MAYBE
826.22/297.10	MAYBE
826.22/297.10	
826.22/297.10	We are left with following problem, upon which TcT provides the
826.22/297.10	certificate MAYBE.
826.22/297.10	
826.22/297.10	Strict Trs:
826.22/297.10	  { lt(x, 0()) -> false()
826.22/297.10	  , lt(0(), s(x)) -> true()
826.22/297.10	  , lt(s(x), s(y)) -> lt(x, y)
826.22/297.10	  , fibo(0()) -> fib(0())
826.22/297.10	  , fibo(s(0())) -> fib(s(0()))
826.22/297.10	  , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
826.22/297.10	  , fib(0()) -> s(0())
826.22/297.10	  , fib(s(0())) -> s(0())
826.22/297.10	  , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
826.22/297.10	  , sum(x, 0()) -> x
826.22/297.10	  , sum(x, s(y)) -> s(sum(x, y))
826.22/297.10	  , if(true(), c, s(s(x)), a, b) ->
826.22/297.10	    if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c)
826.22/297.10	  , if(false(), c, s(s(x)), a, b) -> sum(fibo(a), fibo(b)) }
826.22/297.10	Obligation:
826.22/297.10	  runtime complexity
826.22/297.10	Answer:
826.22/297.10	  MAYBE
826.22/297.10	
826.22/297.10	None of the processors succeeded.
826.22/297.10	
826.22/297.10	Details of failed attempt(s):
826.22/297.10	-----------------------------
826.22/297.10	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
826.22/297.10	   following reason:
826.22/297.10	   
826.22/297.10	   Computation stopped due to timeout after 297.0 seconds.
826.22/297.10	
826.22/297.10	2) 'Best' failed due to the following reason:
826.22/297.10	   
826.22/297.10	   None of the processors succeeded.
826.22/297.10	   
826.22/297.10	   Details of failed attempt(s):
826.22/297.10	   -----------------------------
826.22/297.10	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
826.22/297.10	      seconds)' failed due to the following reason:
826.22/297.10	      
826.22/297.10	      Computation stopped due to timeout after 148.0 seconds.
826.22/297.10	   
826.22/297.10	   2) 'Best' failed due to the following reason:
826.22/297.10	      
826.22/297.10	      None of the processors succeeded.
826.22/297.10	      
826.22/297.10	      Details of failed attempt(s):
826.22/297.10	      -----------------------------
826.22/297.10	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
826.22/297.10	         to the following reason:
826.22/297.10	         
826.22/297.10	         The processor is inapplicable, reason:
826.22/297.10	           Processor only applicable for innermost runtime complexity analysis
826.22/297.10	      
826.22/297.10	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
826.22/297.10	         following reason:
826.22/297.10	         
826.22/297.10	         The processor is inapplicable, reason:
826.22/297.10	           Processor only applicable for innermost runtime complexity analysis
826.22/297.10	      
826.22/297.10	   
826.22/297.10	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
826.22/297.10	      failed due to the following reason:
826.22/297.10	      
826.22/297.10	      None of the processors succeeded.
826.22/297.10	      
826.22/297.10	      Details of failed attempt(s):
826.22/297.10	      -----------------------------
826.22/297.10	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
826.22/297.10	         failed due to the following reason:
826.22/297.10	         
826.22/297.10	         match-boundness of the problem could not be verified.
826.22/297.10	      
826.22/297.10	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
826.22/297.10	         failed due to the following reason:
826.22/297.10	         
826.22/297.10	         match-boundness of the problem could not be verified.
826.22/297.10	      
826.22/297.10	   
826.22/297.10	
826.22/297.10	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
826.22/297.10	   the following reason:
826.22/297.10	   
826.22/297.10	   We add the following weak dependency pairs:
826.22/297.10	   
826.22/297.10	   Strict DPs:
826.22/297.10	     { lt^#(x, 0()) -> c_1()
826.22/297.10	     , lt^#(0(), s(x)) -> c_2()
826.22/297.10	     , lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
826.22/297.10	     , fibo^#(0()) -> c_4(fib^#(0()))
826.22/297.10	     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
826.22/297.10	     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
826.22/297.10	     , fib^#(0()) -> c_7()
826.22/297.10	     , fib^#(s(0())) -> c_8()
826.22/297.10	     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
826.22/297.10	     , sum^#(x, 0()) -> c_10(x)
826.22/297.10	     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
826.22/297.10	     , if^#(true(), c, s(s(x)), a, b) ->
826.22/297.10	       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
826.22/297.10	     , if^#(false(), c, s(s(x)), a, b) ->
826.22/297.10	       c_13(sum^#(fibo(a), fibo(b))) }
826.22/297.10	   
826.22/297.10	   and mark the set of starting terms.
826.22/297.10	   
826.22/297.10	   We are left with following problem, upon which TcT provides the
826.22/297.10	   certificate MAYBE.
826.22/297.10	   
826.22/297.10	   Strict DPs:
826.22/297.10	     { lt^#(x, 0()) -> c_1()
826.22/297.10	     , lt^#(0(), s(x)) -> c_2()
826.22/297.10	     , lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
826.22/297.10	     , fibo^#(0()) -> c_4(fib^#(0()))
826.22/297.10	     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
826.22/297.10	     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
826.22/297.10	     , fib^#(0()) -> c_7()
826.22/297.10	     , fib^#(s(0())) -> c_8()
826.22/297.10	     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
826.22/297.10	     , sum^#(x, 0()) -> c_10(x)
826.22/297.10	     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
826.22/297.10	     , if^#(true(), c, s(s(x)), a, b) ->
826.22/297.10	       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
826.22/297.10	     , if^#(false(), c, s(s(x)), a, b) ->
826.22/297.10	       c_13(sum^#(fibo(a), fibo(b))) }
826.22/297.10	   Strict Trs:
826.22/297.10	     { lt(x, 0()) -> false()
826.22/297.10	     , lt(0(), s(x)) -> true()
826.22/297.10	     , lt(s(x), s(y)) -> lt(x, y)
826.22/297.10	     , fibo(0()) -> fib(0())
826.22/297.10	     , fibo(s(0())) -> fib(s(0()))
826.22/297.10	     , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
826.22/297.10	     , fib(0()) -> s(0())
826.22/297.10	     , fib(s(0())) -> s(0())
826.22/297.10	     , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
826.22/297.10	     , sum(x, 0()) -> x
826.22/297.10	     , sum(x, s(y)) -> s(sum(x, y))
826.22/297.10	     , if(true(), c, s(s(x)), a, b) ->
826.22/297.10	       if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c)
826.22/297.10	     , if(false(), c, s(s(x)), a, b) -> sum(fibo(a), fibo(b)) }
826.22/297.10	   Obligation:
826.22/297.10	     runtime complexity
826.22/297.10	   Answer:
826.22/297.10	     MAYBE
826.22/297.10	   
826.22/297.10	   We estimate the number of application of {1,2,7,8} by applications
826.22/297.10	   of Pre({1,2,7,8}) = {3,4,5,10}. Here rules are labeled as follows:
826.22/297.10	   
826.22/297.10	     DPs:
826.22/297.10	       { 1: lt^#(x, 0()) -> c_1()
826.22/297.10	       , 2: lt^#(0(), s(x)) -> c_2()
826.22/297.10	       , 3: lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
826.22/297.10	       , 4: fibo^#(0()) -> c_4(fib^#(0()))
826.22/297.10	       , 5: fibo^#(s(0())) -> c_5(fib^#(s(0())))
826.22/297.10	       , 6: fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
826.22/297.10	       , 7: fib^#(0()) -> c_7()
826.22/297.10	       , 8: fib^#(s(0())) -> c_8()
826.22/297.10	       , 9: fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
826.22/297.10	       , 10: sum^#(x, 0()) -> c_10(x)
826.22/297.10	       , 11: sum^#(x, s(y)) -> c_11(sum^#(x, y))
826.22/297.10	       , 12: if^#(true(), c, s(s(x)), a, b) ->
826.22/297.10	             c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
826.22/297.10	       , 13: if^#(false(), c, s(s(x)), a, b) ->
826.22/297.10	             c_13(sum^#(fibo(a), fibo(b))) }
826.22/297.10	   
826.22/297.10	   We are left with following problem, upon which TcT provides the
826.22/297.10	   certificate MAYBE.
826.22/297.10	   
826.22/297.10	   Strict DPs:
826.22/297.10	     { lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
826.22/297.10	     , fibo^#(0()) -> c_4(fib^#(0()))
826.22/297.10	     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
826.22/297.10	     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
826.22/297.10	     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
826.22/297.10	     , sum^#(x, 0()) -> c_10(x)
826.22/297.10	     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
826.22/297.10	     , if^#(true(), c, s(s(x)), a, b) ->
826.22/297.10	       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
826.22/297.10	     , if^#(false(), c, s(s(x)), a, b) ->
826.22/297.10	       c_13(sum^#(fibo(a), fibo(b))) }
826.22/297.10	   Strict Trs:
826.22/297.10	     { lt(x, 0()) -> false()
826.22/297.10	     , lt(0(), s(x)) -> true()
826.22/297.10	     , lt(s(x), s(y)) -> lt(x, y)
826.22/297.10	     , fibo(0()) -> fib(0())
826.22/297.10	     , fibo(s(0())) -> fib(s(0()))
826.22/297.10	     , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
826.22/297.10	     , fib(0()) -> s(0())
826.22/297.10	     , fib(s(0())) -> s(0())
826.22/297.10	     , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
826.22/297.10	     , sum(x, 0()) -> x
826.22/297.10	     , sum(x, s(y)) -> s(sum(x, y))
826.22/297.10	     , if(true(), c, s(s(x)), a, b) ->
826.22/297.10	       if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c)
826.22/297.10	     , if(false(), c, s(s(x)), a, b) -> sum(fibo(a), fibo(b)) }
826.22/297.10	   Weak DPs:
826.22/297.10	     { lt^#(x, 0()) -> c_1()
826.22/297.10	     , lt^#(0(), s(x)) -> c_2()
826.22/297.10	     , fib^#(0()) -> c_7()
826.22/297.10	     , fib^#(s(0())) -> c_8() }
826.22/297.10	   Obligation:
826.22/297.10	     runtime complexity
826.22/297.10	   Answer:
826.22/297.10	     MAYBE
826.22/297.10	   
826.22/297.10	   We estimate the number of application of {2,3} by applications of
826.22/297.10	   Pre({2,3}) = {6}. Here rules are labeled as follows:
826.22/297.10	   
826.22/297.10	     DPs:
826.22/297.10	       { 1: lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
826.22/297.10	       , 2: fibo^#(0()) -> c_4(fib^#(0()))
826.22/297.10	       , 3: fibo^#(s(0())) -> c_5(fib^#(s(0())))
826.22/297.10	       , 4: fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
826.22/297.10	       , 5: fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
826.22/297.10	       , 6: sum^#(x, 0()) -> c_10(x)
826.22/297.10	       , 7: sum^#(x, s(y)) -> c_11(sum^#(x, y))
826.22/297.10	       , 8: if^#(true(), c, s(s(x)), a, b) ->
826.22/297.10	            c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
826.22/297.10	       , 9: if^#(false(), c, s(s(x)), a, b) ->
826.22/297.10	            c_13(sum^#(fibo(a), fibo(b)))
826.22/297.10	       , 10: lt^#(x, 0()) -> c_1()
826.22/297.10	       , 11: lt^#(0(), s(x)) -> c_2()
826.22/297.10	       , 12: fib^#(0()) -> c_7()
826.22/297.10	       , 13: fib^#(s(0())) -> c_8() }
826.22/297.10	   
826.22/297.10	   We are left with following problem, upon which TcT provides the
826.22/297.10	   certificate MAYBE.
826.22/297.10	   
826.22/297.10	   Strict DPs:
826.22/297.10	     { lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
826.22/297.10	     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
826.22/297.10	     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
826.22/297.10	     , sum^#(x, 0()) -> c_10(x)
826.22/297.10	     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
826.22/297.10	     , if^#(true(), c, s(s(x)), a, b) ->
826.22/297.10	       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
826.22/297.10	     , if^#(false(), c, s(s(x)), a, b) ->
826.22/297.10	       c_13(sum^#(fibo(a), fibo(b))) }
826.22/297.10	   Strict Trs:
826.22/297.10	     { lt(x, 0()) -> false()
826.22/297.10	     , lt(0(), s(x)) -> true()
826.22/297.10	     , lt(s(x), s(y)) -> lt(x, y)
826.22/297.10	     , fibo(0()) -> fib(0())
826.22/297.10	     , fibo(s(0())) -> fib(s(0()))
826.22/297.10	     , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
826.22/297.10	     , fib(0()) -> s(0())
826.22/297.10	     , fib(s(0())) -> s(0())
826.22/297.10	     , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
826.22/297.10	     , sum(x, 0()) -> x
826.22/297.10	     , sum(x, s(y)) -> s(sum(x, y))
826.22/297.10	     , if(true(), c, s(s(x)), a, b) ->
826.22/297.10	       if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c)
826.22/297.10	     , if(false(), c, s(s(x)), a, b) -> sum(fibo(a), fibo(b)) }
826.22/297.10	   Weak DPs:
826.22/297.10	     { lt^#(x, 0()) -> c_1()
826.22/297.10	     , lt^#(0(), s(x)) -> c_2()
826.22/297.10	     , fibo^#(0()) -> c_4(fib^#(0()))
826.22/297.10	     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
826.22/297.10	     , fib^#(0()) -> c_7()
826.22/297.10	     , fib^#(s(0())) -> c_8() }
826.22/297.10	   Obligation:
826.22/297.10	     runtime complexity
826.22/297.10	   Answer:
826.22/297.10	     MAYBE
826.22/297.10	   
826.22/297.10	   Empty strict component of the problem is NOT empty.
826.22/297.10	
826.22/297.10	
826.22/297.10	Arrrr..
826.42/297.36	EOF