MAYBE
783.15/297.11	MAYBE
783.15/297.11	
783.15/297.11	We are left with following problem, upon which TcT provides the
783.15/297.11	certificate MAYBE.
783.15/297.11	
783.15/297.11	Strict Trs:
783.15/297.11	  { numbers() -> d(0())
783.15/297.11	  , d(x) -> if(le(x, nr()), x)
783.15/297.11	  , if(true(), x) -> cons(x, d(s(x)))
783.15/297.11	  , if(false(), x) -> nil()
783.15/297.11	  , le(0(), y) -> true()
783.15/297.11	  , le(s(x), 0()) -> false()
783.15/297.11	  , le(s(x), s(y)) -> le(x, y)
783.15/297.11	  , nr() -> ack(s(s(s(s(s(s(0())))))), 0())
783.15/297.11	  , ack(0(), x) -> s(x)
783.15/297.11	  , ack(s(x), 0()) -> ack(x, s(0()))
783.15/297.11	  , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
783.15/297.11	Obligation:
783.15/297.11	  runtime complexity
783.15/297.11	Answer:
783.15/297.11	  MAYBE
783.15/297.11	
783.15/297.11	None of the processors succeeded.
783.15/297.11	
783.15/297.11	Details of failed attempt(s):
783.15/297.11	-----------------------------
783.15/297.11	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
783.15/297.11	   following reason:
783.15/297.11	   
783.15/297.11	   Computation stopped due to timeout after 297.0 seconds.
783.15/297.11	
783.15/297.11	2) 'Best' failed due to the following reason:
783.15/297.11	   
783.15/297.11	   None of the processors succeeded.
783.15/297.11	   
783.15/297.11	   Details of failed attempt(s):
783.15/297.11	   -----------------------------
783.15/297.11	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
783.15/297.11	      seconds)' failed due to the following reason:
783.15/297.11	      
783.15/297.11	      Computation stopped due to timeout after 148.0 seconds.
783.15/297.11	   
783.15/297.11	   2) 'Best' failed due to the following reason:
783.15/297.11	      
783.15/297.11	      None of the processors succeeded.
783.15/297.11	      
783.15/297.11	      Details of failed attempt(s):
783.15/297.11	      -----------------------------
783.15/297.11	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
783.15/297.11	         to the following reason:
783.15/297.11	         
783.15/297.11	         The processor is inapplicable, reason:
783.15/297.11	           Processor only applicable for innermost runtime complexity analysis
783.15/297.11	      
783.15/297.11	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
783.15/297.11	         following reason:
783.15/297.11	         
783.15/297.11	         The processor is inapplicable, reason:
783.15/297.11	           Processor only applicable for innermost runtime complexity analysis
783.15/297.11	      
783.15/297.11	   
783.15/297.11	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
783.15/297.11	      failed due to the following reason:
783.15/297.11	      
783.15/297.11	      None of the processors succeeded.
783.15/297.11	      
783.15/297.11	      Details of failed attempt(s):
783.15/297.11	      -----------------------------
783.15/297.11	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
783.15/297.11	         failed due to the following reason:
783.15/297.11	         
783.15/297.11	         match-boundness of the problem could not be verified.
783.15/297.11	      
783.15/297.11	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
783.15/297.11	         failed due to the following reason:
783.15/297.11	         
783.15/297.11	         match-boundness of the problem could not be verified.
783.15/297.11	      
783.15/297.11	   
783.15/297.11	
783.15/297.11	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
783.15/297.11	   the following reason:
783.15/297.11	   
783.15/297.11	   We add the following weak dependency pairs:
783.15/297.11	   
783.15/297.11	   Strict DPs:
783.15/297.11	     { numbers^#() -> c_1(d^#(0()))
783.15/297.11	     , d^#(x) -> c_2(if^#(le(x, nr()), x))
783.15/297.11	     , if^#(true(), x) -> c_3(x, d^#(s(x)))
783.15/297.11	     , if^#(false(), x) -> c_4()
783.15/297.11	     , le^#(0(), y) -> c_5()
783.15/297.11	     , le^#(s(x), 0()) -> c_6()
783.15/297.11	     , le^#(s(x), s(y)) -> c_7(le^#(x, y))
783.15/297.11	     , nr^#() -> c_8(ack^#(s(s(s(s(s(s(0())))))), 0()))
783.15/297.11	     , ack^#(0(), x) -> c_9(x)
783.15/297.11	     , ack^#(s(x), 0()) -> c_10(ack^#(x, s(0())))
783.15/297.11	     , ack^#(s(x), s(y)) -> c_11(ack^#(x, ack(s(x), y))) }
783.15/297.11	   
783.15/297.11	   and mark the set of starting terms.
783.15/297.11	   
783.15/297.11	   We are left with following problem, upon which TcT provides the
783.15/297.11	   certificate MAYBE.
783.15/297.11	   
783.15/297.11	   Strict DPs:
783.15/297.11	     { numbers^#() -> c_1(d^#(0()))
783.15/297.11	     , d^#(x) -> c_2(if^#(le(x, nr()), x))
783.15/297.11	     , if^#(true(), x) -> c_3(x, d^#(s(x)))
783.15/297.11	     , if^#(false(), x) -> c_4()
783.15/297.11	     , le^#(0(), y) -> c_5()
783.15/297.11	     , le^#(s(x), 0()) -> c_6()
783.15/297.11	     , le^#(s(x), s(y)) -> c_7(le^#(x, y))
783.15/297.11	     , nr^#() -> c_8(ack^#(s(s(s(s(s(s(0())))))), 0()))
783.15/297.11	     , ack^#(0(), x) -> c_9(x)
783.15/297.11	     , ack^#(s(x), 0()) -> c_10(ack^#(x, s(0())))
783.15/297.11	     , ack^#(s(x), s(y)) -> c_11(ack^#(x, ack(s(x), y))) }
783.15/297.11	   Strict Trs:
783.15/297.11	     { numbers() -> d(0())
783.15/297.11	     , d(x) -> if(le(x, nr()), x)
783.15/297.11	     , if(true(), x) -> cons(x, d(s(x)))
783.15/297.11	     , if(false(), x) -> nil()
783.15/297.11	     , le(0(), y) -> true()
783.15/297.11	     , le(s(x), 0()) -> false()
783.15/297.11	     , le(s(x), s(y)) -> le(x, y)
783.15/297.11	     , nr() -> ack(s(s(s(s(s(s(0())))))), 0())
783.15/297.11	     , ack(0(), x) -> s(x)
783.15/297.11	     , ack(s(x), 0()) -> ack(x, s(0()))
783.15/297.11	     , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
783.15/297.11	   Obligation:
783.15/297.11	     runtime complexity
783.15/297.11	   Answer:
783.15/297.11	     MAYBE
783.15/297.11	   
783.15/297.11	   We estimate the number of application of {4,5,6} by applications of
783.15/297.11	   Pre({4,5,6}) = {2,3,7,9}. Here rules are labeled as follows:
783.15/297.11	   
783.15/297.11	     DPs:
783.15/297.11	       { 1: numbers^#() -> c_1(d^#(0()))
783.15/297.11	       , 2: d^#(x) -> c_2(if^#(le(x, nr()), x))
783.15/297.11	       , 3: if^#(true(), x) -> c_3(x, d^#(s(x)))
783.15/297.11	       , 4: if^#(false(), x) -> c_4()
783.15/297.11	       , 5: le^#(0(), y) -> c_5()
783.15/297.11	       , 6: le^#(s(x), 0()) -> c_6()
783.15/297.11	       , 7: le^#(s(x), s(y)) -> c_7(le^#(x, y))
783.15/297.11	       , 8: nr^#() -> c_8(ack^#(s(s(s(s(s(s(0())))))), 0()))
783.15/297.11	       , 9: ack^#(0(), x) -> c_9(x)
783.15/297.11	       , 10: ack^#(s(x), 0()) -> c_10(ack^#(x, s(0())))
783.15/297.11	       , 11: ack^#(s(x), s(y)) -> c_11(ack^#(x, ack(s(x), y))) }
783.15/297.11	   
783.15/297.11	   We are left with following problem, upon which TcT provides the
783.15/297.11	   certificate MAYBE.
783.15/297.11	   
783.15/297.11	   Strict DPs:
783.15/297.11	     { numbers^#() -> c_1(d^#(0()))
783.15/297.11	     , d^#(x) -> c_2(if^#(le(x, nr()), x))
783.15/297.11	     , if^#(true(), x) -> c_3(x, d^#(s(x)))
783.15/297.11	     , le^#(s(x), s(y)) -> c_7(le^#(x, y))
783.15/297.11	     , nr^#() -> c_8(ack^#(s(s(s(s(s(s(0())))))), 0()))
783.15/297.11	     , ack^#(0(), x) -> c_9(x)
783.15/297.11	     , ack^#(s(x), 0()) -> c_10(ack^#(x, s(0())))
783.15/297.11	     , ack^#(s(x), s(y)) -> c_11(ack^#(x, ack(s(x), y))) }
783.15/297.11	   Strict Trs:
783.15/297.11	     { numbers() -> d(0())
783.15/297.11	     , d(x) -> if(le(x, nr()), x)
783.15/297.11	     , if(true(), x) -> cons(x, d(s(x)))
783.15/297.11	     , if(false(), x) -> nil()
783.15/297.11	     , le(0(), y) -> true()
783.15/297.11	     , le(s(x), 0()) -> false()
783.15/297.11	     , le(s(x), s(y)) -> le(x, y)
783.15/297.11	     , nr() -> ack(s(s(s(s(s(s(0())))))), 0())
783.15/297.11	     , ack(0(), x) -> s(x)
783.15/297.11	     , ack(s(x), 0()) -> ack(x, s(0()))
783.15/297.11	     , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
783.15/297.11	   Weak DPs:
783.15/297.11	     { if^#(false(), x) -> c_4()
783.15/297.11	     , le^#(0(), y) -> c_5()
783.15/297.11	     , le^#(s(x), 0()) -> c_6() }
783.15/297.11	   Obligation:
783.15/297.11	     runtime complexity
783.15/297.11	   Answer:
783.15/297.11	     MAYBE
783.15/297.11	   
783.15/297.11	   Empty strict component of the problem is NOT empty.
783.15/297.11	
783.15/297.11	
783.15/297.11	Arrrr..
783.37/297.34	EOF