MAYBE
746.74/285.85	MAYBE
746.74/285.85	
746.74/285.85	We are left with following problem, upon which TcT provides the
746.74/285.85	certificate MAYBE.
746.74/285.85	
746.74/285.85	Strict Trs:
746.74/285.85	  { plus(0(), x) -> x
746.74/285.85	  , plus(s(x), y) -> s(plus(p(s(x)), y))
746.74/285.85	  , p(s(0())) -> 0()
746.74/285.85	  , p(s(s(x))) -> s(p(s(x)))
746.74/285.85	  , times(0(), y) -> 0()
746.74/285.85	  , times(s(x), y) -> plus(y, times(p(s(x)), y))
746.74/285.85	  , fac(0(), x) -> x
746.74/285.85	  , fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
746.74/285.85	  , factorial(x) -> fac(x, s(0())) }
746.74/285.85	Obligation:
746.74/285.85	  runtime complexity
746.74/285.85	Answer:
746.74/285.85	  MAYBE
746.74/285.85	
746.74/285.85	None of the processors succeeded.
746.74/285.85	
746.74/285.85	Details of failed attempt(s):
746.74/285.85	-----------------------------
746.74/285.85	1) 'Best' failed due to the following reason:
746.74/285.85	   
746.74/285.85	   None of the processors succeeded.
746.74/285.85	   
746.74/285.85	   Details of failed attempt(s):
746.74/285.85	   -----------------------------
746.74/285.85	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
746.74/285.85	      seconds)' failed due to the following reason:
746.74/285.85	      
746.74/285.85	      Computation stopped due to timeout after 148.0 seconds.
746.74/285.85	   
746.74/285.85	   2) 'Best' failed due to the following reason:
746.74/285.85	      
746.74/285.85	      None of the processors succeeded.
746.74/285.85	      
746.74/285.85	      Details of failed attempt(s):
746.74/285.85	      -----------------------------
746.74/285.85	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
746.74/285.85	         following reason:
746.74/285.85	         
746.74/285.85	         The processor is inapplicable, reason:
746.74/285.85	           Processor only applicable for innermost runtime complexity analysis
746.74/285.85	      
746.74/285.85	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
746.74/285.85	         to the following reason:
746.74/285.85	         
746.74/285.85	         The processor is inapplicable, reason:
746.74/285.85	           Processor only applicable for innermost runtime complexity analysis
746.74/285.85	      
746.74/285.85	   
746.74/285.85	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
746.74/285.85	      failed due to the following reason:
746.74/285.85	      
746.74/285.85	      None of the processors succeeded.
746.74/285.85	      
746.74/285.85	      Details of failed attempt(s):
746.74/285.85	      -----------------------------
746.74/285.85	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
746.74/285.85	         failed due to the following reason:
746.74/285.85	         
746.74/285.85	         match-boundness of the problem could not be verified.
746.74/285.85	      
746.74/285.85	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
746.74/285.86	         failed due to the following reason:
746.74/285.86	         
746.74/285.86	         match-boundness of the problem could not be verified.
746.74/285.86	      
746.74/285.86	   
746.74/285.86	
746.74/285.86	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
746.74/285.86	   the following reason:
746.74/285.86	   
746.74/285.86	   We add the following weak dependency pairs:
746.74/285.86	   
746.74/285.86	   Strict DPs:
746.74/285.86	     { plus^#(0(), x) -> c_1(x)
746.74/285.86	     , plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
746.74/285.86	     , p^#(s(0())) -> c_3()
746.74/285.86	     , p^#(s(s(x))) -> c_4(p^#(s(x)))
746.74/285.86	     , times^#(0(), y) -> c_5()
746.74/285.86	     , times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
746.74/285.86	     , fac^#(0(), x) -> c_7(x)
746.74/285.86	     , fac^#(s(x), y) -> c_8(fac^#(p(s(x)), times(s(x), y)))
746.74/285.86	     , factorial^#(x) -> c_9(fac^#(x, s(0()))) }
746.74/285.86	   
746.74/285.86	   and mark the set of starting terms.
746.74/285.86	   
746.74/285.86	   We are left with following problem, upon which TcT provides the
746.74/285.86	   certificate MAYBE.
746.74/285.86	   
746.74/285.86	   Strict DPs:
746.74/285.86	     { plus^#(0(), x) -> c_1(x)
746.74/285.86	     , plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
746.74/285.86	     , p^#(s(0())) -> c_3()
746.74/285.86	     , p^#(s(s(x))) -> c_4(p^#(s(x)))
746.74/285.86	     , times^#(0(), y) -> c_5()
746.74/285.86	     , times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
746.74/285.86	     , fac^#(0(), x) -> c_7(x)
746.74/285.86	     , fac^#(s(x), y) -> c_8(fac^#(p(s(x)), times(s(x), y)))
746.74/285.86	     , factorial^#(x) -> c_9(fac^#(x, s(0()))) }
746.74/285.86	   Strict Trs:
746.74/285.86	     { plus(0(), x) -> x
746.74/285.86	     , plus(s(x), y) -> s(plus(p(s(x)), y))
746.74/285.86	     , p(s(0())) -> 0()
746.74/285.86	     , p(s(s(x))) -> s(p(s(x)))
746.74/285.86	     , times(0(), y) -> 0()
746.74/285.86	     , times(s(x), y) -> plus(y, times(p(s(x)), y))
746.74/285.86	     , fac(0(), x) -> x
746.74/285.86	     , fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
746.74/285.86	     , factorial(x) -> fac(x, s(0())) }
746.74/285.86	   Obligation:
746.74/285.86	     runtime complexity
746.74/285.86	   Answer:
746.74/285.86	     MAYBE
746.74/285.86	   
746.74/285.86	   We estimate the number of application of {3,5} by applications of
746.74/285.86	   Pre({3,5}) = {1,4,7}. Here rules are labeled as follows:
746.74/285.86	   
746.74/285.86	     DPs:
746.74/285.86	       { 1: plus^#(0(), x) -> c_1(x)
746.74/285.86	       , 2: plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
746.74/285.86	       , 3: p^#(s(0())) -> c_3()
746.74/285.86	       , 4: p^#(s(s(x))) -> c_4(p^#(s(x)))
746.74/285.86	       , 5: times^#(0(), y) -> c_5()
746.74/285.86	       , 6: times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
746.74/285.86	       , 7: fac^#(0(), x) -> c_7(x)
746.74/285.86	       , 8: fac^#(s(x), y) -> c_8(fac^#(p(s(x)), times(s(x), y)))
746.74/285.86	       , 9: factorial^#(x) -> c_9(fac^#(x, s(0()))) }
746.74/285.86	   
746.74/285.86	   We are left with following problem, upon which TcT provides the
746.74/285.86	   certificate MAYBE.
746.74/285.86	   
746.74/285.86	   Strict DPs:
746.74/285.86	     { plus^#(0(), x) -> c_1(x)
746.74/285.86	     , plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
746.74/285.86	     , p^#(s(s(x))) -> c_4(p^#(s(x)))
746.74/285.86	     , times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
746.74/285.86	     , fac^#(0(), x) -> c_7(x)
746.74/285.86	     , fac^#(s(x), y) -> c_8(fac^#(p(s(x)), times(s(x), y)))
746.74/285.86	     , factorial^#(x) -> c_9(fac^#(x, s(0()))) }
746.74/285.86	   Strict Trs:
746.74/285.86	     { plus(0(), x) -> x
746.74/285.86	     , plus(s(x), y) -> s(plus(p(s(x)), y))
746.74/285.86	     , p(s(0())) -> 0()
746.74/285.86	     , p(s(s(x))) -> s(p(s(x)))
746.74/285.86	     , times(0(), y) -> 0()
746.74/285.86	     , times(s(x), y) -> plus(y, times(p(s(x)), y))
746.74/285.86	     , fac(0(), x) -> x
746.74/285.86	     , fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
746.74/285.86	     , factorial(x) -> fac(x, s(0())) }
746.74/285.86	   Weak DPs:
746.74/285.86	     { p^#(s(0())) -> c_3()
746.74/285.86	     , times^#(0(), y) -> c_5() }
746.74/285.86	   Obligation:
746.74/285.86	     runtime complexity
746.74/285.86	   Answer:
746.74/285.86	     MAYBE
746.74/285.86	   
746.74/285.86	   Empty strict component of the problem is NOT empty.
746.74/285.86	
746.74/285.86	
746.74/285.86	Arrrr..
747.17/286.26	EOF