MAYBE
884.22/297.04	MAYBE
884.22/297.04	
884.22/297.04	We are left with following problem, upon which TcT provides the
884.22/297.04	certificate MAYBE.
884.22/297.04	
884.22/297.04	Strict Trs:
884.22/297.04	  { last(nil()) -> 0()
884.22/297.04	  , last(cons(x, nil())) -> x
884.22/297.04	  , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
884.22/297.04	  , del(x, nil()) -> nil()
884.22/297.04	  , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
884.22/297.04	  , if(true(), x, y, xs) -> xs
884.22/297.04	  , if(false(), x, y, xs) -> cons(y, del(x, xs))
884.22/297.04	  , eq(0(), 0()) -> true()
884.22/297.04	  , eq(0(), s(y)) -> false()
884.22/297.04	  , eq(s(x), 0()) -> false()
884.22/297.04	  , eq(s(x), s(y)) -> eq(x, y)
884.22/297.04	  , reverse(nil()) -> nil()
884.22/297.04	  , reverse(cons(x, xs)) ->
884.22/297.04	    cons(last(cons(x, xs)),
884.22/297.04	         reverse(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	Obligation:
884.22/297.04	  runtime complexity
884.22/297.04	Answer:
884.22/297.04	  MAYBE
884.22/297.04	
884.22/297.04	None of the processors succeeded.
884.22/297.04	
884.22/297.04	Details of failed attempt(s):
884.22/297.04	-----------------------------
884.22/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
884.22/297.04	   following reason:
884.22/297.04	   
884.22/297.04	   Computation stopped due to timeout after 297.0 seconds.
884.22/297.04	
884.22/297.04	2) 'Best' failed due to the following reason:
884.22/297.04	   
884.22/297.04	   None of the processors succeeded.
884.22/297.04	   
884.22/297.04	   Details of failed attempt(s):
884.22/297.04	   -----------------------------
884.22/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
884.22/297.04	      seconds)' failed due to the following reason:
884.22/297.04	      
884.22/297.04	      Computation stopped due to timeout after 148.0 seconds.
884.22/297.04	   
884.22/297.04	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
884.22/297.04	      failed due to the following reason:
884.22/297.04	      
884.22/297.04	      None of the processors succeeded.
884.22/297.04	      
884.22/297.04	      Details of failed attempt(s):
884.22/297.04	      -----------------------------
884.22/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
884.22/297.04	         failed due to the following reason:
884.22/297.04	         
884.22/297.04	         match-boundness of the problem could not be verified.
884.22/297.04	      
884.22/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
884.22/297.04	         failed due to the following reason:
884.22/297.04	         
884.22/297.04	         match-boundness of the problem could not be verified.
884.22/297.04	      
884.22/297.04	   
884.22/297.04	   3) 'Best' failed due to the following reason:
884.22/297.04	      
884.22/297.04	      None of the processors succeeded.
884.22/297.04	      
884.22/297.04	      Details of failed attempt(s):
884.22/297.04	      -----------------------------
884.22/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
884.22/297.04	         following reason:
884.22/297.04	         
884.22/297.04	         The processor is inapplicable, reason:
884.22/297.04	           Processor only applicable for innermost runtime complexity analysis
884.22/297.04	      
884.22/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
884.22/297.04	         to the following reason:
884.22/297.04	         
884.22/297.04	         The processor is inapplicable, reason:
884.22/297.04	           Processor only applicable for innermost runtime complexity analysis
884.22/297.04	      
884.22/297.04	   
884.22/297.04	
884.22/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
884.22/297.04	   the following reason:
884.22/297.04	   
884.22/297.04	   We add the following weak dependency pairs:
884.22/297.04	   
884.22/297.04	   Strict DPs:
884.22/297.04	     { last^#(nil()) -> c_1()
884.22/297.04	     , last^#(cons(x, nil())) -> c_2(x)
884.22/297.04	     , last^#(cons(x, cons(y, xs))) -> c_3(last^#(cons(y, xs)))
884.22/297.04	     , del^#(x, nil()) -> c_4()
884.22/297.04	     , del^#(x, cons(y, xs)) -> c_5(if^#(eq(x, y), x, y, xs))
884.22/297.04	     , if^#(true(), x, y, xs) -> c_6(xs)
884.22/297.04	     , if^#(false(), x, y, xs) -> c_7(y, del^#(x, xs))
884.22/297.04	     , eq^#(0(), 0()) -> c_8()
884.22/297.04	     , eq^#(0(), s(y)) -> c_9()
884.22/297.04	     , eq^#(s(x), 0()) -> c_10()
884.22/297.04	     , eq^#(s(x), s(y)) -> c_11(eq^#(x, y))
884.22/297.04	     , reverse^#(nil()) -> c_12()
884.22/297.04	     , reverse^#(cons(x, xs)) ->
884.22/297.04	       c_13(last^#(cons(x, xs)),
884.22/297.04	            reverse^#(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	   
884.22/297.04	   and mark the set of starting terms.
884.22/297.04	   
884.22/297.04	   We are left with following problem, upon which TcT provides the
884.22/297.04	   certificate MAYBE.
884.22/297.04	   
884.22/297.04	   Strict DPs:
884.22/297.04	     { last^#(nil()) -> c_1()
884.22/297.04	     , last^#(cons(x, nil())) -> c_2(x)
884.22/297.04	     , last^#(cons(x, cons(y, xs))) -> c_3(last^#(cons(y, xs)))
884.22/297.04	     , del^#(x, nil()) -> c_4()
884.22/297.04	     , del^#(x, cons(y, xs)) -> c_5(if^#(eq(x, y), x, y, xs))
884.22/297.04	     , if^#(true(), x, y, xs) -> c_6(xs)
884.22/297.04	     , if^#(false(), x, y, xs) -> c_7(y, del^#(x, xs))
884.22/297.04	     , eq^#(0(), 0()) -> c_8()
884.22/297.04	     , eq^#(0(), s(y)) -> c_9()
884.22/297.04	     , eq^#(s(x), 0()) -> c_10()
884.22/297.04	     , eq^#(s(x), s(y)) -> c_11(eq^#(x, y))
884.22/297.04	     , reverse^#(nil()) -> c_12()
884.22/297.04	     , reverse^#(cons(x, xs)) ->
884.22/297.04	       c_13(last^#(cons(x, xs)),
884.22/297.04	            reverse^#(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	   Strict Trs:
884.22/297.04	     { last(nil()) -> 0()
884.22/297.04	     , last(cons(x, nil())) -> x
884.22/297.04	     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
884.22/297.04	     , del(x, nil()) -> nil()
884.22/297.04	     , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
884.22/297.04	     , if(true(), x, y, xs) -> xs
884.22/297.04	     , if(false(), x, y, xs) -> cons(y, del(x, xs))
884.22/297.04	     , eq(0(), 0()) -> true()
884.22/297.04	     , eq(0(), s(y)) -> false()
884.22/297.04	     , eq(s(x), 0()) -> false()
884.22/297.04	     , eq(s(x), s(y)) -> eq(x, y)
884.22/297.04	     , reverse(nil()) -> nil()
884.22/297.04	     , reverse(cons(x, xs)) ->
884.22/297.04	       cons(last(cons(x, xs)),
884.22/297.04	            reverse(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	   Obligation:
884.22/297.04	     runtime complexity
884.22/297.04	   Answer:
884.22/297.04	     MAYBE
884.22/297.04	   
884.22/297.04	   We estimate the number of application of {1,4,8,9,10,12} by
884.22/297.04	   applications of Pre({1,4,8,9,10,12}) = {2,6,7,11,13}. Here rules
884.22/297.04	   are labeled as follows:
884.22/297.04	   
884.22/297.04	     DPs:
884.22/297.04	       { 1: last^#(nil()) -> c_1()
884.22/297.04	       , 2: last^#(cons(x, nil())) -> c_2(x)
884.22/297.04	       , 3: last^#(cons(x, cons(y, xs))) -> c_3(last^#(cons(y, xs)))
884.22/297.04	       , 4: del^#(x, nil()) -> c_4()
884.22/297.04	       , 5: del^#(x, cons(y, xs)) -> c_5(if^#(eq(x, y), x, y, xs))
884.22/297.04	       , 6: if^#(true(), x, y, xs) -> c_6(xs)
884.22/297.04	       , 7: if^#(false(), x, y, xs) -> c_7(y, del^#(x, xs))
884.22/297.04	       , 8: eq^#(0(), 0()) -> c_8()
884.22/297.04	       , 9: eq^#(0(), s(y)) -> c_9()
884.22/297.04	       , 10: eq^#(s(x), 0()) -> c_10()
884.22/297.04	       , 11: eq^#(s(x), s(y)) -> c_11(eq^#(x, y))
884.22/297.04	       , 12: reverse^#(nil()) -> c_12()
884.22/297.04	       , 13: reverse^#(cons(x, xs)) ->
884.22/297.04	             c_13(last^#(cons(x, xs)),
884.22/297.04	                  reverse^#(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	   
884.22/297.04	   We are left with following problem, upon which TcT provides the
884.22/297.04	   certificate MAYBE.
884.22/297.04	   
884.22/297.04	   Strict DPs:
884.22/297.04	     { last^#(cons(x, nil())) -> c_2(x)
884.22/297.04	     , last^#(cons(x, cons(y, xs))) -> c_3(last^#(cons(y, xs)))
884.22/297.04	     , del^#(x, cons(y, xs)) -> c_5(if^#(eq(x, y), x, y, xs))
884.22/297.04	     , if^#(true(), x, y, xs) -> c_6(xs)
884.22/297.04	     , if^#(false(), x, y, xs) -> c_7(y, del^#(x, xs))
884.22/297.04	     , eq^#(s(x), s(y)) -> c_11(eq^#(x, y))
884.22/297.04	     , reverse^#(cons(x, xs)) ->
884.22/297.04	       c_13(last^#(cons(x, xs)),
884.22/297.04	            reverse^#(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	   Strict Trs:
884.22/297.04	     { last(nil()) -> 0()
884.22/297.04	     , last(cons(x, nil())) -> x
884.22/297.04	     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
884.22/297.04	     , del(x, nil()) -> nil()
884.22/297.04	     , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
884.22/297.04	     , if(true(), x, y, xs) -> xs
884.22/297.04	     , if(false(), x, y, xs) -> cons(y, del(x, xs))
884.22/297.04	     , eq(0(), 0()) -> true()
884.22/297.04	     , eq(0(), s(y)) -> false()
884.22/297.04	     , eq(s(x), 0()) -> false()
884.22/297.04	     , eq(s(x), s(y)) -> eq(x, y)
884.22/297.04	     , reverse(nil()) -> nil()
884.22/297.04	     , reverse(cons(x, xs)) ->
884.22/297.04	       cons(last(cons(x, xs)),
884.22/297.04	            reverse(del(last(cons(x, xs)), cons(x, xs)))) }
884.22/297.04	   Weak DPs:
884.22/297.04	     { last^#(nil()) -> c_1()
884.22/297.04	     , del^#(x, nil()) -> c_4()
884.22/297.04	     , eq^#(0(), 0()) -> c_8()
884.22/297.04	     , eq^#(0(), s(y)) -> c_9()
884.22/297.04	     , eq^#(s(x), 0()) -> c_10()
884.22/297.04	     , reverse^#(nil()) -> c_12() }
884.22/297.04	   Obligation:
884.22/297.04	     runtime complexity
884.22/297.04	   Answer:
884.22/297.04	     MAYBE
884.22/297.04	   
884.22/297.04	   Empty strict component of the problem is NOT empty.
884.22/297.04	
884.22/297.04	
884.22/297.04	Arrrr..
884.54/297.32	EOF