MAYBE
204.14/109.00	MAYBE
204.14/109.00	
204.14/109.00	We are left with following problem, upon which TcT provides the
204.14/109.00	certificate MAYBE.
204.14/109.00	
204.14/109.00	Strict Trs:
204.14/109.00	  { half(0()) -> 0()
204.14/109.00	  , half(s(0())) -> 0()
204.14/109.00	  , half(s(s(x))) -> s(half(x))
204.14/109.00	  , lastbit(0()) -> 0()
204.14/109.00	  , lastbit(s(0())) -> s(0())
204.14/109.00	  , lastbit(s(s(x))) -> lastbit(x)
204.14/109.00	  , zero(0()) -> true()
204.14/109.00	  , zero(s(x)) -> false()
204.14/109.00	  , conv(x) -> conviter(x, cons(0(), nil()))
204.14/109.00	  , conviter(x, l) -> if(zero(x), x, l)
204.14/109.00	  , if(true(), x, l) -> l
204.14/109.00	  , if(false(), x, l) -> conviter(half(x), cons(lastbit(x), l)) }
204.14/109.00	Obligation:
204.14/109.00	  runtime complexity
204.14/109.00	Answer:
204.14/109.00	  MAYBE
204.14/109.00	
204.14/109.00	None of the processors succeeded.
204.14/109.00	
204.14/109.00	Details of failed attempt(s):
204.14/109.00	-----------------------------
204.14/109.00	1) 'Best' failed due to the following reason:
204.14/109.00	   
204.14/109.00	   None of the processors succeeded.
204.14/109.00	   
204.14/109.00	   Details of failed attempt(s):
204.14/109.00	   -----------------------------
204.14/109.00	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
204.14/109.00	      seconds)' failed due to the following reason:
204.14/109.00	      
204.14/109.00	      None of the processors succeeded.
204.14/109.00	      
204.14/109.00	      Details of failed attempt(s):
204.14/109.00	      -----------------------------
204.14/109.00	      1) 'empty' failed due to the following reason:
204.14/109.00	         
204.14/109.00	         Empty strict component of the problem is NOT empty.
204.14/109.00	      
204.14/109.00	      2) 'With Problem ...' failed due to the following reason:
204.14/109.00	         
204.14/109.00	         None of the processors succeeded.
204.14/109.00	         
204.14/109.00	         Details of failed attempt(s):
204.14/109.00	         -----------------------------
204.14/109.00	         1) 'empty' failed due to the following reason:
204.14/109.00	            
204.14/109.00	            Empty strict component of the problem is NOT empty.
204.14/109.00	         
204.14/109.00	         2) 'Fastest' failed due to the following reason:
204.14/109.00	            
204.14/109.00	            None of the processors succeeded.
204.14/109.00	            
204.14/109.00	            Details of failed attempt(s):
204.14/109.00	            -----------------------------
204.14/109.00	            1) 'With Problem ...' failed due to the following reason:
204.14/109.00	               
204.14/109.00	               None of the processors succeeded.
204.14/109.00	               
204.14/109.00	               Details of failed attempt(s):
204.14/109.00	               -----------------------------
204.14/109.00	               1) 'empty' failed due to the following reason:
204.14/109.00	                  
204.14/109.00	                  Empty strict component of the problem is NOT empty.
204.14/109.00	               
204.14/109.00	               2) 'With Problem ...' failed due to the following reason:
204.14/109.00	                  
204.14/109.00	                  None of the processors succeeded.
204.14/109.00	                  
204.14/109.00	                  Details of failed attempt(s):
204.14/109.00	                  -----------------------------
204.14/109.00	                  1) 'empty' failed due to the following reason:
204.14/109.00	                     
204.14/109.00	                     Empty strict component of the problem is NOT empty.
204.14/109.00	                  
204.14/109.00	                  2) 'With Problem ...' failed due to the following reason:
204.14/109.00	                     
204.14/109.00	                     None of the processors succeeded.
204.14/109.00	                     
204.14/109.00	                     Details of failed attempt(s):
204.14/109.00	                     -----------------------------
204.14/109.00	                     1) 'empty' failed due to the following reason:
204.14/109.00	                        
204.14/109.00	                        Empty strict component of the problem is NOT empty.
204.14/109.00	                     
204.14/109.00	                     2) 'With Problem ...' failed due to the following reason:
204.14/109.00	                        
204.14/109.00	                        Empty strict component of the problem is NOT empty.
204.14/109.00	                     
204.14/109.00	                  
204.14/109.00	               
204.14/109.00	            
204.14/109.00	            2) 'With Problem ...' failed due to the following reason:
204.14/109.00	               
204.14/109.00	               None of the processors succeeded.
204.14/109.00	               
204.14/109.00	               Details of failed attempt(s):
204.14/109.00	               -----------------------------
204.14/109.00	               1) 'empty' failed due to the following reason:
204.14/109.00	                  
204.14/109.00	                  Empty strict component of the problem is NOT empty.
204.14/109.00	               
204.14/109.00	               2) 'With Problem ...' failed due to the following reason:
204.14/109.00	                  
204.14/109.00	                  Empty strict component of the problem is NOT empty.
204.14/109.00	               
204.14/109.00	            
204.14/109.00	         
204.14/109.00	      
204.14/109.00	   
204.14/109.00	   2) 'Best' failed due to the following reason:
204.14/109.00	      
204.14/109.00	      None of the processors succeeded.
204.14/109.00	      
204.14/109.00	      Details of failed attempt(s):
204.14/109.00	      -----------------------------
204.14/109.00	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
204.14/109.00	         following reason:
204.14/109.00	         
204.14/109.00	         The processor is inapplicable, reason:
204.14/109.00	           Processor only applicable for innermost runtime complexity analysis
204.14/109.00	      
204.14/109.00	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
204.14/109.00	         to the following reason:
204.14/109.00	         
204.14/109.00	         The processor is inapplicable, reason:
204.14/109.00	           Processor only applicable for innermost runtime complexity analysis
204.14/109.00	      
204.14/109.00	   
204.14/109.00	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
204.14/109.00	      failed due to the following reason:
204.14/109.00	      
204.14/109.00	      None of the processors succeeded.
204.14/109.00	      
204.14/109.00	      Details of failed attempt(s):
204.14/109.00	      -----------------------------
204.14/109.00	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
204.14/109.00	         failed due to the following reason:
204.14/109.00	         
204.14/109.00	         match-boundness of the problem could not be verified.
204.14/109.00	      
204.14/109.00	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
204.14/109.00	         failed due to the following reason:
204.14/109.00	         
204.14/109.00	         match-boundness of the problem could not be verified.
204.14/109.00	      
204.14/109.00	   
204.14/109.00	
204.14/109.00	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
204.14/109.00	   the following reason:
204.14/109.00	   
204.14/109.00	   We add the following weak dependency pairs:
204.14/109.00	   
204.14/109.00	   Strict DPs:
204.14/109.00	     { half^#(0()) -> c_1()
204.14/109.00	     , half^#(s(0())) -> c_2()
204.14/109.00	     , half^#(s(s(x))) -> c_3(half^#(x))
204.14/109.00	     , lastbit^#(0()) -> c_4()
204.14/109.00	     , lastbit^#(s(0())) -> c_5()
204.14/109.00	     , lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
204.14/109.00	     , zero^#(0()) -> c_7()
204.14/109.00	     , zero^#(s(x)) -> c_8()
204.14/109.00	     , conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
204.14/109.00	     , conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
204.14/109.00	     , if^#(true(), x, l) -> c_11(l)
204.14/109.00	     , if^#(false(), x, l) ->
204.14/109.00	       c_12(conviter^#(half(x), cons(lastbit(x), l))) }
204.14/109.00	   
204.14/109.00	   and mark the set of starting terms.
204.14/109.00	   
204.14/109.00	   We are left with following problem, upon which TcT provides the
204.14/109.00	   certificate MAYBE.
204.14/109.00	   
204.14/109.00	   Strict DPs:
204.14/109.00	     { half^#(0()) -> c_1()
204.14/109.00	     , half^#(s(0())) -> c_2()
204.14/109.00	     , half^#(s(s(x))) -> c_3(half^#(x))
204.14/109.00	     , lastbit^#(0()) -> c_4()
204.14/109.00	     , lastbit^#(s(0())) -> c_5()
204.14/109.00	     , lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
204.14/109.00	     , zero^#(0()) -> c_7()
204.14/109.00	     , zero^#(s(x)) -> c_8()
204.14/109.00	     , conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
204.14/109.00	     , conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
204.14/109.00	     , if^#(true(), x, l) -> c_11(l)
204.14/109.00	     , if^#(false(), x, l) ->
204.14/109.00	       c_12(conviter^#(half(x), cons(lastbit(x), l))) }
204.14/109.00	   Strict Trs:
204.14/109.00	     { half(0()) -> 0()
204.14/109.00	     , half(s(0())) -> 0()
204.14/109.00	     , half(s(s(x))) -> s(half(x))
204.14/109.00	     , lastbit(0()) -> 0()
204.14/109.00	     , lastbit(s(0())) -> s(0())
204.14/109.00	     , lastbit(s(s(x))) -> lastbit(x)
204.14/109.00	     , zero(0()) -> true()
204.14/109.00	     , zero(s(x)) -> false()
204.14/109.00	     , conv(x) -> conviter(x, cons(0(), nil()))
204.14/109.00	     , conviter(x, l) -> if(zero(x), x, l)
204.14/109.00	     , if(true(), x, l) -> l
204.14/109.00	     , if(false(), x, l) -> conviter(half(x), cons(lastbit(x), l)) }
204.14/109.00	   Obligation:
204.14/109.00	     runtime complexity
204.14/109.00	   Answer:
204.14/109.00	     MAYBE
204.14/109.00	   
204.14/109.00	   We estimate the number of application of {1,2,4,5,7,8} by
204.14/109.00	   applications of Pre({1,2,4,5,7,8}) = {3,6,11}. Here rules are
204.14/109.00	   labeled as follows:
204.14/109.00	   
204.14/109.00	     DPs:
204.14/109.00	       { 1: half^#(0()) -> c_1()
204.14/109.00	       , 2: half^#(s(0())) -> c_2()
204.14/109.00	       , 3: half^#(s(s(x))) -> c_3(half^#(x))
204.14/109.00	       , 4: lastbit^#(0()) -> c_4()
204.14/109.00	       , 5: lastbit^#(s(0())) -> c_5()
204.14/109.00	       , 6: lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
204.14/109.00	       , 7: zero^#(0()) -> c_7()
204.14/109.00	       , 8: zero^#(s(x)) -> c_8()
204.14/109.00	       , 9: conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
204.14/109.00	       , 10: conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
204.14/109.00	       , 11: if^#(true(), x, l) -> c_11(l)
204.14/109.00	       , 12: if^#(false(), x, l) ->
204.14/109.00	             c_12(conviter^#(half(x), cons(lastbit(x), l))) }
204.14/109.00	   
204.14/109.00	   We are left with following problem, upon which TcT provides the
204.14/109.00	   certificate MAYBE.
204.14/109.00	   
204.14/109.00	   Strict DPs:
204.14/109.00	     { half^#(s(s(x))) -> c_3(half^#(x))
204.14/109.00	     , lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
204.14/109.00	     , conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
204.14/109.00	     , conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
204.14/109.00	     , if^#(true(), x, l) -> c_11(l)
204.14/109.00	     , if^#(false(), x, l) ->
204.14/109.00	       c_12(conviter^#(half(x), cons(lastbit(x), l))) }
204.14/109.00	   Strict Trs:
204.14/109.00	     { half(0()) -> 0()
204.14/109.00	     , half(s(0())) -> 0()
204.14/109.00	     , half(s(s(x))) -> s(half(x))
204.14/109.00	     , lastbit(0()) -> 0()
204.14/109.00	     , lastbit(s(0())) -> s(0())
204.14/109.00	     , lastbit(s(s(x))) -> lastbit(x)
204.14/109.00	     , zero(0()) -> true()
204.14/109.00	     , zero(s(x)) -> false()
204.14/109.00	     , conv(x) -> conviter(x, cons(0(), nil()))
204.14/109.00	     , conviter(x, l) -> if(zero(x), x, l)
204.14/109.00	     , if(true(), x, l) -> l
204.14/109.00	     , if(false(), x, l) -> conviter(half(x), cons(lastbit(x), l)) }
204.14/109.00	   Weak DPs:
204.14/109.00	     { half^#(0()) -> c_1()
204.14/109.00	     , half^#(s(0())) -> c_2()
204.14/109.00	     , lastbit^#(0()) -> c_4()
204.14/109.00	     , lastbit^#(s(0())) -> c_5()
204.14/109.00	     , zero^#(0()) -> c_7()
204.14/109.00	     , zero^#(s(x)) -> c_8() }
204.14/109.00	   Obligation:
204.14/109.00	     runtime complexity
204.14/109.00	   Answer:
204.14/109.00	     MAYBE
204.14/109.00	   
204.14/109.00	   Empty strict component of the problem is NOT empty.
204.14/109.00	
204.14/109.00	
204.14/109.00	Arrrr..
204.24/109.15	EOF