MAYBE
868.38/297.04	MAYBE
868.38/297.04	
868.38/297.04	We are left with following problem, upon which TcT provides the
868.38/297.04	certificate MAYBE.
868.38/297.04	
868.38/297.04	Strict Trs:
868.38/297.04	  { times(x, plus(y, 1())) ->
868.38/297.04	    plus(times(x, plus(y, times(1(), 0()))), x)
868.38/297.04	  , times(x, 1()) -> x
868.38/297.04	  , times(x, 0()) -> 0()
868.38/297.04	  , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
868.38/297.04	  , plus(s(x), s(y)) ->
868.38/297.04	    s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
868.38/297.04	  , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	  , plus(zero(), y) -> y
868.38/297.04	  , if(true(), x, y) -> x
868.38/297.04	  , if(false(), x, y) -> y
868.38/297.04	  , gt(s(x), s(y)) -> gt(x, y)
868.38/297.04	  , gt(s(x), zero()) -> true()
868.38/297.04	  , gt(zero(), y) -> false()
868.38/297.04	  , not(x) -> if(x, false(), true())
868.38/297.04	  , id(x) -> x }
868.38/297.04	Obligation:
868.38/297.04	  runtime complexity
868.38/297.04	Answer:
868.38/297.04	  MAYBE
868.38/297.04	
868.38/297.04	None of the processors succeeded.
868.38/297.04	
868.38/297.04	Details of failed attempt(s):
868.38/297.04	-----------------------------
868.38/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
868.38/297.04	   following reason:
868.38/297.04	   
868.38/297.04	   Computation stopped due to timeout after 297.0 seconds.
868.38/297.04	
868.38/297.04	2) 'Best' failed due to the following reason:
868.38/297.04	   
868.38/297.04	   None of the processors succeeded.
868.38/297.04	   
868.38/297.04	   Details of failed attempt(s):
868.38/297.04	   -----------------------------
868.38/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
868.38/297.04	      seconds)' failed due to the following reason:
868.38/297.04	      
868.38/297.04	      Computation stopped due to timeout after 148.0 seconds.
868.38/297.04	   
868.38/297.04	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
868.38/297.04	      failed due to the following reason:
868.38/297.04	      
868.38/297.04	      None of the processors succeeded.
868.38/297.04	      
868.38/297.04	      Details of failed attempt(s):
868.38/297.04	      -----------------------------
868.38/297.04	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
868.38/297.04	         failed due to the following reason:
868.38/297.04	         
868.38/297.04	         match-boundness of the problem could not be verified.
868.38/297.04	      
868.38/297.04	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
868.38/297.04	         failed due to the following reason:
868.38/297.04	         
868.38/297.04	         match-boundness of the problem could not be verified.
868.38/297.04	      
868.38/297.04	   
868.38/297.04	   3) 'Best' failed due to the following reason:
868.38/297.04	      
868.38/297.04	      None of the processors succeeded.
868.38/297.04	      
868.38/297.04	      Details of failed attempt(s):
868.38/297.04	      -----------------------------
868.38/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
868.38/297.04	         following reason:
868.38/297.04	         
868.38/297.04	         The processor is inapplicable, reason:
868.38/297.04	           Processor only applicable for innermost runtime complexity analysis
868.38/297.04	      
868.38/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
868.38/297.04	         to the following reason:
868.38/297.04	         
868.38/297.04	         The processor is inapplicable, reason:
868.38/297.04	           Processor only applicable for innermost runtime complexity analysis
868.38/297.04	      
868.38/297.04	   
868.38/297.04	
868.38/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
868.38/297.04	   the following reason:
868.38/297.04	   
868.38/297.04	   We add the following weak dependency pairs:
868.38/297.04	   
868.38/297.04	   Strict DPs:
868.38/297.04	     { times^#(x, plus(y, 1())) ->
868.38/297.04	       c_1(plus^#(times(x, plus(y, times(1(), 0()))), x))
868.38/297.04	     , times^#(x, 1()) -> c_2(x)
868.38/297.04	     , times^#(x, 0()) -> c_3()
868.38/297.04	     , plus^#(s(x), x) -> c_4(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
868.38/297.04	     , plus^#(s(x), s(y)) ->
868.38/297.04	       c_5(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
868.38/297.04	     , plus^#(id(x), s(y)) -> c_6(plus^#(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	     , plus^#(zero(), y) -> c_7(y)
868.38/297.04	     , if^#(true(), x, y) -> c_8(x)
868.38/297.04	     , if^#(false(), x, y) -> c_9(y)
868.38/297.04	     , gt^#(s(x), s(y)) -> c_10(gt^#(x, y))
868.38/297.04	     , gt^#(s(x), zero()) -> c_11()
868.38/297.04	     , gt^#(zero(), y) -> c_12()
868.38/297.04	     , not^#(x) -> c_13(if^#(x, false(), true()))
868.38/297.04	     , id^#(x) -> c_14(x) }
868.38/297.04	   
868.38/297.04	   and mark the set of starting terms.
868.38/297.04	   
868.38/297.04	   We are left with following problem, upon which TcT provides the
868.38/297.04	   certificate MAYBE.
868.38/297.04	   
868.38/297.04	   Strict DPs:
868.38/297.04	     { times^#(x, plus(y, 1())) ->
868.38/297.04	       c_1(plus^#(times(x, plus(y, times(1(), 0()))), x))
868.38/297.04	     , times^#(x, 1()) -> c_2(x)
868.38/297.04	     , times^#(x, 0()) -> c_3()
868.38/297.04	     , plus^#(s(x), x) -> c_4(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
868.38/297.04	     , plus^#(s(x), s(y)) ->
868.38/297.04	       c_5(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
868.38/297.04	     , plus^#(id(x), s(y)) -> c_6(plus^#(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	     , plus^#(zero(), y) -> c_7(y)
868.38/297.04	     , if^#(true(), x, y) -> c_8(x)
868.38/297.04	     , if^#(false(), x, y) -> c_9(y)
868.38/297.04	     , gt^#(s(x), s(y)) -> c_10(gt^#(x, y))
868.38/297.04	     , gt^#(s(x), zero()) -> c_11()
868.38/297.04	     , gt^#(zero(), y) -> c_12()
868.38/297.04	     , not^#(x) -> c_13(if^#(x, false(), true()))
868.38/297.04	     , id^#(x) -> c_14(x) }
868.38/297.04	   Strict Trs:
868.38/297.04	     { times(x, plus(y, 1())) ->
868.38/297.04	       plus(times(x, plus(y, times(1(), 0()))), x)
868.38/297.04	     , times(x, 1()) -> x
868.38/297.04	     , times(x, 0()) -> 0()
868.38/297.04	     , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
868.38/297.04	     , plus(s(x), s(y)) ->
868.38/297.04	       s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
868.38/297.04	     , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	     , plus(zero(), y) -> y
868.38/297.04	     , if(true(), x, y) -> x
868.38/297.04	     , if(false(), x, y) -> y
868.38/297.04	     , gt(s(x), s(y)) -> gt(x, y)
868.38/297.04	     , gt(s(x), zero()) -> true()
868.38/297.04	     , gt(zero(), y) -> false()
868.38/297.04	     , not(x) -> if(x, false(), true())
868.38/297.04	     , id(x) -> x }
868.38/297.04	   Obligation:
868.38/297.04	     runtime complexity
868.38/297.04	   Answer:
868.38/297.04	     MAYBE
868.38/297.04	   
868.38/297.04	   We estimate the number of application of {3,11,12} by applications
868.38/297.04	   of Pre({3,11,12}) = {2,7,8,9,10,14}. Here rules are labeled as
868.38/297.04	   follows:
868.38/297.04	   
868.38/297.04	     DPs:
868.38/297.04	       { 1: times^#(x, plus(y, 1())) ->
868.38/297.04	            c_1(plus^#(times(x, plus(y, times(1(), 0()))), x))
868.38/297.04	       , 2: times^#(x, 1()) -> c_2(x)
868.38/297.04	       , 3: times^#(x, 0()) -> c_3()
868.38/297.04	       , 4: plus^#(s(x), x) ->
868.38/297.04	            c_4(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
868.38/297.04	       , 5: plus^#(s(x), s(y)) ->
868.38/297.04	            c_5(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
868.38/297.04	       , 6: plus^#(id(x), s(y)) ->
868.38/297.04	            c_6(plus^#(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	       , 7: plus^#(zero(), y) -> c_7(y)
868.38/297.04	       , 8: if^#(true(), x, y) -> c_8(x)
868.38/297.04	       , 9: if^#(false(), x, y) -> c_9(y)
868.38/297.04	       , 10: gt^#(s(x), s(y)) -> c_10(gt^#(x, y))
868.38/297.04	       , 11: gt^#(s(x), zero()) -> c_11()
868.38/297.04	       , 12: gt^#(zero(), y) -> c_12()
868.38/297.04	       , 13: not^#(x) -> c_13(if^#(x, false(), true()))
868.38/297.04	       , 14: id^#(x) -> c_14(x) }
868.38/297.04	   
868.38/297.04	   We are left with following problem, upon which TcT provides the
868.38/297.04	   certificate MAYBE.
868.38/297.04	   
868.38/297.04	   Strict DPs:
868.38/297.04	     { times^#(x, plus(y, 1())) ->
868.38/297.04	       c_1(plus^#(times(x, plus(y, times(1(), 0()))), x))
868.38/297.04	     , times^#(x, 1()) -> c_2(x)
868.38/297.04	     , plus^#(s(x), x) -> c_4(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
868.38/297.04	     , plus^#(s(x), s(y)) ->
868.38/297.04	       c_5(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
868.38/297.04	     , plus^#(id(x), s(y)) -> c_6(plus^#(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	     , plus^#(zero(), y) -> c_7(y)
868.38/297.04	     , if^#(true(), x, y) -> c_8(x)
868.38/297.04	     , if^#(false(), x, y) -> c_9(y)
868.38/297.04	     , gt^#(s(x), s(y)) -> c_10(gt^#(x, y))
868.38/297.04	     , not^#(x) -> c_13(if^#(x, false(), true()))
868.38/297.04	     , id^#(x) -> c_14(x) }
868.38/297.04	   Strict Trs:
868.38/297.04	     { times(x, plus(y, 1())) ->
868.38/297.04	       plus(times(x, plus(y, times(1(), 0()))), x)
868.38/297.04	     , times(x, 1()) -> x
868.38/297.04	     , times(x, 0()) -> 0()
868.38/297.04	     , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
868.38/297.04	     , plus(s(x), s(y)) ->
868.38/297.04	       s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
868.38/297.04	     , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
868.38/297.04	     , plus(zero(), y) -> y
868.38/297.04	     , if(true(), x, y) -> x
868.38/297.04	     , if(false(), x, y) -> y
868.38/297.04	     , gt(s(x), s(y)) -> gt(x, y)
868.38/297.04	     , gt(s(x), zero()) -> true()
868.38/297.04	     , gt(zero(), y) -> false()
868.38/297.04	     , not(x) -> if(x, false(), true())
868.38/297.04	     , id(x) -> x }
868.38/297.04	   Weak DPs:
868.38/297.04	     { times^#(x, 0()) -> c_3()
868.38/297.04	     , gt^#(s(x), zero()) -> c_11()
868.38/297.04	     , gt^#(zero(), y) -> c_12() }
868.38/297.04	   Obligation:
868.38/297.04	     runtime complexity
868.38/297.04	   Answer:
868.38/297.04	     MAYBE
868.38/297.04	   
868.38/297.04	   Empty strict component of the problem is NOT empty.
868.38/297.04	
868.38/297.04	
868.38/297.04	Arrrr..
868.59/297.23	EOF