MAYBE
606.64/205.85	MAYBE
606.64/205.85	
606.64/205.85	We are left with following problem, upon which TcT provides the
606.64/205.85	certificate MAYBE.
606.64/205.85	
606.64/205.85	Strict Trs:
606.64/205.85	  { half(0()) -> 0()
606.64/205.85	  , half(s(0())) -> 0()
606.64/205.85	  , half(s(s(x))) -> s(half(x))
606.64/205.85	  , le(0(), y) -> true()
606.64/205.85	  , le(s(x), 0()) -> false()
606.64/205.85	  , le(s(x), s(y)) -> le(x, y)
606.64/205.85	  , inc(0()) -> s(0())
606.64/205.85	  , inc(s(x)) -> s(inc(x))
606.64/205.85	  , logarithm(x) -> logIter(x, 0())
606.64/205.85	  , logIter(x, y) ->
606.64/205.85	    if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
606.64/205.85	  , if(true(), true(), x, y) -> logIter(x, y)
606.64/205.85	  , if(true(), false(), x, s(y)) -> y
606.64/205.85	  , if(false(), b, x, y) -> logZeroError()
606.64/205.85	  , f() -> g()
606.64/205.85	  , f() -> h() }
606.64/205.85	Obligation:
606.64/205.85	  runtime complexity
606.64/205.85	Answer:
606.64/205.85	  MAYBE
606.64/205.85	
606.64/205.85	None of the processors succeeded.
606.64/205.85	
606.64/205.85	Details of failed attempt(s):
606.64/205.85	-----------------------------
606.64/205.85	1) 'Best' failed due to the following reason:
606.64/205.85	   
606.64/205.85	   None of the processors succeeded.
606.64/205.85	   
606.64/205.85	   Details of failed attempt(s):
606.64/205.85	   -----------------------------
606.64/205.85	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
606.64/205.85	      seconds)' failed due to the following reason:
606.64/205.85	      
606.64/205.85	      Computation stopped due to timeout after 148.0 seconds.
606.64/205.85	   
606.64/205.85	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
606.64/205.85	      failed due to the following reason:
606.64/205.85	      
606.64/205.85	      None of the processors succeeded.
606.64/205.85	      
606.64/205.85	      Details of failed attempt(s):
606.64/205.85	      -----------------------------
606.64/205.85	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
606.64/205.85	         failed due to the following reason:
606.64/205.85	         
606.64/205.85	         match-boundness of the problem could not be verified.
606.64/205.85	      
606.64/205.85	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
606.64/205.85	         failed due to the following reason:
606.64/205.85	         
606.64/205.85	         match-boundness of the problem could not be verified.
606.64/205.85	      
606.64/205.85	   
606.64/205.85	   3) 'Best' failed due to the following reason:
606.64/205.85	      
606.64/205.85	      None of the processors succeeded.
606.64/205.85	      
606.64/205.85	      Details of failed attempt(s):
606.64/205.85	      -----------------------------
606.64/205.85	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
606.64/205.85	         following reason:
606.64/205.85	         
606.64/205.85	         The processor is inapplicable, reason:
606.64/205.85	           Processor only applicable for innermost runtime complexity analysis
606.64/205.85	      
606.64/205.85	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
606.64/205.85	         to the following reason:
606.64/205.85	         
606.64/205.85	         The processor is inapplicable, reason:
606.64/205.85	           Processor only applicable for innermost runtime complexity analysis
606.64/205.85	      
606.64/205.85	   
606.64/205.85	
606.64/205.85	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
606.64/205.85	   the following reason:
606.64/205.85	   
606.64/205.85	   We add the following weak dependency pairs:
606.64/205.85	   
606.64/205.85	   Strict DPs:
606.64/205.85	     { half^#(0()) -> c_1()
606.64/205.85	     , half^#(s(0())) -> c_2()
606.64/205.85	     , half^#(s(s(x))) -> c_3(half^#(x))
606.64/205.85	     , le^#(0(), y) -> c_4()
606.64/205.85	     , le^#(s(x), 0()) -> c_5()
606.64/205.85	     , le^#(s(x), s(y)) -> c_6(le^#(x, y))
606.64/205.85	     , inc^#(0()) -> c_7()
606.64/205.85	     , inc^#(s(x)) -> c_8(inc^#(x))
606.64/205.85	     , logarithm^#(x) -> c_9(logIter^#(x, 0()))
606.64/205.85	     , logIter^#(x, y) ->
606.64/205.85	       c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
606.64/205.85	     , if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
606.64/205.85	     , if^#(true(), false(), x, s(y)) -> c_12(y)
606.64/205.85	     , if^#(false(), b, x, y) -> c_13()
606.64/205.85	     , f^#() -> c_14()
606.64/205.85	     , f^#() -> c_15() }
606.64/205.85	   
606.64/205.85	   and mark the set of starting terms.
606.64/205.85	   
606.64/205.85	   We are left with following problem, upon which TcT provides the
606.64/205.85	   certificate MAYBE.
606.64/205.85	   
606.64/205.85	   Strict DPs:
606.64/205.85	     { half^#(0()) -> c_1()
606.64/205.85	     , half^#(s(0())) -> c_2()
606.64/205.85	     , half^#(s(s(x))) -> c_3(half^#(x))
606.64/205.85	     , le^#(0(), y) -> c_4()
606.64/205.85	     , le^#(s(x), 0()) -> c_5()
606.64/205.85	     , le^#(s(x), s(y)) -> c_6(le^#(x, y))
606.64/205.85	     , inc^#(0()) -> c_7()
606.64/205.85	     , inc^#(s(x)) -> c_8(inc^#(x))
606.64/205.85	     , logarithm^#(x) -> c_9(logIter^#(x, 0()))
606.64/205.85	     , logIter^#(x, y) ->
606.64/205.85	       c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
606.64/205.85	     , if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
606.64/205.85	     , if^#(true(), false(), x, s(y)) -> c_12(y)
606.64/205.85	     , if^#(false(), b, x, y) -> c_13()
606.64/205.85	     , f^#() -> c_14()
606.64/205.85	     , f^#() -> c_15() }
606.64/205.85	   Strict Trs:
606.64/205.85	     { half(0()) -> 0()
606.64/205.85	     , half(s(0())) -> 0()
606.64/205.85	     , half(s(s(x))) -> s(half(x))
606.64/205.85	     , le(0(), y) -> true()
606.64/205.85	     , le(s(x), 0()) -> false()
606.64/205.85	     , le(s(x), s(y)) -> le(x, y)
606.64/205.85	     , inc(0()) -> s(0())
606.64/205.85	     , inc(s(x)) -> s(inc(x))
606.64/205.85	     , logarithm(x) -> logIter(x, 0())
606.64/205.85	     , logIter(x, y) ->
606.64/205.85	       if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
606.64/205.85	     , if(true(), true(), x, y) -> logIter(x, y)
606.64/205.85	     , if(true(), false(), x, s(y)) -> y
606.64/205.85	     , if(false(), b, x, y) -> logZeroError()
606.64/205.85	     , f() -> g()
606.64/205.85	     , f() -> h() }
606.64/205.85	   Obligation:
606.64/205.85	     runtime complexity
606.64/205.85	   Answer:
606.64/205.85	     MAYBE
606.64/205.85	   
606.64/205.85	   We estimate the number of application of {1,2,4,5,7,13,14,15} by
606.64/205.85	   applications of Pre({1,2,4,5,7,13,14,15}) = {3,6,8,10,12}. Here
606.64/205.85	   rules are labeled as follows:
606.64/205.85	   
606.64/205.85	     DPs:
606.64/205.85	       { 1: half^#(0()) -> c_1()
606.64/205.85	       , 2: half^#(s(0())) -> c_2()
606.64/205.85	       , 3: half^#(s(s(x))) -> c_3(half^#(x))
606.64/205.85	       , 4: le^#(0(), y) -> c_4()
606.64/205.85	       , 5: le^#(s(x), 0()) -> c_5()
606.64/205.85	       , 6: le^#(s(x), s(y)) -> c_6(le^#(x, y))
606.64/205.85	       , 7: inc^#(0()) -> c_7()
606.64/205.85	       , 8: inc^#(s(x)) -> c_8(inc^#(x))
606.64/205.85	       , 9: logarithm^#(x) -> c_9(logIter^#(x, 0()))
606.64/205.85	       , 10: logIter^#(x, y) ->
606.64/205.85	             c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
606.64/205.85	       , 11: if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
606.64/205.85	       , 12: if^#(true(), false(), x, s(y)) -> c_12(y)
606.64/205.85	       , 13: if^#(false(), b, x, y) -> c_13()
606.64/205.85	       , 14: f^#() -> c_14()
606.64/205.85	       , 15: f^#() -> c_15() }
606.64/205.85	   
606.64/205.85	   We are left with following problem, upon which TcT provides the
606.64/205.85	   certificate MAYBE.
606.64/205.85	   
606.64/205.85	   Strict DPs:
606.64/205.85	     { half^#(s(s(x))) -> c_3(half^#(x))
606.64/205.85	     , le^#(s(x), s(y)) -> c_6(le^#(x, y))
606.64/205.85	     , inc^#(s(x)) -> c_8(inc^#(x))
606.64/205.85	     , logarithm^#(x) -> c_9(logIter^#(x, 0()))
606.64/205.85	     , logIter^#(x, y) ->
606.64/205.85	       c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
606.64/205.85	     , if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
606.64/205.85	     , if^#(true(), false(), x, s(y)) -> c_12(y) }
606.64/205.85	   Strict Trs:
606.64/205.85	     { half(0()) -> 0()
606.64/205.85	     , half(s(0())) -> 0()
606.64/205.85	     , half(s(s(x))) -> s(half(x))
606.64/205.85	     , le(0(), y) -> true()
606.64/205.85	     , le(s(x), 0()) -> false()
606.64/205.85	     , le(s(x), s(y)) -> le(x, y)
606.64/205.85	     , inc(0()) -> s(0())
606.64/205.85	     , inc(s(x)) -> s(inc(x))
606.64/205.85	     , logarithm(x) -> logIter(x, 0())
606.64/205.85	     , logIter(x, y) ->
606.64/205.85	       if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
606.64/205.85	     , if(true(), true(), x, y) -> logIter(x, y)
606.64/205.85	     , if(true(), false(), x, s(y)) -> y
606.64/205.85	     , if(false(), b, x, y) -> logZeroError()
606.64/205.85	     , f() -> g()
606.64/205.85	     , f() -> h() }
606.64/205.85	   Weak DPs:
606.64/205.85	     { half^#(0()) -> c_1()
606.64/205.85	     , half^#(s(0())) -> c_2()
606.64/205.85	     , le^#(0(), y) -> c_4()
606.64/205.85	     , le^#(s(x), 0()) -> c_5()
606.64/205.85	     , inc^#(0()) -> c_7()
606.64/205.85	     , if^#(false(), b, x, y) -> c_13()
606.64/205.85	     , f^#() -> c_14()
606.64/205.85	     , f^#() -> c_15() }
606.64/205.85	   Obligation:
606.64/205.85	     runtime complexity
606.64/205.85	   Answer:
606.64/205.85	     MAYBE
606.64/205.85	   
606.64/205.85	   Empty strict component of the problem is NOT empty.
606.64/205.85	
606.64/205.85	
606.64/205.85	Arrrr..
607.19/206.35	EOF