s(X)))
1180.37/297.03	  , a__from(X) -> from(X)
1180.37/297.03	  , mark(cons(X1, X2)) -> cons(mark(X1), X2)
1180.37/297.03	  , mark(from(X)) -> a__from(mark(X))
1180.37/297.03	  , mark(s(X)) -> s(mark(X))
1180.37/297.03	  , mark(0()) -> 0()
1180.37/297.03	  , mark(nil()) -> nil()
1180.37/297.03	  , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
1180.37/297.03	  , mark(head(X)) -> a__head(mark(X))
1180.37/297.03	  , mark(2nd(X)) -> a__2nd(mark(X))
1180.37/297.03	  , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
1180.37/297.03	  , a__head(X) -> head(X)
1180.37/297.03	  , a__head(cons(X, XS)) -> mark(X)
1180.37/297.03	  , a__2nd(X) -> 2nd(X)
1180.37/297.03	  , a__2nd(cons(X, XS)) -> a__head(mark(XS))
1180.37/297.03	  , a__take(X1, X2) -> take(X1, X2)
1180.37/297.03	  , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
1180.37/297.03	  , a__take(0(), XS) -> nil()
1180.37/297.03	  , a__sel(X1, X2) -> sel(X1, X2)
1180.37/297.03	  , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
1180.37/297.03	  , a__sel(0(), cons(X, XS)) -> mark(X) }
1180.37/297.03	Obligation:
1180.37/297.03	  runtime complexity
1180.37/297.03	Answer:
1180.37/297.03	  MAYBE
1180.37/297.03	
1180.37/297.03	None of the processors succeeded.
1180.37/297.03	
1180.37/297.03	Details of failed attempt(s):
1180.37/297.03	-----------------------------
1180.37/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1180.37/297.03	   following reason:
1180.37/297.03	   
1180.37/297.03	   Computation stopped due to timeout after 297.0 seconds.
1180.37/297.03	
1180.37/297.03	2) 'Best' failed due to the following reason:
1180.37/297.03	   
1180.37/297.03	   None of the processors succeeded.
1180.37/297.03	   
1180.37/297.03	   Details of failed attempt(s):
1180.37/297.03	   -----------------------------
1180.37/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1180.37/297.03	      seconds)' failed due to the following reason:
1180.37/297.03	      
1180.37/297.03	      None of the processors succeeded.
1180.37/297.03	      
1180.37/297.03	      Details of failed attempt(s):
1180.37/297.03	      -----------------------------
1180.37/297.03	      1) 'empty' failed due to the following reason:
1180.37/297.03	         
1180.37/297.03	         Empty strict component of the problem is NOT empty.
1180.37/297.03	      
1180.37/297.03	      2) 'With Problem ...' failed due to the following reason:
1180.37/297.03	         
1180.37/297.03	         None of the processors succeeded.
1180.37/297.03	         
1180.37/297.03	         Details of failed attempt(s):
1180.37/297.03	         -----------------------------
1180.37/297.03	         1) 'empty' failed due to the following reason:
1180.37/297.03	            
1180.37/297.03	            Empty strict component of the problem is NOT empty.
1180.37/297.03	         
1180.37/297.03	         2) 'Fastest' failed due to the following reason:
1180.37/297.03	            
1180.37/297.03	            None of the processors succeeded.
1180.37/297.03	            
1180.37/297.03	            Details of failed attempt(s):
1180.37/297.03	            -----------------------------
1180.37/297.03	            1) 'With Problem ...' failed due to the following reason:
1180.37/297.03	               
1180.37/297.03	               None of the processors succeeded.
1180.37/297.03	               
1180.37/297.03	               Details of failed attempt(s):
1180.37/297.03	               -----------------------------
1180.37/297.03	               1) 'empty' failed due to the following reason:
1180.37/297.03	                  
1180.37/297.03	                  Empty strict component of the problem is NOT empty.
1180.37/297.03	               
1180.37/297.03	               2) 'With Problem ...' failed due to the following reason:
1180.37/297.03	                  
1180.37/297.03	                  None of the processors succeeded.
1180.37/297.03	                  
1180.37/297.03	                  Details of failed attempt(s):
1180.37/297.03	                  -----------------------------
1180.37/297.03	                  1) 'empty' failed due to the following reason:
1180.37/297.03	                     
1180.37/297.03	                     Empty strict component of the problem is NOT empty.
1180.37/297.03	                  
1180.37/297.03	                  2) 'With Problem ...' failed due to the following reason:
1180.37/297.03	                     
1180.37/297.03	                     None of the processors succeeded.
1180.37/297.03	                     
1180.37/297.03	                     Details of failed attempt(s):
1180.37/297.03	                     -----------------------------
1180.37/297.03	                     1) 'empty' failed due to the following reason:
1180.37/297.03	                        
1180.37/297.03	                        Empty strict component of the problem is NOT empty.
1180.37/297.03	                     
1180.37/297.03	                     2) 'With Problem ...' failed due to the following reason:
1180.37/297.03	                        
1180.37/297.03	                        Empty strict component of the problem is NOT empty.
1180.37/297.03	                     
1180.37/297.03	                  
1180.37/297.03	               
1180.37/297.03	            
1180.37/297.03	            2) 'With Problem ...' failed due to the following reason:
1180.37/297.03	               
1180.37/297.03	               None of the processors succeeded.
1180.37/297.03	               
1180.37/297.03	               Details of failed attempt(s):
1180.37/297.03	               -----------------------------
1180.37/297.03	               1) 'empty' failed due to the following reason:
1180.37/297.03	                  
1180.37/297.03	                  Empty strict component of the problem is NOT empty.
1180.37/297.03	               
1180.37/297.03	               2) 'With Problem ...' failed due to the following reason:
1180.37/297.03	                  
1180.37/297.03	                  Empty strict component of the problem is NOT empty.
1180.37/297.03	               
1180.37/297.03	            
1180.37/297.03	         
1180.37/297.03	      
1180.37/297.03	   
1180.37/297.03	   2) 'Best' failed due to the following reason:
1180.37/297.03	      
1180.37/297.03	      None of the processors succeeded.
1180.37/297.03	      
1180.37/297.03	      Details of failed attempt(s):
1180.37/297.03	      -----------------------------
1180.37/297.03	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1180.37/297.03	         following reason:
1180.37/297.03	         
1180.37/297.03	         The processor is inapplicable, reason:
1180.37/297.03	           Processor only applicable for innermost runtime complexity analysis
1180.37/297.03	      
1180.37/297.03	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1180.37/297.03	         to the following reason:
1180.37/297.03	         
1180.37/297.03	         The processor is inapplicable, reason:
1180.37/297.03	           Processor only applicable for innermost runtime complexity analysis
1180.37/297.03	      
1180.37/297.03	   
1180.37/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1180.37/297.03	      failed due to the following reason:
1180.37/297.03	      
1180.37/297.03	      None of the processors succeeded.
1180.37/297.03	      
1180.37/297.03	      Details of failed attempt(s):
1180.37/297.03	      -----------------------------
1180.37/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1180.37/297.03	         failed due to the following reason:
1180.37/297.03	         
1180.37/297.03	         match-boundness of the problem could not be verified.
1180.37/297.03	      
1180.37/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1180.37/297.03	         failed due to the following reason:
1180.37/297.03	         
1180.37/297.03	         match-boundness of the problem could not be verified.
1180.37/297.03	      
1180.37/297.03	   
1180.37/297.03	
1180.37/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1180.37/297.03	   the following reason:
1180.37/297.03	   
1180.37/297.03	   We add the following weak dependency pairs:
1180.37/297.03	   
1180.37/297.03	   Strict DPs:
1180.37/297.03	     { a__from^#(X) -> c_1(mark^#(X), X)
1180.37/297.03	     , a__from^#(X) -> c_2(X)
1180.37/297.03	     , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2)
1180.37/297.03	     , mark^#(from(X)) -> c_4(a__from^#(mark(X)))
1180.37/297.03	     , mark^#(s(X)) -> c_5(mark^#(X))
1180.37/297.03	     , mark^#(0()) -> c_6()
1180.37/297.03	     , mark^#(nil()) -> c_7()
1180.37/297.03	     , mark^#(take(X1, X2)) -> c_8(a__take^#(mark(X1), mark(X2)))
1180.37/297.03	     , mark^#(head(X)) -> c_9(a__head^#(mark(X)))
1180.37/297.03	     , mark^#(2nd(X)) -> c_10(a__2nd^#(mark(X)))
1180.37/297.03	     , mark^#(sel(X1, X2)) -> c_11(a__sel^#(mark(X1), mark(X2)))
1180.37/297.03	     , a__take^#(X1, X2) -> c_16(X1, X2)
1180.37/297.03	     , a__take^#(s(N), cons(X, XS)) -> c_17(mark^#(X), N, XS)
1180.37/297.03	     , a__take^#(0(), XS) -> c_18()
1180.37/297.03	     , a__head^#(X) -> c_12(X)
1180.37/297.03	     , a__head^#(cons(X, XS)) -> c_13(mark^#(X))
1180.37/297.03	     , a__2nd^#(X) -> c_14(X)
1180.37/297.03	     , a__2nd^#(cons(X, XS)) -> c_15(a__head^#(mark(XS)))
1180.37/297.03	     , a__sel^#(X1, X2) -> c_19(X1, X2)
1180.37/297.03	     , a__sel^#(s(N), cons(X, XS)) -> c_20(a__sel^#(mark(N), mark(XS)))
1180.37/297.03	     , a__sel^#(0(), cons(X, XS)) -> c_21(mark^#(X)) }
1180.37/297.03	   
1180.37/297.03	   and mark the set of starting terms.
1180.37/297.03	   
1180.37/297.03	   We are left with following problem, upon which TcT provides the
1180.37/297.03	   certificate MAYBE.
1180.37/297.03	   
1180.37/297.03	   Strict DPs:
1180.37/297.03	     { a__from^#(X) -> c_1(mark^#(X), X)
1180.37/297.03	     , a__from^#(X) -> c_2(X)
1180.37/297.03	     , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2)
1180.37/297.03	     , mark^#(from(X)) -> c_4(a__from^#(mark(X)))
1180.37/297.03	     , mark^#(s(X)) -> c_5(mark^#(X))
1180.37/297.03	     , mark^#(0()) -> c_6()
1180.37/297.03	     , mark^#(nil()) -> c_7()
1180.37/297.03	     , mark^#(take(X1, X2)) -> c_8(a__take^#(mark(X1), mark(X2)))
1180.37/297.03	     , mark^#(head(X)) -> c_9(a__head^#(mark(X)))
1180.37/297.03	     , mark^#(2nd(X)) -> c_10(a__2nd^#(mark(X)))
1180.37/297.03	     , mark^#(sel(X1, X2)) -> c_11(a__sel^#(mark(X1), mark(X2)))
1180.37/297.03	     , a__take^#(X1, X2) -> c_16(X1, X2)
1180.37/297.03	     , a__take^#(s(N), cons(X, XS)) -> c_17(mark^#(X), N, XS)
1180.37/297.03	     , a__take^#(0(), XS) -> c_18()
1180.37/297.03	     , a__head^#(X) -> c_12(X)
1180.37/297.03	     , a__head^#(cons(X, XS)) -> c_13(mark^#(X))
1180.37/297.03	     , a__2nd^#(X) -> c_14(X)
1180.37/297.03	     , a__2nd^#(cons(X, XS)) -> c_15(a__head^#(mark(XS)))
1180.37/297.03	     , a__sel^#(X1, X2) -> c_19(X1, X2)
1180.37/297.03	     , a__sel^#(s(N), cons(X, XS)) -> c_20(a__sel^#(mark(N), mark(XS)))
1180.37/297.03	     , a__sel^#(0(), cons(X, XS)) -> c_21(mark^#(X)) }
1180.37/297.03	   Strict Trs:
1180.37/297.03	     { a__from(X) -> cons(mark(X), from(s(X)))
1180.37/297.03	     , a__from(X) -> from(X)
1180.37/297.03	     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
1180.37/297.03	     , mark(from(X)) -> a__from(mark(X))
1180.37/297.03	     , mark(s(X)) -> s(mark(X))
1180.37/297.03	     , mark(0()) -> 0()
1180.37/297.03	     , mark(nil()) -> nil()
1180.37/297.03	     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
1180.37/297.03	     , mark(head(X)) -> a__head(mark(X))
1180.37/297.03	     , mark(2nd(X)) -> a__2nd(mark(X))
1180.37/297.03	     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
1180.37/297.03	     , a__head(X) -> head(X)
1180.37/297.03	     , a__head(cons(X, XS)) -> mark(X)
1180.37/297.03	     , a__2nd(X) -> 2nd(X)
1180.37/297.03	     , a__2nd(cons(X, XS)) -> a__head(mark(XS))
1180.37/297.03	     , a__take(X1, X2) -> take(X1, X2)
1180.37/297.03	     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
1180.37/297.03	     , a__take(0(), XS) -> nil()
1180.37/297.03	     , a__sel(X1, X2) -> sel(X1, X2)
1180.37/297.03	     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
1180.37/297.03	     , a__sel(0(), cons(X, XS)) -> mark(X) }
1180.37/297.03	   Obligation:
1180.37/297.03	     runtime complexity
1180.37/297.03	   Answer:
1180.37/297.03	     MAYBE
1180.37/297.03	   
1180.37/297.03	   We estimate the number of application of {6,7,14} by applications
1180.37/297.03	   of Pre({6,7,14}) = {1,2,3,5,8,12,13,15,16,17,19,21}. Here rules are
1180.37/297.03	   labeled as follows:
1180.37/297.03	   
1180.37/297.03	     DPs:
1180.37/297.03	       { 1: a__from^#(X) -> c_1(mark^#(X), X)
1180.37/297.03	       , 2: a__from^#(X) -> c_2(X)
1180.37/297.03	       , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2)
1180.37/297.03	       , 4: mark^#(from(X)) -> c_4(a__from^#(mark(X)))
1180.37/297.03	       , 5: mark^#(s(X)) -> c_5(mark^#(X))
1180.37/297.03	       , 6: mark^#(0()) -> c_6()
1180.37/297.03	       , 7: mark^#(nil()) -> c_7()
1180.37/297.03	       , 8: mark^#(take(X1, X2)) -> c_8(a__take^#(mark(X1), mark(X2)))
1180.37/297.03	       , 9: mark^#(head(X)) -> c_9(a__head^#(mark(X)))
1180.37/297.03	       , 10: mark^#(2nd(X)) -> c_10(a__2nd^#(mark(X)))
1180.37/297.03	       , 11: mark^#(sel(X1, X2)) -> c_11(a__sel^#(mark(X1), mark(X2)))
1180.37/297.03	       , 12: a__take^#(X1, X2) -> c_16(X1, X2)
1180.37/297.03	       , 13: a__take^#(s(N), cons(X, XS)) -> c_17(mark^#(X), N, XS)
1180.37/297.03	       , 14: a__take^#(0(), XS) -> c_18()
1180.37/297.03	       , 15: a__head^#(X) -> c_12(X)
1180.37/297.03	       , 16: a__head^#(cons(X, XS)) -> c_13(mark^#(X))
1180.37/297.03	       , 17: a__2nd^#(X) -> c_14(X)
1180.37/297.03	       , 18: a__2nd^#(cons(X, XS)) -> c_15(a__head^#(mark(XS)))
1180.37/297.03	       , 19: a__sel^#(X1, X2) -> c_19(X1, X2)
1180.37/297.03	       , 20: a__sel^#(s(N), cons(X, XS)) ->
1180.37/297.03	             c_20(a__sel^#(mark(N), mark(XS)))
1180.37/297.03	       , 21: a__sel^#(0(), cons(X, XS)) -> c_21(mark^#(X)) }
1180.37/297.03	   
1180.37/297.03	   We are left with following problem, upon which TcT provides the
1180.37/297.03	   certificate MAYBE.
1180.37/297.03	   
1180.37/297.03	   Strict DPs:
1180.37/297.03	     { a__from^#(X) -> c_1(mark^#(X), X)
1180.37/297.03	     , a__from^#(X) -> c_2(X)
1180.37/297.03	     , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2)
1180.37/297.03	     , mark^#(from(X)) -> c_4(a__from^#(mark(X)))
1180.37/297.03	     , mark^#(s(X)) -> c_5(mark^#(X))
1180.37/297.03	     , mark^#(take(X1, X2)) -> c_8(a__take^#(mark(X1), mark(X2)))
1180.37/297.03	     , mark^#(head(X)) -> c_9(a__head^#(mark(X)))
1180.37/297.03	     , mark^#(2nd(X)) -> c_10(a__2nd^#(mark(X)))
1180.37/297.03	     , mark^#(sel(X1, X2)) -> c_11(a__sel^#(mark(X1), mark(X2)))
1180.37/297.03	     , a__take^#(X1, X2) -> c_16(X1, X2)
1180.37/297.03	     , a__take^#(s(N), cons(X, XS)) -> c_17(mark^#(X), N, XS)
1180.37/297.03	     , a__head^#(X) -> c_12(X)
1180.37/297.03	     , a__head^#(cons(X, XS)) -> c_13(mark^#(X))
1180.37/297.03	     , a__2nd^#(X) -> c_14(X)
1180.37/297.03	     , a__2nd^#(cons(X, XS)) -> c_15(a__head^#(mark(XS)))
1180.37/297.03	     , a__sel^#(X1, X2) -> c_19(X1, X2)
1180.37/297.03	     , a__sel^#(s(N), cons(X, XS)) -> c_20(a__sel^#(mark(N), mark(XS)))
1180.37/297.03	     , a__sel^#(0(), cons(X, XS)) -> c_21(mark^#(X)) }
1180.37/297.03	   Strict Trs:
1180.37/297.03	     { a__from(X) -> cons(mark(X), from(s(X)))
1180.37/297.03	     , a__from(X) -> from(X)
1180.37/297.03	     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
1180.37/297.03	     , mark(from(X)) -> a__from(mark(X))
1180.37/297.03	     , mark(s(X)) -> s(mark(X))
1180.37/297.03	     , mark(0()) -> 0()
1180.37/297.03	     , mark(nil()) -> nil()
1180.37/297.03	     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
1180.37/297.03	     , mark(head(X)) -> a__head(mark(X))
1180.37/297.03	     , mark(2nd(X)) -> a__2nd(mark(X))
1180.37/297.03	     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
1180.37/297.03	     , a__head(X) -> head(X)
1180.37/297.03	     , a__head(cons(X, XS)) -> mark(X)
1180.37/297.03	     , a__2nd(X) -> 2nd(X)
1180.37/297.03	     , a__2nd(cons(X, XS)) -> a__head(mark(XS))
1180.37/297.03	     , a__take(X1, X2) -> take(X1, X2)
1180.37/297.03	     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
1180.37/297.03	     , a__take(0(), XS) -> nil()
1180.37/297.03	     , a__sel(X1, X2) -> sel(X1, X2)
1180.37/297.03	     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
1180.37/297.03	     , a__sel(0(), cons(X, XS)) -> mark(X) }
1180.37/297.03	   Weak DPs:
1180.37/297.03	     { mark^#(0()) -> c_6()
1180.37/297.03	     , mark^#(nil()) -> c_7()
1180.37/297.03	     , a__take^#(0(), XS) -> c_18() }
1180.37/297.03	   Obligation:
1180.37/297.03	     runtime complexity
1180.37/297.03	   Answer:
1180.37/297.03	     MAYBE
1180.37/297.03	   
1180.37/297.03	   Empty strict component of the problem is NOT empty.
1180.37/297.03	
1180.37/297.03	
1180.37/297.03	Arrrr..
1180.81/297.43	EOF