MAYBE
1174.79/297.03	MAYBE
1174.79/297.03	
1174.79/297.03	We are left with following problem, upon which TcT provides the
1174.79/297.03	certificate MAYBE.
1174.79/297.03	
1174.79/297.03	Strict Trs:
1174.79/297.03	  { a__app(X1, X2) -> app(X1, X2)
1174.79/297.03	  , a__app(nil(), YS) -> mark(YS)
1174.79/297.03	  , a__app(cons(X, XS), YS) -> cons(mark(X), app(XS, YS))
1174.79/297.03	  , mark(nil()) -> nil()
1174.79/297.03	  , mark(cons(X1, X2)) -> cons(mark(X1), X2)
1174.79/297.03	  , mark(app(X1, X2)) -> a__app(mark(X1), mark(X2))
1174.79/297.03	  , mark(from(X)) -> a__from(mark(X))
1174.79/297.03	  , mark(s(X)) -> s(mark(X))
1174.79/297.03	  , mark(zWadr(X1, X2)) -> a__zWadr(mark(X1), mark(X2))
1174.79/297.03	  , mark(prefix(X)) -> a__prefix(mark(X))
1174.79/297.03	  , a__from(X) -> cons(mark(X), from(s(X)))
1174.79/297.03	  , a__from(X) -> from(X)
1174.79/297.03	  , a__zWadr(X1, X2) -> zWadr(X1, X2)
1174.79/297.03	  , a__zWadr(XS, nil()) -> nil()
1174.79/297.03	  , a__zWadr(nil(), YS) -> nil()
1174.79/297.03	  , a__zWadr(cons(X, XS), cons(Y, YS)) ->
1174.79/297.03	    cons(a__app(mark(Y), cons(mark(X), nil())), zWadr(XS, YS))
1174.79/297.03	  , a__prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
1174.79/297.03	  , a__prefix(X) -> prefix(X) }
1174.79/297.03	Obligation:
1174.79/297.03	  runtime complexity
1174.79/297.03	Answer:
1174.79/297.03	  MAYBE
1174.79/297.03	
1174.79/297.03	None of the processors succeeded.
1174.79/297.03	
1174.79/297.03	Details of failed attempt(s):
1174.79/297.03	-----------------------------
1174.79/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1174.79/297.03	   following reason:
1174.79/297.03	   
1174.79/297.03	   Computation stopped due to timeout after 297.0 seconds.
1174.79/297.03	
1174.79/297.03	2) 'Best' failed due to the following reason:
1174.79/297.03	   
1174.79/297.03	   None of the processors succeeded.
1174.79/297.03	   
1174.79/297.03	   Details of failed attempt(s):
1174.79/297.03	   -----------------------------
1174.79/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1174.79/297.03	      seconds)' failed due to the following reason:
1174.79/297.03	      
1174.79/297.03	      None of the processors succeeded.
1174.79/297.03	      
1174.79/297.03	      Details of failed attempt(s):
1174.79/297.03	      -----------------------------
1174.79/297.03	      1) 'empty' failed due to the following reason:
1174.79/297.03	         
1174.79/297.03	         Empty strict component of the problem is NOT empty.
1174.79/297.03	      
1174.79/297.03	      2) 'With Problem ...' failed due to the following reason:
1174.79/297.03	         
1174.79/297.03	         None of the processors succeeded.
1174.79/297.03	         
1174.79/297.03	         Details of failed attempt(s):
1174.79/297.03	         -----------------------------
1174.79/297.03	         1) 'empty' failed due to the following reason:
1174.79/297.03	            
1174.79/297.03	            Empty strict component of the problem is NOT empty.
1174.79/297.03	         
1174.79/297.04	         2) 'Fastest' failed due to the following reason:
1174.79/297.04	            
1174.79/297.04	            None of the processors succeeded.
1174.79/297.04	            
1174.79/297.04	            Details of failed attempt(s):
1174.79/297.04	            -----------------------------
1174.79/297.04	            1) 'With Problem ...' failed due to the following reason:
1174.79/297.04	               
1174.79/297.04	               None of the processors succeeded.
1174.79/297.04	               
1174.79/297.04	               Details of failed attempt(s):
1174.79/297.04	               -----------------------------
1174.79/297.04	               1) 'empty' failed due to the following reason:
1174.79/297.04	                  
1174.79/297.04	                  Empty strict component of the problem is NOT empty.
1174.79/297.04	               
1174.79/297.04	               2) 'With Problem ...' failed due to the following reason:
1174.79/297.04	                  
1174.79/297.04	                  None of the processors succeeded.
1174.79/297.04	                  
1174.79/297.04	                  Details of failed attempt(s):
1174.79/297.04	                  -----------------------------
1174.79/297.04	                  1) 'empty' failed due to the following reason:
1174.79/297.04	                     
1174.79/297.04	                     Empty strict component of the problem is NOT empty.
1174.79/297.04	                  
1174.79/297.04	                  2) 'With Problem ...' failed due to the following reason:
1174.79/297.04	                     
1174.79/297.04	                     None of the processors succeeded.
1174.79/297.04	                     
1174.79/297.04	                     Details of failed attempt(s):
1174.79/297.04	                     -----------------------------
1174.79/297.04	                     1) 'empty' failed due to the following reason:
1174.79/297.04	                        
1174.79/297.04	                        Empty strict component of the problem is NOT empty.
1174.79/297.04	                     
1174.79/297.04	                     2) 'With Problem ...' failed due to the following reason:
1174.79/297.04	                        
1174.79/297.04	                        Empty strict component of the problem is NOT empty.
1174.79/297.04	                     
1174.79/297.04	                  
1174.79/297.04	               
1174.79/297.04	            
1174.79/297.04	            2) 'With Problem ...' failed due to the following reason:
1174.79/297.04	               
1174.79/297.04	               None of the processors succeeded.
1174.79/297.04	               
1174.79/297.04	               Details of failed attempt(s):
1174.79/297.04	               -----------------------------
1174.79/297.04	               1) 'empty' failed due to the following reason:
1174.79/297.04	                  
1174.79/297.04	                  Empty strict component of the problem is NOT empty.
1174.79/297.04	               
1174.79/297.04	               2) 'With Problem ...' failed due to the following reason:
1174.79/297.04	                  
1174.79/297.04	                  Empty strict component of the problem is NOT empty.
1174.79/297.04	               
1174.79/297.04	            
1174.79/297.04	         
1174.79/297.04	      
1174.79/297.04	   
1174.79/297.04	   2) 'Best' failed due to the following reason:
1174.79/297.04	      
1174.79/297.04	      None of the processors succeeded.
1174.79/297.04	      
1174.79/297.04	      Details of failed attempt(s):
1174.79/297.04	      -----------------------------
1174.79/297.04	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1174.79/297.04	         to the following reason:
1174.79/297.04	         
1174.79/297.04	         The processor is inapplicable, reason:
1174.79/297.04	           Processor only applicable for innermost runtime complexity analysis
1174.79/297.04	      
1174.79/297.04	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1174.79/297.04	         following reason:
1174.79/297.04	         
1174.79/297.04	         The processor is inapplicable, reason:
1174.79/297.04	           Processor only applicable for innermost runtime complexity analysis
1174.79/297.04	      
1174.79/297.04	   
1174.79/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1174.79/297.04	      failed due to the following reason:
1174.79/297.04	      
1174.79/297.04	      None of the processors succeeded.
1174.79/297.04	      
1174.79/297.04	      Details of failed attempt(s):
1174.79/297.04	      -----------------------------
1174.79/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1174.79/297.04	         failed due to the following reason:
1174.79/297.04	         
1174.79/297.04	         match-boundness of the problem could not be verified.
1174.79/297.04	      
1174.79/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1174.79/297.04	         failed due to the following reason:
1174.79/297.04	         
1174.79/297.04	         match-boundness of the problem could not be verified.
1174.79/297.04	      
1174.79/297.04	   
1174.79/297.04	
1174.79/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1174.79/297.04	   the following reason:
1174.79/297.04	   
1174.79/297.04	   We add the following weak dependency pairs:
1174.79/297.04	   
1174.79/297.04	   Strict DPs:
1174.79/297.04	     { a__app^#(X1, X2) -> c_1(X1, X2)
1174.79/297.04	     , a__app^#(nil(), YS) -> c_2(mark^#(YS))
1174.79/297.04	     , a__app^#(cons(X, XS), YS) -> c_3(mark^#(X), XS, YS)
1174.79/297.04	     , mark^#(nil()) -> c_4()
1174.79/297.04	     , mark^#(cons(X1, X2)) -> c_5(mark^#(X1), X2)
1174.79/297.04	     , mark^#(app(X1, X2)) -> c_6(a__app^#(mark(X1), mark(X2)))
1174.79/297.04	     , mark^#(from(X)) -> c_7(a__from^#(mark(X)))
1174.79/297.04	     , mark^#(s(X)) -> c_8(mark^#(X))
1174.79/297.04	     , mark^#(zWadr(X1, X2)) -> c_9(a__zWadr^#(mark(X1), mark(X2)))
1174.79/297.04	     , mark^#(prefix(X)) -> c_10(a__prefix^#(mark(X)))
1174.79/297.04	     , a__from^#(X) -> c_11(mark^#(X), X)
1174.79/297.04	     , a__from^#(X) -> c_12(X)
1174.79/297.04	     , a__zWadr^#(X1, X2) -> c_13(X1, X2)
1174.79/297.04	     , a__zWadr^#(XS, nil()) -> c_14()
1174.79/297.04	     , a__zWadr^#(nil(), YS) -> c_15()
1174.79/297.04	     , a__zWadr^#(cons(X, XS), cons(Y, YS)) ->
1174.79/297.04	       c_16(a__app^#(mark(Y), cons(mark(X), nil())), XS, YS)
1174.79/297.04	     , a__prefix^#(L) -> c_17(L, L)
1174.79/297.04	     , a__prefix^#(X) -> c_18(X) }
1174.79/297.04	   
1174.79/297.04	   and mark the set of starting terms.
1174.79/297.04	   
1174.79/297.04	   We are left with following problem, upon which TcT provides the
1174.79/297.04	   certificate MAYBE.
1174.79/297.04	   
1174.79/297.04	   Strict DPs:
1174.79/297.04	     { a__app^#(X1, X2) -> c_1(X1, X2)
1174.79/297.04	     , a__app^#(nil(), YS) -> c_2(mark^#(YS))
1174.79/297.04	     , a__app^#(cons(X, XS), YS) -> c_3(mark^#(X), XS, YS)
1174.79/297.04	     , mark^#(nil()) -> c_4()
1174.79/297.04	     , mark^#(cons(X1, X2)) -> c_5(mark^#(X1), X2)
1174.79/297.04	     , mark^#(app(X1, X2)) -> c_6(a__app^#(mark(X1), mark(X2)))
1174.79/297.04	     , mark^#(from(X)) -> c_7(a__from^#(mark(X)))
1174.79/297.04	     , mark^#(s(X)) -> c_8(mark^#(X))
1174.79/297.04	     , mark^#(zWadr(X1, X2)) -> c_9(a__zWadr^#(mark(X1), mark(X2)))
1174.79/297.04	     , mark^#(prefix(X)) -> c_10(a__prefix^#(mark(X)))
1174.79/297.04	     , a__from^#(X) -> c_11(mark^#(X), X)
1174.79/297.04	     , a__from^#(X) -> c_12(X)
1174.79/297.04	     , a__zWadr^#(X1, X2) -> c_13(X1, X2)
1174.79/297.04	     , a__zWadr^#(XS, nil()) -> c_14()
1174.79/297.04	     , a__zWadr^#(nil(), YS) -> c_15()
1174.79/297.04	     , a__zWadr^#(cons(X, XS), cons(Y, YS)) ->
1174.79/297.04	       c_16(a__app^#(mark(Y), cons(mark(X), nil())), XS, YS)
1174.79/297.04	     , a__prefix^#(L) -> c_17(L, L)
1174.79/297.04	     , a__prefix^#(X) -> c_18(X) }
1174.79/297.04	   Strict Trs:
1174.79/297.04	     { a__app(X1, X2) -> app(X1, X2)
1174.79/297.04	     , a__app(nil(), YS) -> mark(YS)
1174.79/297.04	     , a__app(cons(X, XS), YS) -> cons(mark(X), app(XS, YS))
1174.79/297.04	     , mark(nil()) -> nil()
1174.79/297.04	     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
1174.79/297.04	     , mark(app(X1, X2)) -> a__app(mark(X1), mark(X2))
1174.79/297.04	     , mark(from(X)) -> a__from(mark(X))
1174.79/297.04	     , mark(s(X)) -> s(mark(X))
1174.79/297.04	     , mark(zWadr(X1, X2)) -> a__zWadr(mark(X1), mark(X2))
1174.79/297.04	     , mark(prefix(X)) -> a__prefix(mark(X))
1174.79/297.04	     , a__from(X) -> cons(mark(X), from(s(X)))
1174.79/297.04	     , a__from(X) -> from(X)
1174.79/297.04	     , a__zWadr(X1, X2) -> zWadr(X1, X2)
1174.79/297.04	     , a__zWadr(XS, nil()) -> nil()
1174.79/297.04	     , a__zWadr(nil(), YS) -> nil()
1174.79/297.04	     , a__zWadr(cons(X, XS), cons(Y, YS)) ->
1174.79/297.04	       cons(a__app(mark(Y), cons(mark(X), nil())), zWadr(XS, YS))
1174.79/297.04	     , a__prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
1174.79/297.04	     , a__prefix(X) -> prefix(X) }
1174.79/297.04	   Obligation:
1174.79/297.04	     runtime complexity
1174.79/297.04	   Answer:
1174.79/297.04	     MAYBE
1174.79/297.04	   
1174.79/297.04	   We estimate the number of application of {4,14,15} by applications
1174.79/297.04	   of Pre({4,14,15}) = {1,2,3,5,8,9,11,12,13,16,17,18}. Here rules are
1174.79/297.04	   labeled as follows:
1174.79/297.04	   
1174.79/297.04	     DPs:
1174.79/297.04	       { 1: a__app^#(X1, X2) -> c_1(X1, X2)
1174.79/297.04	       , 2: a__app^#(nil(), YS) -> c_2(mark^#(YS))
1174.79/297.04	       , 3: a__app^#(cons(X, XS), YS) -> c_3(mark^#(X), XS, YS)
1174.79/297.04	       , 4: mark^#(nil()) -> c_4()
1174.79/297.04	       , 5: mark^#(cons(X1, X2)) -> c_5(mark^#(X1), X2)
1174.79/297.04	       , 6: mark^#(app(X1, X2)) -> c_6(a__app^#(mark(X1), mark(X2)))
1174.79/297.04	       , 7: mark^#(from(X)) -> c_7(a__from^#(mark(X)))
1174.79/297.04	       , 8: mark^#(s(X)) -> c_8(mark^#(X))
1174.79/297.04	       , 9: mark^#(zWadr(X1, X2)) -> c_9(a__zWadr^#(mark(X1), mark(X2)))
1174.79/297.04	       , 10: mark^#(prefix(X)) -> c_10(a__prefix^#(mark(X)))
1174.79/297.04	       , 11: a__from^#(X) -> c_11(mark^#(X), X)
1174.79/297.04	       , 12: a__from^#(X) -> c_12(X)
1174.79/297.04	       , 13: a__zWadr^#(X1, X2) -> c_13(X1, X2)
1174.79/297.04	       , 14: a__zWadr^#(XS, nil()) -> c_14()
1174.79/297.04	       , 15: a__zWadr^#(nil(), YS) -> c_15()
1174.79/297.04	       , 16: a__zWadr^#(cons(X, XS), cons(Y, YS)) ->
1174.79/297.04	             c_16(a__app^#(mark(Y), cons(mark(X), nil())), XS, YS)
1174.79/297.04	       , 17: a__prefix^#(L) -> c_17(L, L)
1174.79/297.04	       , 18: a__prefix^#(X) -> c_18(X) }
1174.79/297.04	   
1174.79/297.04	   We are left with following problem, upon which TcT provides the
1174.79/297.04	   certificate MAYBE.
1174.79/297.04	   
1174.79/297.04	   Strict DPs:
1174.79/297.04	     { a__app^#(X1, X2) -> c_1(X1, X2)
1174.79/297.04	     , a__app^#(nil(), YS) -> c_2(mark^#(YS))
1174.79/297.04	     , a__app^#(cons(X, XS), YS) -> c_3(mark^#(X), XS, YS)
1174.79/297.04	     , mark^#(cons(X1, X2)) -> c_5(mark^#(X1), X2)
1174.79/297.04	     , mark^#(app(X1, X2)) -> c_6(a__app^#(mark(X1), mark(X2)))
1174.79/297.04	     , mark^#(from(X)) -> c_7(a__from^#(mark(X)))
1174.79/297.04	     , mark^#(s(X)) -> c_8(mark^#(X))
1174.79/297.04	     , mark^#(zWadr(X1, X2)) -> c_9(a__zWadr^#(mark(X1), mark(X2)))
1174.79/297.04	     , mark^#(prefix(X)) -> c_10(a__prefix^#(mark(X)))
1174.79/297.04	     , a__from^#(X) -> c_11(mark^#(X), X)
1174.79/297.04	     , a__from^#(X) -> c_12(X)
1174.79/297.04	     , a__zWadr^#(X1, X2) -> c_13(X1, X2)
1174.79/297.04	     , a__zWadr^#(cons(X, XS), cons(Y, YS)) ->
1174.79/297.04	       c_16(a__app^#(mark(Y), cons(mark(X), nil())), XS, YS)
1174.79/297.04	     , a__prefix^#(L) -> c_17(L, L)
1174.79/297.04	     , a__prefix^#(X) -> c_18(X) }
1174.79/297.04	   Strict Trs:
1174.79/297.04	     { a__app(X1, X2) -> app(X1, X2)
1174.79/297.04	     , a__app(nil(), YS) -> mark(YS)
1174.79/297.04	     , a__app(cons(X, XS), YS) -> cons(mark(X), app(XS, YS))
1174.79/297.04	     , mark(nil()) -> nil()
1174.79/297.04	     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
1174.79/297.04	     , mark(app(X1, X2)) -> a__app(mark(X1), mark(X2))
1174.79/297.04	     , mark(from(X)) -> a__from(mark(X))
1174.79/297.04	     , mark(s(X)) -> s(mark(X))
1174.79/297.04	     , mark(zWadr(X1, X2)) -> a__zWadr(mark(X1), mark(X2))
1174.79/297.04	     , mark(prefix(X)) -> a__prefix(mark(X))
1174.79/297.04	     , a__from(X) -> cons(mark(X), from(s(X)))
1174.79/297.04	     , a__from(X) -> from(X)
1174.79/297.04	     , a__zWadr(X1, X2) -> zWadr(X1, X2)
1174.79/297.04	     , a__zWadr(XS, nil()) -> nil()
1174.79/297.04	     , a__zWadr(nil(), YS) -> nil()
1174.79/297.04	     , a__zWadr(cons(X, XS), cons(Y, YS)) ->
1174.79/297.04	       cons(a__app(mark(Y), cons(mark(X), nil())), zWadr(XS, YS))
1174.79/297.04	     , a__prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
1174.79/297.04	     , a__prefix(X) -> prefix(X) }
1174.79/297.04	   Weak DPs:
1174.79/297.04	     { mark^#(nil()) -> c_4()
1174.79/297.04	     , a__zWadr^#(XS, nil()) -> c_14()
1174.79/297.04	     , a__zWadr^#(nil(), YS) -> c_15() }
1174.79/297.04	   Obligation:
1174.79/297.04	     runtime complexity
1174.79/297.04	   Answer:
1174.79/297.04	     MAYBE
1174.79/297.04	   
1174.79/297.04	   Empty strict component of the problem is NOT empty.
1174.79/297.04	
1174.79/297.04	
1174.79/297.04	Arrrr..
1175.47/297.65	EOF