MAYBE
818.69/297.03	MAYBE
818.69/297.03	
818.69/297.03	We are left with following problem, upon which TcT provides the
818.69/297.03	certificate MAYBE.
818.69/297.03	
818.69/297.03	Strict Trs:
818.69/297.03	  { check(0()) -> zero()
818.69/297.03	  , check(s(0())) -> odd()
818.69/297.03	  , check(s(s(0()))) -> even()
818.69/297.03	  , check(s(s(s(x)))) -> check(s(x))
818.69/297.03	  , half(0()) -> 0()
818.69/297.03	  , half(s(0())) -> 0()
818.69/297.03	  , half(s(s(x))) -> s(half(x))
818.69/297.03	  , plus(0(), y) -> y
818.69/297.03	  , plus(s(x), y) -> s(plus(x, y))
818.69/297.03	  , times(x, y) -> timesIter(x, y, 0())
818.69/297.03	  , timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
818.69/297.03	  , if(zero(), x, y, z, u) -> z
818.69/297.03	  , if(odd(), x, y, z, u) -> timesIter(p(x), y, u)
818.69/297.03	  , if(even(), x, y, z, u) ->
818.69/297.03	    plus(timesIter(half(x), y, half(z)),
818.69/297.03	         timesIter(half(x), y, half(s(z))))
818.69/297.03	  , p(0()) -> 0()
818.69/297.03	  , p(s(x)) -> x }
818.69/297.03	Obligation:
818.69/297.03	  runtime complexity
818.69/297.03	Answer:
818.69/297.03	  MAYBE
818.69/297.03	
818.69/297.03	None of the processors succeeded.
818.69/297.03	
818.69/297.03	Details of failed attempt(s):
818.69/297.03	-----------------------------
818.69/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
818.69/297.03	   following reason:
818.69/297.03	   
818.69/297.03	   Computation stopped due to timeout after 297.0 seconds.
818.69/297.03	
818.69/297.03	2) 'Best' failed due to the following reason:
818.69/297.03	   
818.69/297.03	   None of the processors succeeded.
818.69/297.03	   
818.69/297.03	   Details of failed attempt(s):
818.69/297.03	   -----------------------------
818.69/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
818.69/297.03	      seconds)' failed due to the following reason:
818.69/297.03	      
818.69/297.03	      Computation stopped due to timeout after 148.0 seconds.
818.69/297.03	   
818.69/297.03	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
818.69/297.03	      failed due to the following reason:
818.69/297.03	      
818.69/297.03	      None of the processors succeeded.
818.69/297.03	      
818.69/297.03	      Details of failed attempt(s):
818.69/297.03	      -----------------------------
818.69/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
818.69/297.03	         failed due to the following reason:
818.69/297.03	         
818.69/297.03	         match-boundness of the problem could not be verified.
818.69/297.03	      
818.69/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
818.69/297.03	         failed due to the following reason:
818.69/297.03	         
818.69/297.03	         match-boundness of the problem could not be verified.
818.69/297.03	      
818.69/297.03	   
818.69/297.03	   3) 'Best' failed due to the following reason:
818.69/297.03	      
818.69/297.03	      None of the processors succeeded.
818.69/297.03	      
818.69/297.03	      Details of failed attempt(s):
818.69/297.03	      -----------------------------
818.69/297.03	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
818.69/297.03	         following reason:
818.69/297.03	         
818.69/297.03	         The processor is inapplicable, reason:
818.69/297.03	           Processor only applicable for innermost runtime complexity analysis
818.69/297.03	      
818.69/297.03	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
818.69/297.03	         to the following reason:
818.69/297.03	         
818.69/297.03	         The processor is inapplicable, reason:
818.69/297.03	           Processor only applicable for innermost runtime complexity analysis
818.69/297.03	      
818.69/297.03	   
818.69/297.03	
818.69/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
818.69/297.03	   the following reason:
818.69/297.03	   
818.69/297.03	   We add the following weak dependency pairs:
818.69/297.03	   
818.69/297.03	   Strict DPs:
818.69/297.03	     { check^#(0()) -> c_1()
818.69/297.03	     , check^#(s(0())) -> c_2()
818.69/297.03	     , check^#(s(s(0()))) -> c_3()
818.69/297.03	     , check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
818.69/297.03	     , half^#(0()) -> c_5()
818.69/297.03	     , half^#(s(0())) -> c_6()
818.69/297.03	     , half^#(s(s(x))) -> c_7(half^#(x))
818.69/297.03	     , plus^#(0(), y) -> c_8(y)
818.69/297.03	     , plus^#(s(x), y) -> c_9(plus^#(x, y))
818.69/297.03	     , times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
818.69/297.03	     , timesIter^#(x, y, z) -> c_11(if^#(check(x), x, y, z, plus(z, y)))
818.69/297.03	     , if^#(zero(), x, y, z, u) -> c_12(z)
818.69/297.03	     , if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
818.69/297.03	     , if^#(even(), x, y, z, u) ->
818.69/297.03	       c_14(plus^#(timesIter(half(x), y, half(z)),
818.69/297.03	                   timesIter(half(x), y, half(s(z)))))
818.69/297.03	     , p^#(0()) -> c_15()
818.69/297.03	     , p^#(s(x)) -> c_16(x) }
818.69/297.03	   
818.69/297.03	   and mark the set of starting terms.
818.69/297.03	   
818.69/297.03	   We are left with following problem, upon which TcT provides the
818.69/297.03	   certificate MAYBE.
818.69/297.03	   
818.69/297.03	   Strict DPs:
818.69/297.03	     { check^#(0()) -> c_1()
818.69/297.03	     , check^#(s(0())) -> c_2()
818.69/297.03	     , check^#(s(s(0()))) -> c_3()
818.69/297.03	     , check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
818.69/297.03	     , half^#(0()) -> c_5()
818.69/297.03	     , half^#(s(0())) -> c_6()
818.69/297.03	     , half^#(s(s(x))) -> c_7(half^#(x))
818.69/297.03	     , plus^#(0(), y) -> c_8(y)
818.69/297.03	     , plus^#(s(x), y) -> c_9(plus^#(x, y))
818.69/297.03	     , times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
818.69/297.03	     , timesIter^#(x, y, z) -> c_11(if^#(check(x), x, y, z, plus(z, y)))
818.69/297.03	     , if^#(zero(), x, y, z, u) -> c_12(z)
818.69/297.03	     , if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
818.69/297.03	     , if^#(even(), x, y, z, u) ->
818.69/297.03	       c_14(plus^#(timesIter(half(x), y, half(z)),
818.69/297.03	                   timesIter(half(x), y, half(s(z)))))
818.69/297.03	     , p^#(0()) -> c_15()
818.69/297.03	     , p^#(s(x)) -> c_16(x) }
818.69/297.03	   Strict Trs:
818.69/297.03	     { check(0()) -> zero()
818.69/297.03	     , check(s(0())) -> odd()
818.69/297.03	     , check(s(s(0()))) -> even()
818.69/297.03	     , check(s(s(s(x)))) -> check(s(x))
818.69/297.03	     , half(0()) -> 0()
818.69/297.03	     , half(s(0())) -> 0()
818.69/297.03	     , half(s(s(x))) -> s(half(x))
818.69/297.03	     , plus(0(), y) -> y
818.69/297.03	     , plus(s(x), y) -> s(plus(x, y))
818.69/297.03	     , times(x, y) -> timesIter(x, y, 0())
818.69/297.03	     , timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
818.69/297.03	     , if(zero(), x, y, z, u) -> z
818.69/297.03	     , if(odd(), x, y, z, u) -> timesIter(p(x), y, u)
818.69/297.03	     , if(even(), x, y, z, u) ->
818.69/297.03	       plus(timesIter(half(x), y, half(z)),
818.69/297.03	            timesIter(half(x), y, half(s(z))))
818.69/297.03	     , p(0()) -> 0()
818.69/297.03	     , p(s(x)) -> x }
818.69/297.03	   Obligation:
818.69/297.03	     runtime complexity
818.69/297.03	   Answer:
818.69/297.03	     MAYBE
818.69/297.03	   
818.69/297.03	   We estimate the number of application of {1,2,3,5,6,15} by
818.69/297.03	   applications of Pre({1,2,3,5,6,15}) = {4,7,8,12,16}. Here rules are
818.69/297.03	   labeled as follows:
818.69/297.03	   
818.69/297.03	     DPs:
818.69/297.03	       { 1: check^#(0()) -> c_1()
818.69/297.03	       , 2: check^#(s(0())) -> c_2()
818.69/297.03	       , 3: check^#(s(s(0()))) -> c_3()
818.69/297.03	       , 4: check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
818.69/297.03	       , 5: half^#(0()) -> c_5()
818.69/297.03	       , 6: half^#(s(0())) -> c_6()
818.69/297.03	       , 7: half^#(s(s(x))) -> c_7(half^#(x))
818.69/297.03	       , 8: plus^#(0(), y) -> c_8(y)
818.69/297.03	       , 9: plus^#(s(x), y) -> c_9(plus^#(x, y))
818.69/297.03	       , 10: times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
818.69/297.03	       , 11: timesIter^#(x, y, z) ->
818.69/297.03	             c_11(if^#(check(x), x, y, z, plus(z, y)))
818.69/297.03	       , 12: if^#(zero(), x, y, z, u) -> c_12(z)
818.69/297.03	       , 13: if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
818.69/297.03	       , 14: if^#(even(), x, y, z, u) ->
818.69/297.03	             c_14(plus^#(timesIter(half(x), y, half(z)),
818.69/297.03	                         timesIter(half(x), y, half(s(z)))))
818.69/297.03	       , 15: p^#(0()) -> c_15()
818.69/297.03	       , 16: p^#(s(x)) -> c_16(x) }
818.69/297.03	   
818.69/297.03	   We are left with following problem, upon which TcT provides the
818.69/297.03	   certificate MAYBE.
818.69/297.03	   
818.69/297.03	   Strict DPs:
818.69/297.03	     { check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
818.69/297.03	     , half^#(s(s(x))) -> c_7(half^#(x))
818.69/297.03	     , plus^#(0(), y) -> c_8(y)
818.69/297.03	     , plus^#(s(x), y) -> c_9(plus^#(x, y))
818.69/297.03	     , times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
818.69/297.03	     , timesIter^#(x, y, z) -> c_11(if^#(check(x), x, y, z, plus(z, y)))
818.69/297.03	     , if^#(zero(), x, y, z, u) -> c_12(z)
818.69/297.03	     , if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
818.69/297.03	     , if^#(even(), x, y, z, u) ->
818.69/297.03	       c_14(plus^#(timesIter(half(x), y, half(z)),
818.69/297.03	                   timesIter(half(x), y, half(s(z)))))
818.69/297.03	     , p^#(s(x)) -> c_16(x) }
818.69/297.03	   Strict Trs:
818.69/297.03	     { check(0()) -> zero()
818.69/297.03	     , check(s(0())) -> odd()
818.69/297.03	     , check(s(s(0()))) -> even()
818.69/297.03	     , check(s(s(s(x)))) -> check(s(x))
818.69/297.03	     , half(0()) -> 0()
818.69/297.03	     , half(s(0())) -> 0()
818.69/297.03	     , half(s(s(x))) -> s(half(x))
818.69/297.03	     , plus(0(), y) -> y
818.69/297.03	     , plus(s(x), y) -> s(plus(x, y))
818.69/297.03	     , times(x, y) -> timesIter(x, y, 0())
818.69/297.03	     , timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
818.69/297.03	     , if(zero(), x, y, z, u) -> z
818.69/297.03	     , if(odd(), x, y, z, u) -> timesIter(p(x), y, u)
818.69/297.03	     , if(even(), x, y, z, u) ->
818.69/297.03	       plus(timesIter(half(x), y, half(z)),
818.69/297.03	            timesIter(half(x), y, half(s(z))))
818.69/297.03	     , p(0()) -> 0()
818.69/297.03	     , p(s(x)) -> x }
818.69/297.03	   Weak DPs:
818.69/297.03	     { check^#(0()) -> c_1()
818.69/297.03	     , check^#(s(0())) -> c_2()
818.69/297.03	     , check^#(s(s(0()))) -> c_3()
818.69/297.03	     , half^#(0()) -> c_5()
818.69/297.03	     , half^#(s(0())) -> c_6()
818.69/297.03	     , p^#(0()) -> c_15() }
818.69/297.03	   Obligation:
818.69/297.03	     runtime complexity
818.69/297.03	   Answer:
818.69/297.03	     MAYBE
818.69/297.03	   
818.69/297.03	   Empty strict component of the problem is NOT empty.
818.69/297.03	
818.69/297.03	
818.69/297.03	Arrrr..
818.89/297.24	EOF