MAYBE
352.98/141.82	MAYBE
352.98/141.82	
352.98/141.82	We are left with following problem, upon which TcT provides the
352.98/141.82	certificate MAYBE.
352.98/141.82	
352.98/141.82	Strict Trs:
352.98/141.82	  { half(0()) -> 0()
352.98/141.82	  , half(s(0())) -> 0()
352.98/141.82	  , half(s(s(x))) -> s(half(x))
352.98/141.82	  , le(0(), y) -> true()
352.98/141.82	  , le(s(x), 0()) -> false()
352.98/141.82	  , le(s(x), s(y)) -> le(x, y)
352.98/141.82	  , inc(0()) -> 0()
352.98/141.82	  , inc(s(x)) -> s(inc(x))
352.98/141.82	  , log(x) -> log2(x, 0())
352.98/141.82	  , log2(x, y) -> if(le(x, s(0())), x, inc(y))
352.98/141.82	  , if(true(), x, s(y)) -> y
352.98/141.82	  , if(false(), x, y) -> log2(half(x), y) }
352.98/141.82	Obligation:
352.98/141.82	  runtime complexity
352.98/141.82	Answer:
352.98/141.82	  MAYBE
352.98/141.82	
352.98/141.82	None of the processors succeeded.
352.98/141.82	
352.98/141.82	Details of failed attempt(s):
352.98/141.82	-----------------------------
352.98/141.82	1) 'Best' failed due to the following reason:
352.98/141.82	   
352.98/141.82	   None of the processors succeeded.
352.98/141.82	   
352.98/141.82	   Details of failed attempt(s):
352.98/141.82	   -----------------------------
352.98/141.82	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
352.98/141.82	      seconds)' failed due to the following reason:
352.98/141.82	      
352.98/141.82	      None of the processors succeeded.
352.98/141.82	      
352.98/141.82	      Details of failed attempt(s):
352.98/141.82	      -----------------------------
352.98/141.82	      1) 'empty' failed due to the following reason:
352.98/141.82	         
352.98/141.82	         Empty strict component of the problem is NOT empty.
352.98/141.82	      
352.98/141.82	      2) 'With Problem ...' failed due to the following reason:
352.98/141.82	         
352.98/141.82	         None of the processors succeeded.
352.98/141.82	         
352.98/141.82	         Details of failed attempt(s):
352.98/141.82	         -----------------------------
352.98/141.82	         1) 'empty' failed due to the following reason:
352.98/141.82	            
352.98/141.82	            Empty strict component of the problem is NOT empty.
352.98/141.82	         
352.98/141.82	         2) 'Fastest' failed due to the following reason:
352.98/141.82	            
352.98/141.82	            None of the processors succeeded.
352.98/141.82	            
352.98/141.82	            Details of failed attempt(s):
352.98/141.82	            -----------------------------
352.98/141.82	            1) 'With Problem ...' failed due to the following reason:
352.98/141.82	               
352.98/141.82	               None of the processors succeeded.
352.98/141.82	               
352.98/141.82	               Details of failed attempt(s):
352.98/141.82	               -----------------------------
352.98/141.82	               1) 'empty' failed due to the following reason:
352.98/141.82	                  
352.98/141.82	                  Empty strict component of the problem is NOT empty.
352.98/141.82	               
352.98/141.82	               2) 'With Problem ...' failed due to the following reason:
352.98/141.82	                  
352.98/141.82	                  Empty strict component of the problem is NOT empty.
352.98/141.82	               
352.98/141.82	            
352.98/141.82	            2) 'With Problem ...' failed due to the following reason:
352.98/141.82	               
352.98/141.82	               None of the processors succeeded.
352.98/141.82	               
352.98/141.82	               Details of failed attempt(s):
352.98/141.82	               -----------------------------
352.98/141.82	               1) 'empty' failed due to the following reason:
352.98/141.82	                  
352.98/141.82	                  Empty strict component of the problem is NOT empty.
352.98/141.82	               
352.98/141.82	               2) 'With Problem ...' failed due to the following reason:
352.98/141.82	                  
352.98/141.82	                  None of the processors succeeded.
352.98/141.82	                  
352.98/141.82	                  Details of failed attempt(s):
352.98/141.82	                  -----------------------------
352.98/141.82	                  1) 'empty' failed due to the following reason:
352.98/141.82	                     
352.98/141.82	                     Empty strict component of the problem is NOT empty.
352.98/141.82	                  
352.98/141.82	                  2) 'With Problem ...' failed due to the following reason:
352.98/141.82	                     
352.98/141.82	                     None of the processors succeeded.
352.98/141.82	                     
352.98/141.82	                     Details of failed attempt(s):
352.98/141.82	                     -----------------------------
352.98/141.82	                     1) 'empty' failed due to the following reason:
352.98/141.82	                        
352.98/141.82	                        Empty strict component of the problem is NOT empty.
352.98/141.82	                     
352.98/141.82	                     2) 'With Problem ...' failed due to the following reason:
352.98/141.82	                        
352.98/141.82	                        Empty strict component of the problem is NOT empty.
352.98/141.82	                     
352.98/141.82	                  
352.98/141.82	               
352.98/141.82	            
352.98/141.82	         
352.98/141.82	      
352.98/141.82	   
352.98/141.82	   2) 'Best' failed due to the following reason:
352.98/141.82	      
352.98/141.82	      None of the processors succeeded.
352.98/141.82	      
352.98/141.82	      Details of failed attempt(s):
352.98/141.82	      -----------------------------
352.98/141.82	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
352.98/141.82	         following reason:
352.98/141.82	         
352.98/141.82	         The processor is inapplicable, reason:
352.98/141.82	           Processor only applicable for innermost runtime complexity analysis
352.98/141.82	      
352.98/141.82	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
352.98/141.82	         to the following reason:
352.98/141.82	         
352.98/141.82	         The processor is inapplicable, reason:
352.98/141.82	           Processor only applicable for innermost runtime complexity analysis
352.98/141.82	      
352.98/141.82	   
352.98/141.82	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
352.98/141.82	      failed due to the following reason:
352.98/141.82	      
352.98/141.82	      None of the processors succeeded.
352.98/141.82	      
352.98/141.82	      Details of failed attempt(s):
352.98/141.82	      -----------------------------
352.98/141.82	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
352.98/141.82	         failed due to the following reason:
352.98/141.82	         
352.98/141.82	         match-boundness of the problem could not be verified.
352.98/141.82	      
352.98/141.82	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
352.98/141.82	         failed due to the following reason:
352.98/141.82	         
352.98/141.82	         match-boundness of the problem could not be verified.
352.98/141.82	      
352.98/141.82	   
352.98/141.82	
352.98/141.82	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
352.98/141.82	   the following reason:
352.98/141.82	   
352.98/141.82	   We add the following weak dependency pairs:
352.98/141.82	   
352.98/141.82	   Strict DPs:
352.98/141.82	     { half^#(0()) -> c_1()
352.98/141.82	     , half^#(s(0())) -> c_2()
352.98/141.82	     , half^#(s(s(x))) -> c_3(half^#(x))
352.98/141.82	     , le^#(0(), y) -> c_4()
352.98/141.82	     , le^#(s(x), 0()) -> c_5()
352.98/141.82	     , le^#(s(x), s(y)) -> c_6(le^#(x, y))
352.98/141.82	     , inc^#(0()) -> c_7()
352.98/141.82	     , inc^#(s(x)) -> c_8(inc^#(x))
352.98/141.82	     , log^#(x) -> c_9(log2^#(x, 0()))
352.98/141.82	     , log2^#(x, y) -> c_10(if^#(le(x, s(0())), x, inc(y)))
352.98/141.82	     , if^#(true(), x, s(y)) -> c_11(y)
352.98/141.82	     , if^#(false(), x, y) -> c_12(log2^#(half(x), y)) }
352.98/141.82	   
352.98/141.82	   and mark the set of starting terms.
352.98/141.82	   
352.98/141.82	   We are left with following problem, upon which TcT provides the
352.98/141.82	   certificate MAYBE.
352.98/141.82	   
352.98/141.82	   Strict DPs:
352.98/141.82	     { half^#(0()) -> c_1()
352.98/141.82	     , half^#(s(0())) -> c_2()
352.98/141.82	     , half^#(s(s(x))) -> c_3(half^#(x))
352.98/141.82	     , le^#(0(), y) -> c_4()
352.98/141.82	     , le^#(s(x), 0()) -> c_5()
352.98/141.82	     , le^#(s(x), s(y)) -> c_6(le^#(x, y))
352.98/141.82	     , inc^#(0()) -> c_7()
352.98/141.82	     , inc^#(s(x)) -> c_8(inc^#(x))
352.98/141.82	     , log^#(x) -> c_9(log2^#(x, 0()))
352.98/141.82	     , log2^#(x, y) -> c_10(if^#(le(x, s(0())), x, inc(y)))
352.98/141.82	     , if^#(true(), x, s(y)) -> c_11(y)
352.98/141.82	     , if^#(false(), x, y) -> c_12(log2^#(half(x), y)) }
352.98/141.82	   Strict Trs:
352.98/141.82	     { half(0()) -> 0()
352.98/141.82	     , half(s(0())) -> 0()
352.98/141.82	     , half(s(s(x))) -> s(half(x))
352.98/141.82	     , le(0(), y) -> true()
352.98/141.82	     , le(s(x), 0()) -> false()
352.98/141.82	     , le(s(x), s(y)) -> le(x, y)
352.98/141.82	     , inc(0()) -> 0()
352.98/141.82	     , inc(s(x)) -> s(inc(x))
352.98/141.82	     , log(x) -> log2(x, 0())
352.98/141.82	     , log2(x, y) -> if(le(x, s(0())), x, inc(y))
352.98/141.82	     , if(true(), x, s(y)) -> y
352.98/141.82	     , if(false(), x, y) -> log2(half(x), y) }
352.98/141.82	   Obligation:
352.98/141.82	     runtime complexity
352.98/141.82	   Answer:
352.98/141.82	     MAYBE
352.98/141.82	   
352.98/141.82	   We estimate the number of application of {1,2,4,5,7} by
352.98/141.82	   applications of Pre({1,2,4,5,7}) = {3,6,8,11}. Here rules are
352.98/141.82	   labeled as follows:
352.98/141.82	   
352.98/141.82	     DPs:
352.98/141.82	       { 1: half^#(0()) -> c_1()
352.98/141.82	       , 2: half^#(s(0())) -> c_2()
352.98/141.82	       , 3: half^#(s(s(x))) -> c_3(half^#(x))
352.98/141.82	       , 4: le^#(0(), y) -> c_4()
352.98/141.82	       , 5: le^#(s(x), 0()) -> c_5()
352.98/141.82	       , 6: le^#(s(x), s(y)) -> c_6(le^#(x, y))
352.98/141.82	       , 7: inc^#(0()) -> c_7()
352.98/141.82	       , 8: inc^#(s(x)) -> c_8(inc^#(x))
352.98/141.82	       , 9: log^#(x) -> c_9(log2^#(x, 0()))
352.98/141.82	       , 10: log2^#(x, y) -> c_10(if^#(le(x, s(0())), x, inc(y)))
352.98/141.82	       , 11: if^#(true(), x, s(y)) -> c_11(y)
352.98/141.82	       , 12: if^#(false(), x, y) -> c_12(log2^#(half(x), y)) }
352.98/141.82	   
352.98/141.82	   We are left with following problem, upon which TcT provides the
352.98/141.82	   certificate MAYBE.
352.98/141.82	   
352.98/141.82	   Strict DPs:
352.98/141.82	     { half^#(s(s(x))) -> c_3(half^#(x))
352.98/141.82	     , le^#(s(x), s(y)) -> c_6(le^#(x, y))
352.98/141.82	     , inc^#(s(x)) -> c_8(inc^#(x))
352.98/141.82	     , log^#(x) -> c_9(log2^#(x, 0()))
352.98/141.82	     , log2^#(x, y) -> c_10(if^#(le(x, s(0())), x, inc(y)))
352.98/141.82	     , if^#(true(), x, s(y)) -> c_11(y)
352.98/141.82	     , if^#(false(), x, y) -> c_12(log2^#(half(x), y)) }
352.98/141.82	   Strict Trs:
352.98/141.82	     { half(0()) -> 0()
352.98/141.82	     , half(s(0())) -> 0()
352.98/141.82	     , half(s(s(x))) -> s(half(x))
352.98/141.82	     , le(0(), y) -> true()
352.98/141.82	     , le(s(x), 0()) -> false()
352.98/141.82	     , le(s(x), s(y)) -> le(x, y)
352.98/141.82	     , inc(0()) -> 0()
352.98/141.82	     , inc(s(x)) -> s(inc(x))
352.98/141.82	     , log(x) -> log2(x, 0())
352.98/141.82	     , log2(x, y) -> if(le(x, s(0())), x, inc(y))
352.98/141.82	     , if(true(), x, s(y)) -> y
352.98/141.82	     , if(false(), x, y) -> log2(half(x), y) }
352.98/141.82	   Weak DPs:
352.98/141.82	     { half^#(0()) -> c_1()
352.98/141.82	     , half^#(s(0())) -> c_2()
352.98/141.82	     , le^#(0(), y) -> c_4()
352.98/141.82	     , le^#(s(x), 0()) -> c_5()
352.98/141.82	     , inc^#(0()) -> c_7() }
352.98/141.82	   Obligation:
352.98/141.82	     runtime complexity
352.98/141.82	   Answer:
352.98/141.82	     MAYBE
352.98/141.82	   
352.98/141.82	   Empty strict component of the problem is NOT empty.
352.98/141.82	
352.98/141.82	
352.98/141.82	Arrrr..
353.10/142.00	EOF