MAYBE
537.98/175.78	MAYBE
537.98/175.78	
537.98/175.78	We are left with following problem, upon which TcT provides the
537.98/175.78	certificate MAYBE.
537.98/175.78	
537.98/175.78	Strict Trs:
537.98/175.78	  { cond1(true(), x, y) -> cond2(gr(x, 0()), x, y)
537.98/175.78	  , cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y)
537.98/175.78	  , cond2(false(), x, y) -> cond3(gr(y, 0()), x, y)
537.98/175.78	  , gr(0(), x) -> false()
537.98/175.78	  , gr(s(x), 0()) -> true()
537.98/175.78	  , gr(s(x), s(y)) -> gr(x, y)
537.98/175.78	  , add(0(), x) -> x
537.98/175.78	  , add(s(x), y) -> s(add(x, y))
537.98/175.78	  , p(0()) -> 0()
537.98/175.78	  , p(s(x)) -> x
537.98/175.78	  , cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y))
537.98/175.78	  , cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y) }
537.98/175.78	Obligation:
537.98/175.78	  runtime complexity
537.98/175.78	Answer:
537.98/175.78	  MAYBE
537.98/175.78	
537.98/175.78	None of the processors succeeded.
537.98/175.78	
537.98/175.78	Details of failed attempt(s):
537.98/175.78	-----------------------------
537.98/175.78	1) 'Best' failed due to the following reason:
537.98/175.78	   
537.98/175.78	   None of the processors succeeded.
537.98/175.78	   
537.98/175.78	   Details of failed attempt(s):
537.98/175.78	   -----------------------------
537.98/175.78	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
537.98/175.78	      seconds)' failed due to the following reason:
537.98/175.78	      
537.98/175.78	      Computation stopped due to timeout after 148.0 seconds.
537.98/175.78	   
537.98/175.78	   2) 'Best' failed due to the following reason:
537.98/175.78	      
537.98/175.78	      None of the processors succeeded.
537.98/175.78	      
537.98/175.78	      Details of failed attempt(s):
537.98/175.78	      -----------------------------
537.98/175.78	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
537.98/175.78	         following reason:
537.98/175.78	         
537.98/175.78	         The processor is inapplicable, reason:
537.98/175.78	           Processor only applicable for innermost runtime complexity analysis
537.98/175.78	      
537.98/175.78	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
537.98/175.78	         to the following reason:
537.98/175.78	         
537.98/175.78	         The processor is inapplicable, reason:
537.98/175.78	           Processor only applicable for innermost runtime complexity analysis
537.98/175.78	      
537.98/175.78	   
537.98/175.78	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
537.98/175.78	      failed due to the following reason:
537.98/175.78	      
537.98/175.78	      None of the processors succeeded.
537.98/175.78	      
537.98/175.78	      Details of failed attempt(s):
537.98/175.78	      -----------------------------
537.98/175.78	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
537.98/175.78	         failed due to the following reason:
537.98/175.78	         
537.98/175.78	         match-boundness of the problem could not be verified.
537.98/175.78	      
537.98/175.78	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
537.98/175.78	         failed due to the following reason:
537.98/175.78	         
537.98/175.78	         match-boundness of the problem could not be verified.
537.98/175.78	      
537.98/175.78	   
537.98/175.78	
537.98/175.78	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
537.98/175.78	   the following reason:
537.98/175.78	   
537.98/175.78	   We add the following weak dependency pairs:
537.98/175.78	   
537.98/175.78	   Strict DPs:
537.98/175.78	     { cond1^#(true(), x, y) -> c_1(cond2^#(gr(x, 0()), x, y))
537.98/175.78	     , cond2^#(true(), x, y) ->
537.98/175.78	       c_2(cond1^#(gr(add(x, y), 0()), p(x), y))
537.98/175.78	     , cond2^#(false(), x, y) -> c_3(cond3^#(gr(y, 0()), x, y))
537.98/175.78	     , cond3^#(true(), x, y) ->
537.98/175.78	       c_11(cond1^#(gr(add(x, y), 0()), x, p(y)))
537.98/175.78	     , cond3^#(false(), x, y) -> c_12(cond1^#(gr(add(x, y), 0()), x, y))
537.98/175.78	     , gr^#(0(), x) -> c_4()
537.98/175.78	     , gr^#(s(x), 0()) -> c_5()
537.98/175.78	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
537.98/175.78	     , add^#(0(), x) -> c_7(x)
537.98/175.78	     , add^#(s(x), y) -> c_8(add^#(x, y))
537.98/175.78	     , p^#(0()) -> c_9()
537.98/175.78	     , p^#(s(x)) -> c_10(x) }
537.98/175.78	   
537.98/175.78	   and mark the set of starting terms.
537.98/175.78	   
537.98/175.78	   We are left with following problem, upon which TcT provides the
537.98/175.78	   certificate MAYBE.
537.98/175.78	   
537.98/175.78	   Strict DPs:
537.98/175.78	     { cond1^#(true(), x, y) -> c_1(cond2^#(gr(x, 0()), x, y))
537.98/175.78	     , cond2^#(true(), x, y) ->
537.98/175.78	       c_2(cond1^#(gr(add(x, y), 0()), p(x), y))
537.98/175.78	     , cond2^#(false(), x, y) -> c_3(cond3^#(gr(y, 0()), x, y))
537.98/175.78	     , cond3^#(true(), x, y) ->
537.98/175.78	       c_11(cond1^#(gr(add(x, y), 0()), x, p(y)))
537.98/175.78	     , cond3^#(false(), x, y) -> c_12(cond1^#(gr(add(x, y), 0()), x, y))
537.98/175.78	     , gr^#(0(), x) -> c_4()
537.98/175.78	     , gr^#(s(x), 0()) -> c_5()
537.98/175.78	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
537.98/175.78	     , add^#(0(), x) -> c_7(x)
537.98/175.78	     , add^#(s(x), y) -> c_8(add^#(x, y))
537.98/175.78	     , p^#(0()) -> c_9()
537.98/175.78	     , p^#(s(x)) -> c_10(x) }
537.98/175.78	   Strict Trs:
537.98/175.78	     { cond1(true(), x, y) -> cond2(gr(x, 0()), x, y)
537.98/175.78	     , cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y)
537.98/175.78	     , cond2(false(), x, y) -> cond3(gr(y, 0()), x, y)
537.98/175.78	     , gr(0(), x) -> false()
537.98/175.78	     , gr(s(x), 0()) -> true()
537.98/175.78	     , gr(s(x), s(y)) -> gr(x, y)
537.98/175.78	     , add(0(), x) -> x
537.98/175.78	     , add(s(x), y) -> s(add(x, y))
537.98/175.78	     , p(0()) -> 0()
537.98/175.78	     , p(s(x)) -> x
537.98/175.78	     , cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y))
537.98/175.78	     , cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y) }
537.98/175.78	   Obligation:
537.98/175.78	     runtime complexity
537.98/175.78	   Answer:
537.98/175.78	     MAYBE
537.98/175.78	   
537.98/175.78	   We estimate the number of application of {6,7,11} by applications
537.98/175.78	   of Pre({6,7,11}) = {8,9,12}. Here rules are labeled as follows:
537.98/175.78	   
537.98/175.78	     DPs:
537.98/175.78	       { 1: cond1^#(true(), x, y) -> c_1(cond2^#(gr(x, 0()), x, y))
537.98/175.78	       , 2: cond2^#(true(), x, y) ->
537.98/175.78	            c_2(cond1^#(gr(add(x, y), 0()), p(x), y))
537.98/175.78	       , 3: cond2^#(false(), x, y) -> c_3(cond3^#(gr(y, 0()), x, y))
537.98/175.78	       , 4: cond3^#(true(), x, y) ->
537.98/175.78	            c_11(cond1^#(gr(add(x, y), 0()), x, p(y)))
537.98/175.78	       , 5: cond3^#(false(), x, y) ->
537.98/175.78	            c_12(cond1^#(gr(add(x, y), 0()), x, y))
537.98/175.78	       , 6: gr^#(0(), x) -> c_4()
537.98/175.78	       , 7: gr^#(s(x), 0()) -> c_5()
537.98/175.78	       , 8: gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
537.98/175.78	       , 9: add^#(0(), x) -> c_7(x)
537.98/175.78	       , 10: add^#(s(x), y) -> c_8(add^#(x, y))
537.98/175.78	       , 11: p^#(0()) -> c_9()
537.98/175.78	       , 12: p^#(s(x)) -> c_10(x) }
537.98/175.78	   
537.98/175.78	   We are left with following problem, upon which TcT provides the
537.98/175.78	   certificate MAYBE.
537.98/175.78	   
537.98/175.78	   Strict DPs:
537.98/175.78	     { cond1^#(true(), x, y) -> c_1(cond2^#(gr(x, 0()), x, y))
537.98/175.78	     , cond2^#(true(), x, y) ->
537.98/175.78	       c_2(cond1^#(gr(add(x, y), 0()), p(x), y))
537.98/175.78	     , cond2^#(false(), x, y) -> c_3(cond3^#(gr(y, 0()), x, y))
537.98/175.78	     , cond3^#(true(), x, y) ->
537.98/175.78	       c_11(cond1^#(gr(add(x, y), 0()), x, p(y)))
537.98/175.78	     , cond3^#(false(), x, y) -> c_12(cond1^#(gr(add(x, y), 0()), x, y))
537.98/175.78	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
537.98/175.78	     , add^#(0(), x) -> c_7(x)
537.98/175.78	     , add^#(s(x), y) -> c_8(add^#(x, y))
537.98/175.78	     , p^#(s(x)) -> c_10(x) }
537.98/175.78	   Strict Trs:
537.98/175.78	     { cond1(true(), x, y) -> cond2(gr(x, 0()), x, y)
537.98/175.78	     , cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y)
537.98/175.78	     , cond2(false(), x, y) -> cond3(gr(y, 0()), x, y)
537.98/175.78	     , gr(0(), x) -> false()
537.98/175.78	     , gr(s(x), 0()) -> true()
537.98/175.78	     , gr(s(x), s(y)) -> gr(x, y)
537.98/175.78	     , add(0(), x) -> x
537.98/175.78	     , add(s(x), y) -> s(add(x, y))
537.98/175.78	     , p(0()) -> 0()
537.98/175.78	     , p(s(x)) -> x
537.98/175.78	     , cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y))
537.98/175.78	     , cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y) }
537.98/175.78	   Weak DPs:
537.98/175.78	     { gr^#(0(), x) -> c_4()
537.98/175.78	     , gr^#(s(x), 0()) -> c_5()
537.98/175.78	     , p^#(0()) -> c_9() }
537.98/175.78	   Obligation:
537.98/175.78	     runtime complexity
537.98/175.78	   Answer:
537.98/175.78	     MAYBE
537.98/175.78	   
537.98/175.78	   Empty strict component of the problem is NOT empty.
537.98/175.78	
537.98/175.78	
537.98/175.78	Arrrr..
538.43/176.12	EOF