MAYBE
778.52/297.04	MAYBE
778.52/297.04	
778.52/297.04	We are left with following problem, upon which TcT provides the
778.52/297.04	certificate MAYBE.
778.52/297.04	
778.52/297.04	Strict Trs:
778.52/297.04	  { le(0(), Y) -> true()
778.52/297.04	  , le(s(X), 0()) -> false()
778.52/297.04	  , le(s(X), s(Y)) -> le(X, Y)
778.52/297.04	  , app(nil(), Y) -> Y
778.52/297.04	  , app(cons(N, L), Y) -> cons(N, app(L, Y))
778.52/297.04	  , low(N, nil()) -> nil()
778.52/297.04	  , low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
778.52/297.04	  , iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
778.52/297.04	  , iflow(false(), N, cons(M, L)) -> low(N, L)
778.52/297.04	  , high(N, nil()) -> nil()
778.52/297.04	  , high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
778.52/297.04	  , ifhigh(true(), N, cons(M, L)) -> high(N, L)
778.52/297.04	  , ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
778.52/297.04	  , quicksort(nil()) -> nil()
778.52/297.04	  , quicksort(cons(N, L)) ->
778.52/297.04	    app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) }
778.52/297.04	Obligation:
778.52/297.04	  runtime complexity
778.52/297.04	Answer:
778.52/297.04	  MAYBE
778.52/297.04	
778.52/297.04	None of the processors succeeded.
778.52/297.04	
778.52/297.04	Details of failed attempt(s):
778.52/297.04	-----------------------------
778.52/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
778.52/297.04	   following reason:
778.52/297.04	   
778.52/297.04	   Computation stopped due to timeout after 297.0 seconds.
778.52/297.04	
778.52/297.04	2) 'Best' failed due to the following reason:
778.52/297.04	   
778.52/297.04	   None of the processors succeeded.
778.52/297.04	   
778.52/297.04	   Details of failed attempt(s):
778.52/297.04	   -----------------------------
778.52/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
778.52/297.04	      seconds)' failed due to the following reason:
778.52/297.04	      
778.52/297.04	      Computation stopped due to timeout after 148.0 seconds.
778.52/297.04	   
778.52/297.04	   2) 'Best' failed due to the following reason:
778.52/297.04	      
778.52/297.04	      None of the processors succeeded.
778.52/297.04	      
778.52/297.04	      Details of failed attempt(s):
778.52/297.04	      -----------------------------
778.52/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
778.52/297.04	         following reason:
778.52/297.04	         
778.52/297.04	         The processor is inapplicable, reason:
778.52/297.04	           Processor only applicable for innermost runtime complexity analysis
778.52/297.04	      
778.52/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
778.52/297.04	         to the following reason:
778.52/297.04	         
778.52/297.04	         The processor is inapplicable, reason:
778.52/297.04	           Processor only applicable for innermost runtime complexity analysis
778.52/297.04	      
778.52/297.04	   
778.52/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
778.52/297.04	      failed due to the following reason:
778.52/297.04	      
778.52/297.04	      None of the processors succeeded.
778.52/297.04	      
778.52/297.04	      Details of failed attempt(s):
778.52/297.04	      -----------------------------
778.52/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
778.52/297.04	         failed due to the following reason:
778.52/297.04	         
778.52/297.04	         match-boundness of the problem could not be verified.
778.52/297.04	      
778.52/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
778.52/297.04	         failed due to the following reason:
778.52/297.04	         
778.52/297.04	         match-boundness of the problem could not be verified.
778.52/297.04	      
778.52/297.04	   
778.52/297.04	
778.52/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
778.52/297.04	   the following reason:
778.52/297.04	   
778.52/297.04	   We add the following weak dependency pairs:
778.52/297.04	   
778.52/297.04	   Strict DPs:
778.52/297.04	     { le^#(0(), Y) -> c_1()
778.52/297.04	     , le^#(s(X), 0()) -> c_2()
778.52/297.04	     , le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
778.52/297.04	     , app^#(nil(), Y) -> c_4(Y)
778.52/297.04	     , app^#(cons(N, L), Y) -> c_5(N, app^#(L, Y))
778.52/297.04	     , low^#(N, nil()) -> c_6()
778.52/297.04	     , low^#(N, cons(M, L)) -> c_7(iflow^#(le(M, N), N, cons(M, L)))
778.52/297.04	     , iflow^#(true(), N, cons(M, L)) -> c_8(M, low^#(N, L))
778.52/297.04	     , iflow^#(false(), N, cons(M, L)) -> c_9(low^#(N, L))
778.52/297.04	     , high^#(N, nil()) -> c_10()
778.52/297.04	     , high^#(N, cons(M, L)) -> c_11(ifhigh^#(le(M, N), N, cons(M, L)))
778.52/297.04	     , ifhigh^#(true(), N, cons(M, L)) -> c_12(high^#(N, L))
778.52/297.04	     , ifhigh^#(false(), N, cons(M, L)) -> c_13(M, high^#(N, L))
778.52/297.04	     , quicksort^#(nil()) -> c_14()
778.52/297.04	     , quicksort^#(cons(N, L)) ->
778.52/297.04	       c_15(app^#(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))) }
778.52/297.04	   
778.52/297.04	   and mark the set of starting terms.
778.52/297.04	   
778.52/297.04	   We are left with following problem, upon which TcT provides the
778.52/297.04	   certificate MAYBE.
778.52/297.04	   
778.52/297.04	   Strict DPs:
778.52/297.04	     { le^#(0(), Y) -> c_1()
778.52/297.04	     , le^#(s(X), 0()) -> c_2()
778.52/297.04	     , le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
778.52/297.04	     , app^#(nil(), Y) -> c_4(Y)
778.52/297.04	     , app^#(cons(N, L), Y) -> c_5(N, app^#(L, Y))
778.52/297.04	     , low^#(N, nil()) -> c_6()
778.52/297.04	     , low^#(N, cons(M, L)) -> c_7(iflow^#(le(M, N), N, cons(M, L)))
778.52/297.04	     , iflow^#(true(), N, cons(M, L)) -> c_8(M, low^#(N, L))
778.52/297.04	     , iflow^#(false(), N, cons(M, L)) -> c_9(low^#(N, L))
778.52/297.04	     , high^#(N, nil()) -> c_10()
778.52/297.04	     , high^#(N, cons(M, L)) -> c_11(ifhigh^#(le(M, N), N, cons(M, L)))
778.52/297.04	     , ifhigh^#(true(), N, cons(M, L)) -> c_12(high^#(N, L))
778.52/297.04	     , ifhigh^#(false(), N, cons(M, L)) -> c_13(M, high^#(N, L))
778.52/297.04	     , quicksort^#(nil()) -> c_14()
778.52/297.04	     , quicksort^#(cons(N, L)) ->
778.52/297.04	       c_15(app^#(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))) }
778.52/297.04	   Strict Trs:
778.52/297.04	     { le(0(), Y) -> true()
778.52/297.04	     , le(s(X), 0()) -> false()
778.52/297.04	     , le(s(X), s(Y)) -> le(X, Y)
778.52/297.04	     , app(nil(), Y) -> Y
778.52/297.04	     , app(cons(N, L), Y) -> cons(N, app(L, Y))
778.52/297.04	     , low(N, nil()) -> nil()
778.52/297.04	     , low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
778.52/297.04	     , iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
778.52/297.04	     , iflow(false(), N, cons(M, L)) -> low(N, L)
778.52/297.04	     , high(N, nil()) -> nil()
778.52/297.04	     , high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
778.52/297.04	     , ifhigh(true(), N, cons(M, L)) -> high(N, L)
778.52/297.04	     , ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
778.52/297.04	     , quicksort(nil()) -> nil()
778.52/297.04	     , quicksort(cons(N, L)) ->
778.52/297.04	       app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) }
778.52/297.04	   Obligation:
778.52/297.04	     runtime complexity
778.52/297.04	   Answer:
778.52/297.04	     MAYBE
778.52/297.04	   
778.52/297.04	   We estimate the number of application of {1,2,6,10,14} by
778.52/297.04	   applications of Pre({1,2,6,10,14}) = {3,4,5,8,9,12,13}. Here rules
778.52/297.04	   are labeled as follows:
778.52/297.04	   
778.52/297.04	     DPs:
778.52/297.04	       { 1: le^#(0(), Y) -> c_1()
778.52/297.04	       , 2: le^#(s(X), 0()) -> c_2()
778.52/297.04	       , 3: le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
778.52/297.04	       , 4: app^#(nil(), Y) -> c_4(Y)
778.52/297.04	       , 5: app^#(cons(N, L), Y) -> c_5(N, app^#(L, Y))
778.52/297.04	       , 6: low^#(N, nil()) -> c_6()
778.52/297.04	       , 7: low^#(N, cons(M, L)) -> c_7(iflow^#(le(M, N), N, cons(M, L)))
778.52/297.04	       , 8: iflow^#(true(), N, cons(M, L)) -> c_8(M, low^#(N, L))
778.52/297.04	       , 9: iflow^#(false(), N, cons(M, L)) -> c_9(low^#(N, L))
778.52/297.04	       , 10: high^#(N, nil()) -> c_10()
778.52/297.04	       , 11: high^#(N, cons(M, L)) ->
778.52/297.04	             c_11(ifhigh^#(le(M, N), N, cons(M, L)))
778.52/297.04	       , 12: ifhigh^#(true(), N, cons(M, L)) -> c_12(high^#(N, L))
778.52/297.04	       , 13: ifhigh^#(false(), N, cons(M, L)) -> c_13(M, high^#(N, L))
778.52/297.04	       , 14: quicksort^#(nil()) -> c_14()
778.52/297.04	       , 15: quicksort^#(cons(N, L)) ->
778.52/297.04	             c_15(app^#(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))) }
778.52/297.04	   
778.52/297.04	   We are left with following problem, upon which TcT provides the
778.52/297.04	   certificate MAYBE.
778.52/297.04	   
778.52/297.04	   Strict DPs:
778.52/297.04	     { le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
778.52/297.04	     , app^#(nil(), Y) -> c_4(Y)
778.52/297.04	     , app^#(cons(N, L), Y) -> c_5(N, app^#(L, Y))
778.52/297.04	     , low^#(N, cons(M, L)) -> c_7(iflow^#(le(M, N), N, cons(M, L)))
778.52/297.04	     , iflow^#(true(), N, cons(M, L)) -> c_8(M, low^#(N, L))
778.52/297.04	     , iflow^#(false(), N, cons(M, L)) -> c_9(low^#(N, L))
778.52/297.04	     , high^#(N, cons(M, L)) -> c_11(ifhigh^#(le(M, N), N, cons(M, L)))
778.52/297.04	     , ifhigh^#(true(), N, cons(M, L)) -> c_12(high^#(N, L))
778.52/297.04	     , ifhigh^#(false(), N, cons(M, L)) -> c_13(M, high^#(N, L))
778.52/297.04	     , quicksort^#(cons(N, L)) ->
778.52/297.04	       c_15(app^#(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))) }
778.52/297.04	   Strict Trs:
778.52/297.04	     { le(0(), Y) -> true()
778.52/297.04	     , le(s(X), 0()) -> false()
778.52/297.04	     , le(s(X), s(Y)) -> le(X, Y)
778.52/297.04	     , app(nil(), Y) -> Y
778.52/297.04	     , app(cons(N, L), Y) -> cons(N, app(L, Y))
778.52/297.04	     , low(N, nil()) -> nil()
778.52/297.04	     , low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
778.52/297.04	     , iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
778.52/297.04	     , iflow(false(), N, cons(M, L)) -> low(N, L)
778.52/297.04	     , high(N, nil()) -> nil()
778.52/297.04	     , high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
778.52/297.04	     , ifhigh(true(), N, cons(M, L)) -> high(N, L)
778.52/297.04	     , ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
778.52/297.04	     , quicksort(nil()) -> nil()
778.52/297.04	     , quicksort(cons(N, L)) ->
778.52/297.04	       app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) }
778.52/297.04	   Weak DPs:
778.52/297.04	     { le^#(0(), Y) -> c_1()
778.52/297.04	     , le^#(s(X), 0()) -> c_2()
778.52/297.04	     , low^#(N, nil()) -> c_6()
778.52/297.04	     , high^#(N, nil()) -> c_10()
778.52/297.04	     , quicksort^#(nil()) -> c_14() }
778.52/297.04	   Obligation:
778.52/297.04	     runtime complexity
778.52/297.04	   Answer:
778.52/297.04	     MAYBE
778.52/297.04	   
778.52/297.04	   Empty strict component of the problem is NOT empty.
778.52/297.04	
778.52/297.04	
778.52/297.04	Arrrr..
778.73/297.25	EOF