MAYBE
709.11/297.03	MAYBE
709.11/297.03	
709.11/297.03	We are left with following problem, upon which TcT provides the
709.11/297.03	certificate MAYBE.
709.11/297.03	
709.11/297.03	Strict Trs:
709.11/297.03	  { app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
709.11/297.03	  , helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
709.11/297.03	  , plus(x, 0()) -> x
709.11/297.03	  , plus(x, s(y)) -> s(plus(x, y))
709.11/297.03	  , length(nil()) -> 0()
709.11/297.03	  , length(cons(x, y)) -> s(length(y))
709.11/297.03	  , if(true(), c, l, ys, zs) -> nil()
709.11/297.03	  , if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
709.11/297.03	  , ge(x, 0()) -> true()
709.11/297.03	  , ge(0(), s(x)) -> false()
709.11/297.03	  , ge(s(x), s(y)) -> ge(x, y)
709.11/297.03	  , helpb(c, l, ys, zs) ->
709.11/297.03	    cons(take(c, ys, zs), helpa(s(c), l, ys, zs))
709.11/297.03	  , take(0(), nil(), cons(y, ys)) -> y
709.11/297.03	  , take(0(), cons(x, xs()), ys) -> x
709.11/297.03	  , take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
709.11/297.03	  , take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys) }
709.11/297.03	Obligation:
709.11/297.03	  runtime complexity
709.11/297.03	Answer:
709.11/297.03	  MAYBE
709.11/297.03	
709.11/297.03	None of the processors succeeded.
709.11/297.03	
709.11/297.03	Details of failed attempt(s):
709.11/297.03	-----------------------------
709.11/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
709.11/297.03	   following reason:
709.11/297.03	   
709.11/297.03	   Computation stopped due to timeout after 297.0 seconds.
709.11/297.03	
709.11/297.03	2) 'Best' failed due to the following reason:
709.11/297.03	   
709.11/297.03	   None of the processors succeeded.
709.11/297.03	   
709.11/297.03	   Details of failed attempt(s):
709.11/297.03	   -----------------------------
709.11/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
709.11/297.03	      seconds)' failed due to the following reason:
709.11/297.03	      
709.11/297.03	      Computation stopped due to timeout after 148.0 seconds.
709.11/297.03	   
709.11/297.03	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
709.11/297.03	      failed due to the following reason:
709.11/297.03	      
709.11/297.03	      None of the processors succeeded.
709.11/297.03	      
709.11/297.03	      Details of failed attempt(s):
709.11/297.03	      -----------------------------
709.11/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
709.11/297.03	         failed due to the following reason:
709.11/297.03	         
709.11/297.03	         match-boundness of the problem could not be verified.
709.11/297.03	      
709.11/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
709.11/297.03	         failed due to the following reason:
709.11/297.03	         
709.11/297.03	         match-boundness of the problem could not be verified.
709.11/297.03	      
709.11/297.03	   
709.11/297.03	   3) 'Best' failed due to the following reason:
709.11/297.03	      
709.11/297.03	      None of the processors succeeded.
709.11/297.03	      
709.11/297.03	      Details of failed attempt(s):
709.11/297.03	      -----------------------------
709.11/297.03	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
709.11/297.03	         to the following reason:
709.11/297.03	         
709.11/297.03	         The processor is inapplicable, reason:
709.11/297.03	           Processor only applicable for innermost runtime complexity analysis
709.11/297.03	      
709.11/297.03	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
709.11/297.03	         following reason:
709.11/297.03	         
709.11/297.03	         The processor is inapplicable, reason:
709.11/297.03	           Processor only applicable for innermost runtime complexity analysis
709.11/297.03	      
709.11/297.03	   
709.11/297.03	
709.11/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
709.11/297.03	   the following reason:
709.11/297.03	   
709.11/297.03	   We add the following weak dependency pairs:
709.11/297.03	   
709.11/297.03	   Strict DPs:
709.11/297.03	     { app^#(x, y) ->
709.11/297.03	       c_1(helpa^#(0(), plus(length(x), length(y)), x, y))
709.11/297.03	     , helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs))
709.11/297.03	     , if^#(true(), c, l, ys, zs) -> c_7()
709.11/297.04	     , if^#(false(), c, l, ys, zs) -> c_8(helpb^#(c, l, ys, zs))
709.11/297.04	     , plus^#(x, 0()) -> c_3(x)
709.11/297.04	     , plus^#(x, s(y)) -> c_4(plus^#(x, y))
709.11/297.04	     , length^#(nil()) -> c_5()
709.11/297.04	     , length^#(cons(x, y)) -> c_6(length^#(y))
709.11/297.04	     , helpb^#(c, l, ys, zs) ->
709.11/297.04	       c_12(take^#(c, ys, zs), helpa^#(s(c), l, ys, zs))
709.11/297.04	     , ge^#(x, 0()) -> c_9()
709.11/297.04	     , ge^#(0(), s(x)) -> c_10()
709.11/297.04	     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
709.11/297.04	     , take^#(0(), nil(), cons(y, ys)) -> c_13(y)
709.11/297.04	     , take^#(0(), cons(x, xs()), ys) -> c_14(x)
709.11/297.04	     , take^#(s(c), nil(), cons(y, ys)) -> c_15(take^#(c, nil(), ys))
709.11/297.04	     , take^#(s(c), cons(x, xs()), ys) -> c_16(take^#(c, xs(), ys)) }
709.11/297.04	   
709.11/297.04	   and mark the set of starting terms.
709.11/297.04	   
709.11/297.04	   We are left with following problem, upon which TcT provides the
709.11/297.04	   certificate MAYBE.
709.11/297.04	   
709.11/297.04	   Strict DPs:
709.11/297.04	     { app^#(x, y) ->
709.11/297.04	       c_1(helpa^#(0(), plus(length(x), length(y)), x, y))
709.11/297.04	     , helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs))
709.11/297.04	     , if^#(true(), c, l, ys, zs) -> c_7()
709.11/297.04	     , if^#(false(), c, l, ys, zs) -> c_8(helpb^#(c, l, ys, zs))
709.11/297.04	     , plus^#(x, 0()) -> c_3(x)
709.11/297.04	     , plus^#(x, s(y)) -> c_4(plus^#(x, y))
709.11/297.04	     , length^#(nil()) -> c_5()
709.11/297.04	     , length^#(cons(x, y)) -> c_6(length^#(y))
709.11/297.04	     , helpb^#(c, l, ys, zs) ->
709.11/297.04	       c_12(take^#(c, ys, zs), helpa^#(s(c), l, ys, zs))
709.11/297.04	     , ge^#(x, 0()) -> c_9()
709.11/297.04	     , ge^#(0(), s(x)) -> c_10()
709.11/297.04	     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
709.11/297.04	     , take^#(0(), nil(), cons(y, ys)) -> c_13(y)
709.11/297.04	     , take^#(0(), cons(x, xs()), ys) -> c_14(x)
709.11/297.04	     , take^#(s(c), nil(), cons(y, ys)) -> c_15(take^#(c, nil(), ys))
709.11/297.04	     , take^#(s(c), cons(x, xs()), ys) -> c_16(take^#(c, xs(), ys)) }
709.11/297.04	   Strict Trs:
709.11/297.04	     { app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
709.11/297.04	     , helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
709.11/297.04	     , plus(x, 0()) -> x
709.11/297.04	     , plus(x, s(y)) -> s(plus(x, y))
709.11/297.04	     , length(nil()) -> 0()
709.11/297.04	     , length(cons(x, y)) -> s(length(y))
709.11/297.04	     , if(true(), c, l, ys, zs) -> nil()
709.11/297.04	     , if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
709.11/297.04	     , ge(x, 0()) -> true()
709.11/297.04	     , ge(0(), s(x)) -> false()
709.11/297.04	     , ge(s(x), s(y)) -> ge(x, y)
709.11/297.04	     , helpb(c, l, ys, zs) ->
709.11/297.04	       cons(take(c, ys, zs), helpa(s(c), l, ys, zs))
709.11/297.04	     , take(0(), nil(), cons(y, ys)) -> y
709.11/297.04	     , take(0(), cons(x, xs()), ys) -> x
709.11/297.04	     , take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
709.11/297.04	     , take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys) }
709.11/297.04	   Obligation:
709.11/297.04	     runtime complexity
709.11/297.04	   Answer:
709.11/297.04	     MAYBE
709.11/297.04	   
709.11/297.04	   We estimate the number of application of {3,7,10,11,16} by
709.11/297.04	   applications of Pre({3,7,10,11,16}) = {2,5,8,9,12,13,14}. Here
709.11/297.04	   rules are labeled as follows:
709.11/297.04	   
709.11/297.04	     DPs:
709.11/297.04	       { 1: app^#(x, y) ->
709.11/297.04	            c_1(helpa^#(0(), plus(length(x), length(y)), x, y))
709.11/297.04	       , 2: helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs))
709.11/297.04	       , 3: if^#(true(), c, l, ys, zs) -> c_7()
709.11/297.04	       , 4: if^#(false(), c, l, ys, zs) -> c_8(helpb^#(c, l, ys, zs))
709.11/297.04	       , 5: plus^#(x, 0()) -> c_3(x)
709.11/297.04	       , 6: plus^#(x, s(y)) -> c_4(plus^#(x, y))
709.11/297.04	       , 7: length^#(nil()) -> c_5()
709.11/297.04	       , 8: length^#(cons(x, y)) -> c_6(length^#(y))
709.11/297.04	       , 9: helpb^#(c, l, ys, zs) ->
709.11/297.04	            c_12(take^#(c, ys, zs), helpa^#(s(c), l, ys, zs))
709.11/297.04	       , 10: ge^#(x, 0()) -> c_9()
709.11/297.04	       , 11: ge^#(0(), s(x)) -> c_10()
709.11/297.04	       , 12: ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
709.11/297.04	       , 13: take^#(0(), nil(), cons(y, ys)) -> c_13(y)
709.11/297.04	       , 14: take^#(0(), cons(x, xs()), ys) -> c_14(x)
709.11/297.04	       , 15: take^#(s(c), nil(), cons(y, ys)) ->
709.11/297.04	             c_15(take^#(c, nil(), ys))
709.11/297.04	       , 16: take^#(s(c), cons(x, xs()), ys) ->
709.11/297.04	             c_16(take^#(c, xs(), ys)) }
709.11/297.04	   
709.11/297.04	   We are left with following problem, upon which TcT provides the
709.11/297.04	   certificate MAYBE.
709.11/297.04	   
709.11/297.04	   Strict DPs:
709.11/297.04	     { app^#(x, y) ->
709.11/297.04	       c_1(helpa^#(0(), plus(length(x), length(y)), x, y))
709.11/297.04	     , helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs))
709.11/297.04	     , if^#(false(), c, l, ys, zs) -> c_8(helpb^#(c, l, ys, zs))
709.11/297.04	     , plus^#(x, 0()) -> c_3(x)
709.11/297.04	     , plus^#(x, s(y)) -> c_4(plus^#(x, y))
709.11/297.04	     , length^#(cons(x, y)) -> c_6(length^#(y))
709.11/297.04	     , helpb^#(c, l, ys, zs) ->
709.11/297.04	       c_12(take^#(c, ys, zs), helpa^#(s(c), l, ys, zs))
709.11/297.04	     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
709.11/297.04	     , take^#(0(), nil(), cons(y, ys)) -> c_13(y)
709.11/297.04	     , take^#(0(), cons(x, xs()), ys) -> c_14(x)
709.11/297.04	     , take^#(s(c), nil(), cons(y, ys)) -> c_15(take^#(c, nil(), ys)) }
709.11/297.04	   Strict Trs:
709.11/297.04	     { app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
709.11/297.04	     , helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
709.11/297.04	     , plus(x, 0()) -> x
709.11/297.04	     , plus(x, s(y)) -> s(plus(x, y))
709.11/297.04	     , length(nil()) -> 0()
709.11/297.04	     , length(cons(x, y)) -> s(length(y))
709.11/297.04	     , if(true(), c, l, ys, zs) -> nil()
709.11/297.04	     , if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
709.11/297.04	     , ge(x, 0()) -> true()
709.11/297.04	     , ge(0(), s(x)) -> false()
709.11/297.04	     , ge(s(x), s(y)) -> ge(x, y)
709.11/297.04	     , helpb(c, l, ys, zs) ->
709.11/297.04	       cons(take(c, ys, zs), helpa(s(c), l, ys, zs))
709.11/297.04	     , take(0(), nil(), cons(y, ys)) -> y
709.11/297.04	     , take(0(), cons(x, xs()), ys) -> x
709.11/297.04	     , take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
709.11/297.04	     , take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys) }
709.11/297.04	   Weak DPs:
709.11/297.04	     { if^#(true(), c, l, ys, zs) -> c_7()
709.11/297.04	     , length^#(nil()) -> c_5()
709.11/297.04	     , ge^#(x, 0()) -> c_9()
709.11/297.04	     , ge^#(0(), s(x)) -> c_10()
709.11/297.04	     , take^#(s(c), cons(x, xs()), ys) -> c_16(take^#(c, xs(), ys)) }
709.11/297.04	   Obligation:
709.11/297.04	     runtime complexity
709.11/297.04	   Answer:
709.11/297.04	     MAYBE
709.11/297.04	   
709.11/297.04	   Empty strict component of the problem is NOT empty.
709.11/297.04	
709.11/297.04	
709.11/297.04	Arrrr..
709.42/297.34	EOF