MAYBE
825.02/297.03	MAYBE
825.02/297.03	
825.02/297.03	We are left with following problem, upon which TcT provides the
825.02/297.03	certificate MAYBE.
825.02/297.03	
825.02/297.03	Strict Trs:
825.02/297.03	  { qsort(nil()) -> nil()
825.02/297.03	  , qsort(cons(x, xs)) ->
825.02/297.03	    append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	           cons(last(cons(x, xs)),
825.02/297.03	                qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
825.02/297.03	  , append(nil(), ys()) -> ys()
825.02/297.03	  , append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
825.02/297.03	  , filterlow(n, nil()) -> nil()
825.02/297.03	  , filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
825.02/297.03	  , last(nil()) -> 0()
825.02/297.03	  , last(cons(x, nil())) -> x
825.02/297.03	  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
825.02/297.03	  , filterhigh(n, nil()) -> nil()
825.02/297.03	  , filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
825.02/297.03	  , if1(true(), n, x, xs) -> filterlow(n, xs)
825.02/297.03	  , if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
825.02/297.03	  , ge(x, 0()) -> true()
825.02/297.03	  , ge(0(), s(x)) -> false()
825.02/297.03	  , ge(s(x), s(y)) -> ge(x, y)
825.02/297.03	  , if2(true(), n, x, xs) -> filterhigh(n, xs)
825.02/297.03	  , if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs)) }
825.02/297.03	Obligation:
825.02/297.03	  runtime complexity
825.02/297.03	Answer:
825.02/297.03	  MAYBE
825.02/297.03	
825.02/297.03	None of the processors succeeded.
825.02/297.03	
825.02/297.03	Details of failed attempt(s):
825.02/297.03	-----------------------------
825.02/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
825.02/297.03	   following reason:
825.02/297.03	   
825.02/297.03	   Computation stopped due to timeout after 297.0 seconds.
825.02/297.03	
825.02/297.03	2) 'Best' failed due to the following reason:
825.02/297.03	   
825.02/297.03	   None of the processors succeeded.
825.02/297.03	   
825.02/297.03	   Details of failed attempt(s):
825.02/297.03	   -----------------------------
825.02/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
825.02/297.03	      seconds)' failed due to the following reason:
825.02/297.03	      
825.02/297.03	      Computation stopped due to timeout after 148.0 seconds.
825.02/297.03	   
825.02/297.03	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
825.02/297.03	      failed due to the following reason:
825.02/297.03	      
825.02/297.03	      None of the processors succeeded.
825.02/297.03	      
825.02/297.03	      Details of failed attempt(s):
825.02/297.03	      -----------------------------
825.02/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
825.02/297.03	         failed due to the following reason:
825.02/297.03	         
825.02/297.03	         match-boundness of the problem could not be verified.
825.02/297.03	      
825.02/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
825.02/297.03	         failed due to the following reason:
825.02/297.03	         
825.02/297.03	         match-boundness of the problem could not be verified.
825.02/297.03	      
825.02/297.03	   
825.02/297.03	   3) 'Best' failed due to the following reason:
825.02/297.03	      
825.02/297.03	      None of the processors succeeded.
825.02/297.03	      
825.02/297.03	      Details of failed attempt(s):
825.02/297.03	      -----------------------------
825.02/297.03	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
825.02/297.03	         following reason:
825.02/297.03	         
825.02/297.03	         The processor is inapplicable, reason:
825.02/297.03	           Processor only applicable for innermost runtime complexity analysis
825.02/297.03	      
825.02/297.03	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
825.02/297.03	         to the following reason:
825.02/297.03	         
825.02/297.03	         The processor is inapplicable, reason:
825.02/297.03	           Processor only applicable for innermost runtime complexity analysis
825.02/297.03	      
825.02/297.03	   
825.02/297.03	
825.02/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
825.02/297.03	   the following reason:
825.02/297.03	   
825.02/297.03	   We add the following weak dependency pairs:
825.02/297.03	   
825.02/297.03	   Strict DPs:
825.02/297.03	     { qsort^#(nil()) -> c_1()
825.02/297.03	     , qsort^#(cons(x, xs)) ->
825.02/297.03	       c_2(append^#(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	                    cons(last(cons(x, xs)),
825.02/297.03	                         qsort(filterhigh(last(cons(x, xs)), cons(x, xs))))))
825.02/297.03	     , append^#(nil(), ys()) -> c_3()
825.02/297.03	     , append^#(cons(x, xs), ys()) -> c_4(x, append^#(xs, ys()))
825.02/297.03	     , filterlow^#(n, nil()) -> c_5()
825.02/297.03	     , filterlow^#(n, cons(x, xs)) -> c_6(if1^#(ge(n, x), n, x, xs))
825.02/297.03	     , if1^#(true(), n, x, xs) -> c_12(filterlow^#(n, xs))
825.02/297.03	     , if1^#(false(), n, x, xs) -> c_13(x, filterlow^#(n, xs))
825.02/297.03	     , last^#(nil()) -> c_7()
825.02/297.03	     , last^#(cons(x, nil())) -> c_8(x)
825.02/297.03	     , last^#(cons(x, cons(y, xs))) -> c_9(last^#(cons(y, xs)))
825.02/297.03	     , filterhigh^#(n, nil()) -> c_10()
825.02/297.03	     , filterhigh^#(n, cons(x, xs)) -> c_11(if2^#(ge(x, n), n, x, xs))
825.02/297.03	     , if2^#(true(), n, x, xs) -> c_17(filterhigh^#(n, xs))
825.02/297.03	     , if2^#(false(), n, x, xs) -> c_18(x, filterhigh^#(n, xs))
825.02/297.03	     , ge^#(x, 0()) -> c_14()
825.02/297.03	     , ge^#(0(), s(x)) -> c_15()
825.02/297.03	     , ge^#(s(x), s(y)) -> c_16(ge^#(x, y)) }
825.02/297.03	   
825.02/297.03	   and mark the set of starting terms.
825.02/297.03	   
825.02/297.03	   We are left with following problem, upon which TcT provides the
825.02/297.03	   certificate MAYBE.
825.02/297.03	   
825.02/297.03	   Strict DPs:
825.02/297.03	     { qsort^#(nil()) -> c_1()
825.02/297.03	     , qsort^#(cons(x, xs)) ->
825.02/297.03	       c_2(append^#(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	                    cons(last(cons(x, xs)),
825.02/297.03	                         qsort(filterhigh(last(cons(x, xs)), cons(x, xs))))))
825.02/297.03	     , append^#(nil(), ys()) -> c_3()
825.02/297.03	     , append^#(cons(x, xs), ys()) -> c_4(x, append^#(xs, ys()))
825.02/297.03	     , filterlow^#(n, nil()) -> c_5()
825.02/297.03	     , filterlow^#(n, cons(x, xs)) -> c_6(if1^#(ge(n, x), n, x, xs))
825.02/297.03	     , if1^#(true(), n, x, xs) -> c_12(filterlow^#(n, xs))
825.02/297.03	     , if1^#(false(), n, x, xs) -> c_13(x, filterlow^#(n, xs))
825.02/297.03	     , last^#(nil()) -> c_7()
825.02/297.03	     , last^#(cons(x, nil())) -> c_8(x)
825.02/297.03	     , last^#(cons(x, cons(y, xs))) -> c_9(last^#(cons(y, xs)))
825.02/297.03	     , filterhigh^#(n, nil()) -> c_10()
825.02/297.03	     , filterhigh^#(n, cons(x, xs)) -> c_11(if2^#(ge(x, n), n, x, xs))
825.02/297.03	     , if2^#(true(), n, x, xs) -> c_17(filterhigh^#(n, xs))
825.02/297.03	     , if2^#(false(), n, x, xs) -> c_18(x, filterhigh^#(n, xs))
825.02/297.03	     , ge^#(x, 0()) -> c_14()
825.02/297.03	     , ge^#(0(), s(x)) -> c_15()
825.02/297.03	     , ge^#(s(x), s(y)) -> c_16(ge^#(x, y)) }
825.02/297.03	   Strict Trs:
825.02/297.03	     { qsort(nil()) -> nil()
825.02/297.03	     , qsort(cons(x, xs)) ->
825.02/297.03	       append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	              cons(last(cons(x, xs)),
825.02/297.03	                   qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
825.02/297.03	     , append(nil(), ys()) -> ys()
825.02/297.03	     , append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
825.02/297.03	     , filterlow(n, nil()) -> nil()
825.02/297.03	     , filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
825.02/297.03	     , last(nil()) -> 0()
825.02/297.03	     , last(cons(x, nil())) -> x
825.02/297.03	     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
825.02/297.03	     , filterhigh(n, nil()) -> nil()
825.02/297.03	     , filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
825.02/297.03	     , if1(true(), n, x, xs) -> filterlow(n, xs)
825.02/297.03	     , if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
825.02/297.03	     , ge(x, 0()) -> true()
825.02/297.03	     , ge(0(), s(x)) -> false()
825.02/297.03	     , ge(s(x), s(y)) -> ge(x, y)
825.02/297.03	     , if2(true(), n, x, xs) -> filterhigh(n, xs)
825.02/297.03	     , if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs)) }
825.02/297.03	   Obligation:
825.02/297.03	     runtime complexity
825.02/297.03	   Answer:
825.02/297.03	     MAYBE
825.02/297.03	   
825.02/297.03	   We estimate the number of application of {1,2,3,5,9,12,16,17} by
825.02/297.03	   applications of Pre({1,2,3,5,9,12,16,17}) = {4,7,8,10,14,15,18}.
825.02/297.03	   Here rules are labeled as follows:
825.02/297.03	   
825.02/297.03	     DPs:
825.02/297.03	       { 1: qsort^#(nil()) -> c_1()
825.02/297.03	       , 2: qsort^#(cons(x, xs)) ->
825.02/297.03	            c_2(append^#(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	                         cons(last(cons(x, xs)),
825.02/297.03	                              qsort(filterhigh(last(cons(x, xs)), cons(x, xs))))))
825.02/297.03	       , 3: append^#(nil(), ys()) -> c_3()
825.02/297.03	       , 4: append^#(cons(x, xs), ys()) -> c_4(x, append^#(xs, ys()))
825.02/297.03	       , 5: filterlow^#(n, nil()) -> c_5()
825.02/297.03	       , 6: filterlow^#(n, cons(x, xs)) -> c_6(if1^#(ge(n, x), n, x, xs))
825.02/297.03	       , 7: if1^#(true(), n, x, xs) -> c_12(filterlow^#(n, xs))
825.02/297.03	       , 8: if1^#(false(), n, x, xs) -> c_13(x, filterlow^#(n, xs))
825.02/297.03	       , 9: last^#(nil()) -> c_7()
825.02/297.03	       , 10: last^#(cons(x, nil())) -> c_8(x)
825.02/297.03	       , 11: last^#(cons(x, cons(y, xs))) -> c_9(last^#(cons(y, xs)))
825.02/297.03	       , 12: filterhigh^#(n, nil()) -> c_10()
825.02/297.03	       , 13: filterhigh^#(n, cons(x, xs)) ->
825.02/297.03	             c_11(if2^#(ge(x, n), n, x, xs))
825.02/297.03	       , 14: if2^#(true(), n, x, xs) -> c_17(filterhigh^#(n, xs))
825.02/297.03	       , 15: if2^#(false(), n, x, xs) -> c_18(x, filterhigh^#(n, xs))
825.02/297.03	       , 16: ge^#(x, 0()) -> c_14()
825.02/297.03	       , 17: ge^#(0(), s(x)) -> c_15()
825.02/297.03	       , 18: ge^#(s(x), s(y)) -> c_16(ge^#(x, y)) }
825.02/297.03	   
825.02/297.03	   We are left with following problem, upon which TcT provides the
825.02/297.03	   certificate MAYBE.
825.02/297.03	   
825.02/297.03	   Strict DPs:
825.02/297.03	     { append^#(cons(x, xs), ys()) -> c_4(x, append^#(xs, ys()))
825.02/297.03	     , filterlow^#(n, cons(x, xs)) -> c_6(if1^#(ge(n, x), n, x, xs))
825.02/297.03	     , if1^#(true(), n, x, xs) -> c_12(filterlow^#(n, xs))
825.02/297.03	     , if1^#(false(), n, x, xs) -> c_13(x, filterlow^#(n, xs))
825.02/297.03	     , last^#(cons(x, nil())) -> c_8(x)
825.02/297.03	     , last^#(cons(x, cons(y, xs))) -> c_9(last^#(cons(y, xs)))
825.02/297.03	     , filterhigh^#(n, cons(x, xs)) -> c_11(if2^#(ge(x, n), n, x, xs))
825.02/297.03	     , if2^#(true(), n, x, xs) -> c_17(filterhigh^#(n, xs))
825.02/297.03	     , if2^#(false(), n, x, xs) -> c_18(x, filterhigh^#(n, xs))
825.02/297.03	     , ge^#(s(x), s(y)) -> c_16(ge^#(x, y)) }
825.02/297.03	   Strict Trs:
825.02/297.03	     { qsort(nil()) -> nil()
825.02/297.03	     , qsort(cons(x, xs)) ->
825.02/297.03	       append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	              cons(last(cons(x, xs)),
825.02/297.03	                   qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
825.02/297.03	     , append(nil(), ys()) -> ys()
825.02/297.03	     , append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
825.02/297.03	     , filterlow(n, nil()) -> nil()
825.02/297.03	     , filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
825.02/297.03	     , last(nil()) -> 0()
825.02/297.03	     , last(cons(x, nil())) -> x
825.02/297.03	     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
825.02/297.03	     , filterhigh(n, nil()) -> nil()
825.02/297.03	     , filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
825.02/297.03	     , if1(true(), n, x, xs) -> filterlow(n, xs)
825.02/297.03	     , if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
825.02/297.03	     , ge(x, 0()) -> true()
825.02/297.03	     , ge(0(), s(x)) -> false()
825.02/297.03	     , ge(s(x), s(y)) -> ge(x, y)
825.02/297.03	     , if2(true(), n, x, xs) -> filterhigh(n, xs)
825.02/297.03	     , if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs)) }
825.02/297.03	   Weak DPs:
825.02/297.03	     { qsort^#(nil()) -> c_1()
825.02/297.03	     , qsort^#(cons(x, xs)) ->
825.02/297.03	       c_2(append^#(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
825.02/297.03	                    cons(last(cons(x, xs)),
825.02/297.03	                         qsort(filterhigh(last(cons(x, xs)), cons(x, xs))))))
825.02/297.03	     , append^#(nil(), ys()) -> c_3()
825.02/297.03	     , filterlow^#(n, nil()) -> c_5()
825.02/297.03	     , last^#(nil()) -> c_7()
825.02/297.03	     , filterhigh^#(n, nil()) -> c_10()
825.02/297.03	     , ge^#(x, 0()) -> c_14()
825.02/297.03	     , ge^#(0(), s(x)) -> c_15() }
825.02/297.03	   Obligation:
825.02/297.03	     runtime complexity
825.02/297.03	   Answer:
825.02/297.03	     MAYBE
825.02/297.03	   
825.02/297.03	   Empty strict component of the problem is NOT empty.
825.02/297.03	
825.02/297.03	
825.02/297.03	Arrrr..
825.24/297.23	EOF