MAYBE
115.66/48.17	MAYBE
115.66/48.17	
115.66/48.17	We are left with following problem, upon which TcT provides the
115.66/48.17	certificate MAYBE.
115.66/48.17	
115.66/48.17	Strict Trs:
115.66/48.17	  { cond1(true(), x) -> cond2(even(x), x)
115.66/48.17	  , cond2(true(), x) -> cond1(neq(x, 0()), div2(x))
115.66/48.17	  , cond2(false(), x) -> cond1(neq(x, 0()), p(x))
115.66/48.17	  , even(0()) -> true()
115.66/48.17	  , even(s(0())) -> false()
115.66/48.17	  , even(s(s(x))) -> even(x)
115.66/48.17	  , neq(0(), 0()) -> false()
115.66/48.17	  , neq(0(), s(x)) -> true()
115.66/48.17	  , neq(s(x), 0()) -> true()
115.66/48.17	  , neq(s(x), s(y())) -> neq(x, y())
115.66/48.17	  , div2(0()) -> 0()
115.66/48.17	  , div2(s(0())) -> 0()
115.66/48.17	  , div2(s(s(x))) -> s(div2(x))
115.66/48.17	  , p(0()) -> 0()
115.66/48.17	  , p(s(x)) -> x }
115.66/48.17	Obligation:
115.66/48.17	  runtime complexity
115.66/48.17	Answer:
115.66/48.17	  MAYBE
115.66/48.17	
115.66/48.17	None of the processors succeeded.
115.66/48.17	
115.66/48.17	Details of failed attempt(s):
115.66/48.17	-----------------------------
115.66/48.17	1) 'Best' failed due to the following reason:
115.66/48.17	   
115.66/48.17	   None of the processors succeeded.
115.66/48.17	   
115.66/48.17	   Details of failed attempt(s):
115.66/48.17	   -----------------------------
115.66/48.17	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
115.66/48.17	      seconds)' failed due to the following reason:
115.66/48.17	      
115.66/48.17	      None of the processors succeeded.
115.66/48.17	      
115.66/48.17	      Details of failed attempt(s):
115.66/48.17	      -----------------------------
115.66/48.17	      1) 'empty' failed due to the following reason:
115.66/48.17	         
115.66/48.17	         Empty strict component of the problem is NOT empty.
115.66/48.17	      
115.66/48.17	      2) 'With Problem ...' failed due to the following reason:
115.66/48.17	         
115.66/48.17	         None of the processors succeeded.
115.66/48.17	         
115.66/48.17	         Details of failed attempt(s):
115.66/48.17	         -----------------------------
115.66/48.17	         1) 'empty' failed due to the following reason:
115.66/48.17	            
115.66/48.17	            Empty strict component of the problem is NOT empty.
115.66/48.17	         
115.66/48.17	         2) 'Fastest' failed due to the following reason:
115.66/48.17	            
115.66/48.17	            None of the processors succeeded.
115.66/48.17	            
115.66/48.17	            Details of failed attempt(s):
115.66/48.17	            -----------------------------
115.66/48.17	            1) 'With Problem ...' failed due to the following reason:
115.66/48.17	               
115.66/48.17	               None of the processors succeeded.
115.66/48.17	               
115.66/48.17	               Details of failed attempt(s):
115.66/48.17	               -----------------------------
115.66/48.17	               1) 'empty' failed due to the following reason:
115.66/48.17	                  
115.66/48.17	                  Empty strict component of the problem is NOT empty.
115.66/48.17	               
115.66/48.17	               2) 'With Problem ...' failed due to the following reason:
115.66/48.17	                  
115.66/48.17	                  Empty strict component of the problem is NOT empty.
115.66/48.17	               
115.66/48.17	            
115.66/48.17	            2) 'With Problem ...' failed due to the following reason:
115.66/48.17	               
115.66/48.17	               None of the processors succeeded.
115.66/48.17	               
115.66/48.17	               Details of failed attempt(s):
115.66/48.17	               -----------------------------
115.66/48.17	               1) 'empty' failed due to the following reason:
115.66/48.17	                  
115.66/48.17	                  Empty strict component of the problem is NOT empty.
115.66/48.17	               
115.66/48.17	               2) 'With Problem ...' failed due to the following reason:
115.66/48.17	                  
115.66/48.17	                  None of the processors succeeded.
115.66/48.17	                  
115.66/48.17	                  Details of failed attempt(s):
115.66/48.17	                  -----------------------------
115.66/48.17	                  1) 'empty' failed due to the following reason:
115.66/48.17	                     
115.66/48.17	                     Empty strict component of the problem is NOT empty.
115.66/48.17	                  
115.66/48.17	                  2) 'With Problem ...' failed due to the following reason:
115.66/48.17	                     
115.66/48.17	                     None of the processors succeeded.
115.66/48.17	                     
115.66/48.17	                     Details of failed attempt(s):
115.66/48.17	                     -----------------------------
115.66/48.17	                     1) 'empty' failed due to the following reason:
115.66/48.17	                        
115.66/48.17	                        Empty strict component of the problem is NOT empty.
115.66/48.17	                     
115.66/48.17	                     2) 'With Problem ...' failed due to the following reason:
115.66/48.17	                        
115.66/48.17	                        Empty strict component of the problem is NOT empty.
115.66/48.17	                     
115.66/48.17	                  
115.66/48.17	               
115.66/48.17	            
115.66/48.17	         
115.66/48.17	      
115.66/48.17	   
115.66/48.17	   2) 'Best' failed due to the following reason:
115.66/48.17	      
115.66/48.17	      None of the processors succeeded.
115.66/48.17	      
115.66/48.17	      Details of failed attempt(s):
115.66/48.17	      -----------------------------
115.66/48.17	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
115.66/48.17	         following reason:
115.66/48.17	         
115.66/48.17	         The processor is inapplicable, reason:
115.66/48.17	           Processor only applicable for innermost runtime complexity analysis
115.66/48.17	      
115.66/48.17	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
115.66/48.17	         to the following reason:
115.66/48.17	         
115.66/48.17	         The processor is inapplicable, reason:
115.66/48.17	           Processor only applicable for innermost runtime complexity analysis
115.66/48.17	      
115.66/48.17	   
115.66/48.17	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
115.66/48.17	      failed due to the following reason:
115.66/48.17	      
115.66/48.17	      None of the processors succeeded.
115.66/48.17	      
115.66/48.17	      Details of failed attempt(s):
115.66/48.17	      -----------------------------
115.66/48.17	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
115.66/48.17	         failed due to the following reason:
115.66/48.17	         
115.66/48.17	         match-boundness of the problem could not be verified.
115.66/48.17	      
115.66/48.17	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
115.66/48.17	         failed due to the following reason:
115.66/48.17	         
115.66/48.17	         match-boundness of the problem could not be verified.
115.66/48.17	      
115.66/48.17	   
115.66/48.17	
115.66/48.17	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
115.66/48.17	   the following reason:
115.66/48.17	   
115.66/48.17	   We add the following weak dependency pairs:
115.66/48.17	   
115.66/48.17	   Strict DPs:
115.66/48.17	     { cond1^#(true(), x) -> c_1(cond2^#(even(x), x))
115.66/48.17	     , cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x)))
115.66/48.17	     , cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x)))
115.66/48.17	     , even^#(0()) -> c_4()
115.66/48.17	     , even^#(s(0())) -> c_5()
115.66/48.17	     , even^#(s(s(x))) -> c_6(even^#(x))
115.66/48.17	     , neq^#(0(), 0()) -> c_7()
115.66/48.17	     , neq^#(0(), s(x)) -> c_8()
115.66/48.17	     , neq^#(s(x), 0()) -> c_9()
115.66/48.17	     , neq^#(s(x), s(y())) -> c_10(neq^#(x, y()))
115.66/48.17	     , div2^#(0()) -> c_11()
115.66/48.17	     , div2^#(s(0())) -> c_12()
115.66/48.17	     , div2^#(s(s(x))) -> c_13(div2^#(x))
115.66/48.17	     , p^#(0()) -> c_14()
115.66/48.17	     , p^#(s(x)) -> c_15(x) }
115.66/48.17	   
115.66/48.17	   and mark the set of starting terms.
115.66/48.17	   
115.66/48.17	   We are left with following problem, upon which TcT provides the
115.66/48.17	   certificate MAYBE.
115.66/48.17	   
115.66/48.17	   Strict DPs:
115.66/48.17	     { cond1^#(true(), x) -> c_1(cond2^#(even(x), x))
115.66/48.17	     , cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x)))
115.66/48.17	     , cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x)))
115.66/48.17	     , even^#(0()) -> c_4()
115.66/48.17	     , even^#(s(0())) -> c_5()
115.66/48.17	     , even^#(s(s(x))) -> c_6(even^#(x))
115.66/48.17	     , neq^#(0(), 0()) -> c_7()
115.66/48.17	     , neq^#(0(), s(x)) -> c_8()
115.66/48.17	     , neq^#(s(x), 0()) -> c_9()
115.66/48.17	     , neq^#(s(x), s(y())) -> c_10(neq^#(x, y()))
115.66/48.17	     , div2^#(0()) -> c_11()
115.66/48.17	     , div2^#(s(0())) -> c_12()
115.66/48.17	     , div2^#(s(s(x))) -> c_13(div2^#(x))
115.66/48.17	     , p^#(0()) -> c_14()
115.66/48.17	     , p^#(s(x)) -> c_15(x) }
115.66/48.17	   Strict Trs:
115.66/48.17	     { cond1(true(), x) -> cond2(even(x), x)
115.66/48.17	     , cond2(true(), x) -> cond1(neq(x, 0()), div2(x))
115.66/48.17	     , cond2(false(), x) -> cond1(neq(x, 0()), p(x))
115.66/48.17	     , even(0()) -> true()
115.66/48.17	     , even(s(0())) -> false()
115.66/48.17	     , even(s(s(x))) -> even(x)
115.66/48.17	     , neq(0(), 0()) -> false()
115.66/48.17	     , neq(0(), s(x)) -> true()
115.66/48.17	     , neq(s(x), 0()) -> true()
115.66/48.17	     , neq(s(x), s(y())) -> neq(x, y())
115.66/48.17	     , div2(0()) -> 0()
115.66/48.17	     , div2(s(0())) -> 0()
115.66/48.17	     , div2(s(s(x))) -> s(div2(x))
115.66/48.17	     , p(0()) -> 0()
115.66/48.17	     , p(s(x)) -> x }
115.66/48.17	   Obligation:
115.66/48.17	     runtime complexity
115.66/48.17	   Answer:
115.66/48.17	     MAYBE
115.66/48.17	   
115.66/48.17	   We estimate the number of application of {4,5,7,8,9,10,11,12,14} by
115.66/48.17	   applications of Pre({4,5,7,8,9,10,11,12,14}) = {6,13,15}. Here
115.66/48.17	   rules are labeled as follows:
115.66/48.17	   
115.66/48.17	     DPs:
115.66/48.17	       { 1: cond1^#(true(), x) -> c_1(cond2^#(even(x), x))
115.66/48.17	       , 2: cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x)))
115.66/48.17	       , 3: cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x)))
115.66/48.17	       , 4: even^#(0()) -> c_4()
115.66/48.17	       , 5: even^#(s(0())) -> c_5()
115.66/48.17	       , 6: even^#(s(s(x))) -> c_6(even^#(x))
115.66/48.17	       , 7: neq^#(0(), 0()) -> c_7()
115.66/48.17	       , 8: neq^#(0(), s(x)) -> c_8()
115.66/48.17	       , 9: neq^#(s(x), 0()) -> c_9()
115.66/48.17	       , 10: neq^#(s(x), s(y())) -> c_10(neq^#(x, y()))
115.66/48.17	       , 11: div2^#(0()) -> c_11()
115.66/48.17	       , 12: div2^#(s(0())) -> c_12()
115.66/48.17	       , 13: div2^#(s(s(x))) -> c_13(div2^#(x))
115.66/48.17	       , 14: p^#(0()) -> c_14()
115.66/48.17	       , 15: p^#(s(x)) -> c_15(x) }
115.66/48.17	   
115.66/48.17	   We are left with following problem, upon which TcT provides the
115.66/48.17	   certificate MAYBE.
115.66/48.17	   
115.66/48.17	   Strict DPs:
115.66/48.17	     { cond1^#(true(), x) -> c_1(cond2^#(even(x), x))
115.66/48.17	     , cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x)))
115.66/48.17	     , cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x)))
115.66/48.17	     , even^#(s(s(x))) -> c_6(even^#(x))
115.66/48.17	     , div2^#(s(s(x))) -> c_13(div2^#(x))
115.66/48.17	     , p^#(s(x)) -> c_15(x) }
115.66/48.17	   Strict Trs:
115.66/48.17	     { cond1(true(), x) -> cond2(even(x), x)
115.66/48.17	     , cond2(true(), x) -> cond1(neq(x, 0()), div2(x))
115.66/48.17	     , cond2(false(), x) -> cond1(neq(x, 0()), p(x))
115.66/48.17	     , even(0()) -> true()
115.66/48.17	     , even(s(0())) -> false()
115.66/48.17	     , even(s(s(x))) -> even(x)
115.66/48.17	     , neq(0(), 0()) -> false()
115.66/48.17	     , neq(0(), s(x)) -> true()
115.66/48.17	     , neq(s(x), 0()) -> true()
115.66/48.17	     , neq(s(x), s(y())) -> neq(x, y())
115.66/48.17	     , div2(0()) -> 0()
115.66/48.17	     , div2(s(0())) -> 0()
115.66/48.17	     , div2(s(s(x))) -> s(div2(x))
115.66/48.17	     , p(0()) -> 0()
115.66/48.17	     , p(s(x)) -> x }
115.66/48.17	   Weak DPs:
115.66/48.17	     { even^#(0()) -> c_4()
115.66/48.17	     , even^#(s(0())) -> c_5()
115.66/48.17	     , neq^#(0(), 0()) -> c_7()
115.66/48.17	     , neq^#(0(), s(x)) -> c_8()
115.66/48.17	     , neq^#(s(x), 0()) -> c_9()
115.66/48.17	     , neq^#(s(x), s(y())) -> c_10(neq^#(x, y()))
115.66/48.17	     , div2^#(0()) -> c_11()
115.66/48.17	     , div2^#(s(0())) -> c_12()
115.66/48.17	     , p^#(0()) -> c_14() }
115.66/48.17	   Obligation:
115.66/48.17	     runtime complexity
115.66/48.17	   Answer:
115.66/48.17	     MAYBE
115.66/48.17	   
115.66/48.17	   Empty strict component of the problem is NOT empty.
115.66/48.17	
115.66/48.17	
115.66/48.17	Arrrr..
115.92/48.32	EOF