MAYBE
911.88/297.04	MAYBE
911.88/297.04	
911.88/297.04	We are left with following problem, upon which TcT provides the
911.88/297.04	certificate MAYBE.
911.88/297.04	
911.88/297.04	Strict Trs:
911.88/297.04	  { double(0()) -> 0()
911.88/297.04	  , double(s(x)) -> s(s(double(x)))
911.88/297.04	  , del(x, nil()) -> nil()
911.88/297.04	  , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
911.88/297.04	  , if(true(), x, y, xs) -> xs
911.88/297.04	  , if(false(), x, y, xs) -> cons(y, del(x, xs))
911.88/297.04	  , eq(0(), 0()) -> true()
911.88/297.04	  , eq(0(), s(y)) -> false()
911.88/297.04	  , eq(s(x), 0()) -> false()
911.88/297.04	  , eq(s(x), s(y)) -> eq(x, y)
911.88/297.04	  , first(nil()) -> 0()
911.88/297.04	  , first(cons(x, xs)) -> x
911.88/297.04	  , doublelist(nil()) -> nil()
911.88/297.04	  , doublelist(cons(x, xs)) ->
911.88/297.04	    cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	Obligation:
911.88/297.04	  runtime complexity
911.88/297.04	Answer:
911.88/297.04	  MAYBE
911.88/297.04	
911.88/297.04	None of the processors succeeded.
911.88/297.04	
911.88/297.04	Details of failed attempt(s):
911.88/297.04	-----------------------------
911.88/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
911.88/297.04	   following reason:
911.88/297.04	   
911.88/297.04	   Computation stopped due to timeout after 297.0 seconds.
911.88/297.04	
911.88/297.04	2) 'Best' failed due to the following reason:
911.88/297.04	   
911.88/297.04	   None of the processors succeeded.
911.88/297.04	   
911.88/297.04	   Details of failed attempt(s):
911.88/297.04	   -----------------------------
911.88/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
911.88/297.04	      seconds)' failed due to the following reason:
911.88/297.04	      
911.88/297.04	      Computation stopped due to timeout after 148.0 seconds.
911.88/297.04	   
911.88/297.04	   2) 'Best' failed due to the following reason:
911.88/297.04	      
911.88/297.04	      None of the processors succeeded.
911.88/297.04	      
911.88/297.04	      Details of failed attempt(s):
911.88/297.04	      -----------------------------
911.88/297.04	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
911.88/297.04	         to the following reason:
911.88/297.04	         
911.88/297.04	         The processor is inapplicable, reason:
911.88/297.04	           Processor only applicable for innermost runtime complexity analysis
911.88/297.04	      
911.88/297.04	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
911.88/297.04	         following reason:
911.88/297.04	         
911.88/297.04	         The processor is inapplicable, reason:
911.88/297.04	           Processor only applicable for innermost runtime complexity analysis
911.88/297.04	      
911.88/297.04	   
911.88/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
911.88/297.04	      failed due to the following reason:
911.88/297.04	      
911.88/297.04	      None of the processors succeeded.
911.88/297.04	      
911.88/297.04	      Details of failed attempt(s):
911.88/297.04	      -----------------------------
911.88/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
911.88/297.04	         failed due to the following reason:
911.88/297.04	         
911.88/297.04	         match-boundness of the problem could not be verified.
911.88/297.04	      
911.88/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
911.88/297.04	         failed due to the following reason:
911.88/297.04	         
911.88/297.04	         match-boundness of the problem could not be verified.
911.88/297.04	      
911.88/297.04	   
911.88/297.04	
911.88/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
911.88/297.04	   the following reason:
911.88/297.04	   
911.88/297.04	   We add the following weak dependency pairs:
911.88/297.04	   
911.88/297.04	   Strict DPs:
911.88/297.04	     { double^#(0()) -> c_1()
911.88/297.04	     , double^#(s(x)) -> c_2(double^#(x))
911.88/297.04	     , del^#(x, nil()) -> c_3()
911.88/297.04	     , del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs))
911.88/297.04	     , if^#(true(), x, y, xs) -> c_5(xs)
911.88/297.04	     , if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs))
911.88/297.04	     , eq^#(0(), 0()) -> c_7()
911.88/297.04	     , eq^#(0(), s(y)) -> c_8()
911.88/297.04	     , eq^#(s(x), 0()) -> c_9()
911.88/297.04	     , eq^#(s(x), s(y)) -> c_10(eq^#(x, y))
911.88/297.04	     , first^#(nil()) -> c_11()
911.88/297.04	     , first^#(cons(x, xs)) -> c_12(x)
911.88/297.04	     , doublelist^#(nil()) -> c_13()
911.88/297.04	     , doublelist^#(cons(x, xs)) ->
911.88/297.04	       c_14(double^#(x),
911.88/297.04	            doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	   
911.88/297.04	   and mark the set of starting terms.
911.88/297.04	   
911.88/297.04	   We are left with following problem, upon which TcT provides the
911.88/297.04	   certificate MAYBE.
911.88/297.04	   
911.88/297.04	   Strict DPs:
911.88/297.04	     { double^#(0()) -> c_1()
911.88/297.04	     , double^#(s(x)) -> c_2(double^#(x))
911.88/297.04	     , del^#(x, nil()) -> c_3()
911.88/297.04	     , del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs))
911.88/297.04	     , if^#(true(), x, y, xs) -> c_5(xs)
911.88/297.04	     , if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs))
911.88/297.04	     , eq^#(0(), 0()) -> c_7()
911.88/297.04	     , eq^#(0(), s(y)) -> c_8()
911.88/297.04	     , eq^#(s(x), 0()) -> c_9()
911.88/297.04	     , eq^#(s(x), s(y)) -> c_10(eq^#(x, y))
911.88/297.04	     , first^#(nil()) -> c_11()
911.88/297.04	     , first^#(cons(x, xs)) -> c_12(x)
911.88/297.04	     , doublelist^#(nil()) -> c_13()
911.88/297.04	     , doublelist^#(cons(x, xs)) ->
911.88/297.04	       c_14(double^#(x),
911.88/297.04	            doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	   Strict Trs:
911.88/297.04	     { double(0()) -> 0()
911.88/297.04	     , double(s(x)) -> s(s(double(x)))
911.88/297.04	     , del(x, nil()) -> nil()
911.88/297.04	     , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
911.88/297.04	     , if(true(), x, y, xs) -> xs
911.88/297.04	     , if(false(), x, y, xs) -> cons(y, del(x, xs))
911.88/297.04	     , eq(0(), 0()) -> true()
911.88/297.04	     , eq(0(), s(y)) -> false()
911.88/297.04	     , eq(s(x), 0()) -> false()
911.88/297.04	     , eq(s(x), s(y)) -> eq(x, y)
911.88/297.04	     , first(nil()) -> 0()
911.88/297.04	     , first(cons(x, xs)) -> x
911.88/297.04	     , doublelist(nil()) -> nil()
911.88/297.04	     , doublelist(cons(x, xs)) ->
911.88/297.04	       cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	   Obligation:
911.88/297.04	     runtime complexity
911.88/297.04	   Answer:
911.88/297.04	     MAYBE
911.88/297.04	   
911.88/297.04	   We estimate the number of application of {1,3,7,8,9,11,13} by
911.88/297.04	   applications of Pre({1,3,7,8,9,11,13}) = {2,5,6,10,12,14}. Here
911.88/297.04	   rules are labeled as follows:
911.88/297.04	   
911.88/297.04	     DPs:
911.88/297.04	       { 1: double^#(0()) -> c_1()
911.88/297.04	       , 2: double^#(s(x)) -> c_2(double^#(x))
911.88/297.04	       , 3: del^#(x, nil()) -> c_3()
911.88/297.04	       , 4: del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs))
911.88/297.04	       , 5: if^#(true(), x, y, xs) -> c_5(xs)
911.88/297.04	       , 6: if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs))
911.88/297.04	       , 7: eq^#(0(), 0()) -> c_7()
911.88/297.04	       , 8: eq^#(0(), s(y)) -> c_8()
911.88/297.04	       , 9: eq^#(s(x), 0()) -> c_9()
911.88/297.04	       , 10: eq^#(s(x), s(y)) -> c_10(eq^#(x, y))
911.88/297.04	       , 11: first^#(nil()) -> c_11()
911.88/297.04	       , 12: first^#(cons(x, xs)) -> c_12(x)
911.88/297.04	       , 13: doublelist^#(nil()) -> c_13()
911.88/297.04	       , 14: doublelist^#(cons(x, xs)) ->
911.88/297.04	             c_14(double^#(x),
911.88/297.04	                  doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	   
911.88/297.04	   We are left with following problem, upon which TcT provides the
911.88/297.04	   certificate MAYBE.
911.88/297.04	   
911.88/297.04	   Strict DPs:
911.88/297.04	     { double^#(s(x)) -> c_2(double^#(x))
911.88/297.04	     , del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs))
911.88/297.04	     , if^#(true(), x, y, xs) -> c_5(xs)
911.88/297.04	     , if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs))
911.88/297.04	     , eq^#(s(x), s(y)) -> c_10(eq^#(x, y))
911.88/297.04	     , first^#(cons(x, xs)) -> c_12(x)
911.88/297.04	     , doublelist^#(cons(x, xs)) ->
911.88/297.04	       c_14(double^#(x),
911.88/297.04	            doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	   Strict Trs:
911.88/297.04	     { double(0()) -> 0()
911.88/297.04	     , double(s(x)) -> s(s(double(x)))
911.88/297.04	     , del(x, nil()) -> nil()
911.88/297.04	     , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
911.88/297.04	     , if(true(), x, y, xs) -> xs
911.88/297.04	     , if(false(), x, y, xs) -> cons(y, del(x, xs))
911.88/297.04	     , eq(0(), 0()) -> true()
911.88/297.04	     , eq(0(), s(y)) -> false()
911.88/297.04	     , eq(s(x), 0()) -> false()
911.88/297.04	     , eq(s(x), s(y)) -> eq(x, y)
911.88/297.04	     , first(nil()) -> 0()
911.88/297.04	     , first(cons(x, xs)) -> x
911.88/297.04	     , doublelist(nil()) -> nil()
911.88/297.04	     , doublelist(cons(x, xs)) ->
911.88/297.04	       cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) }
911.88/297.04	   Weak DPs:
911.88/297.04	     { double^#(0()) -> c_1()
911.88/297.04	     , del^#(x, nil()) -> c_3()
911.88/297.04	     , eq^#(0(), 0()) -> c_7()
911.88/297.04	     , eq^#(0(), s(y)) -> c_8()
911.88/297.04	     , eq^#(s(x), 0()) -> c_9()
911.88/297.04	     , first^#(nil()) -> c_11()
911.88/297.04	     , doublelist^#(nil()) -> c_13() }
911.88/297.04	   Obligation:
911.88/297.04	     runtime complexity
911.88/297.04	   Answer:
911.88/297.04	     MAYBE
911.88/297.04	   
911.88/297.04	   Empty strict component of the problem is NOT empty.
911.88/297.04	
911.88/297.04	
911.88/297.04	Arrrr..
912.40/297.51	EOF