MAYBE
504.53/166.26	MAYBE
504.53/166.26	
504.53/166.26	We are left with following problem, upon which TcT provides the
504.53/166.26	certificate MAYBE.
504.53/166.26	
504.53/166.26	Strict Trs:
504.53/166.26	  { cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
504.53/166.26	  , cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p(x), y, z)
504.53/166.26	  , cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
504.53/166.26	  , gr(0(), x) -> false()
504.53/166.26	  , gr(s(x), 0()) -> true()
504.53/166.26	  , gr(s(x), s(y)) -> gr(x, y)
504.53/166.26	  , add(0(), x) -> x
504.53/166.26	  , add(s(x), y) -> s(add(x, y))
504.53/166.26	  , p(0()) -> 0()
504.53/166.26	  , p(s(x)) -> x
504.53/166.26	  , cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p(y), z)
504.53/166.26	  , cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z) }
504.53/166.26	Obligation:
504.53/166.26	  runtime complexity
504.53/166.26	Answer:
504.53/166.26	  MAYBE
504.53/166.26	
504.53/166.26	None of the processors succeeded.
504.53/166.26	
504.53/166.26	Details of failed attempt(s):
504.53/166.26	-----------------------------
504.53/166.26	1) 'Best' failed due to the following reason:
504.53/166.26	   
504.53/166.26	   None of the processors succeeded.
504.53/166.26	   
504.53/166.26	   Details of failed attempt(s):
504.53/166.26	   -----------------------------
504.53/166.26	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
504.53/166.26	      seconds)' failed due to the following reason:
504.53/166.26	      
504.53/166.26	      Computation stopped due to timeout after 148.0 seconds.
504.53/166.26	   
504.53/166.26	   2) 'Best' failed due to the following reason:
504.53/166.26	      
504.53/166.26	      None of the processors succeeded.
504.53/166.26	      
504.53/166.26	      Details of failed attempt(s):
504.53/166.26	      -----------------------------
504.53/166.26	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
504.53/166.26	         following reason:
504.53/166.26	         
504.53/166.26	         The processor is inapplicable, reason:
504.53/166.26	           Processor only applicable for innermost runtime complexity analysis
504.53/166.26	      
504.53/166.26	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
504.53/166.26	         to the following reason:
504.53/166.26	         
504.53/166.26	         The processor is inapplicable, reason:
504.53/166.26	           Processor only applicable for innermost runtime complexity analysis
504.53/166.26	      
504.53/166.26	   
504.53/166.26	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
504.53/166.26	      failed due to the following reason:
504.53/166.26	      
504.53/166.26	      None of the processors succeeded.
504.53/166.26	      
504.53/166.26	      Details of failed attempt(s):
504.53/166.26	      -----------------------------
504.53/166.26	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
504.53/166.26	         failed due to the following reason:
504.53/166.26	         
504.53/166.26	         match-boundness of the problem could not be verified.
504.53/166.26	      
504.53/166.26	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
504.53/166.26	         failed due to the following reason:
504.53/166.26	         
504.53/166.26	         match-boundness of the problem could not be verified.
504.53/166.26	      
504.53/166.26	   
504.53/166.26	
504.53/166.26	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
504.53/166.26	   the following reason:
504.53/166.26	   
504.53/166.26	   We add the following weak dependency pairs:
504.53/166.26	   
504.53/166.26	   Strict DPs:
504.53/166.26	     { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
504.53/166.26	     , cond2^#(true(), x, y, z) ->
504.53/166.26	       c_2(cond1^#(gr(add(x, y), z), p(x), y, z))
504.53/166.26	     , cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
504.53/166.26	     , cond3^#(true(), x, y, z) ->
504.53/166.26	       c_11(cond1^#(gr(add(x, y), z), x, p(y), z))
504.53/166.26	     , cond3^#(false(), x, y, z) ->
504.53/166.26	       c_12(cond1^#(gr(add(x, y), z), x, y, z))
504.53/166.26	     , gr^#(0(), x) -> c_4()
504.53/166.26	     , gr^#(s(x), 0()) -> c_5()
504.53/166.26	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
504.53/166.26	     , add^#(0(), x) -> c_7(x)
504.53/166.26	     , add^#(s(x), y) -> c_8(add^#(x, y))
504.53/166.26	     , p^#(0()) -> c_9()
504.53/166.26	     , p^#(s(x)) -> c_10(x) }
504.53/166.26	   
504.53/166.26	   and mark the set of starting terms.
504.53/166.26	   
504.53/166.26	   We are left with following problem, upon which TcT provides the
504.53/166.26	   certificate MAYBE.
504.53/166.26	   
504.53/166.26	   Strict DPs:
504.53/166.26	     { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
504.53/166.26	     , cond2^#(true(), x, y, z) ->
504.53/166.26	       c_2(cond1^#(gr(add(x, y), z), p(x), y, z))
504.53/166.26	     , cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
504.53/166.26	     , cond3^#(true(), x, y, z) ->
504.53/166.26	       c_11(cond1^#(gr(add(x, y), z), x, p(y), z))
504.53/166.26	     , cond3^#(false(), x, y, z) ->
504.53/166.26	       c_12(cond1^#(gr(add(x, y), z), x, y, z))
504.53/166.26	     , gr^#(0(), x) -> c_4()
504.53/166.26	     , gr^#(s(x), 0()) -> c_5()
504.53/166.26	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
504.53/166.26	     , add^#(0(), x) -> c_7(x)
504.53/166.26	     , add^#(s(x), y) -> c_8(add^#(x, y))
504.53/166.26	     , p^#(0()) -> c_9()
504.53/166.26	     , p^#(s(x)) -> c_10(x) }
504.53/166.26	   Strict Trs:
504.53/166.26	     { cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
504.53/166.26	     , cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p(x), y, z)
504.53/166.26	     , cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
504.53/166.26	     , gr(0(), x) -> false()
504.53/166.26	     , gr(s(x), 0()) -> true()
504.53/166.26	     , gr(s(x), s(y)) -> gr(x, y)
504.53/166.26	     , add(0(), x) -> x
504.53/166.26	     , add(s(x), y) -> s(add(x, y))
504.53/166.26	     , p(0()) -> 0()
504.53/166.26	     , p(s(x)) -> x
504.53/166.26	     , cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p(y), z)
504.53/166.26	     , cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z) }
504.53/166.26	   Obligation:
504.53/166.26	     runtime complexity
504.53/166.26	   Answer:
504.53/166.26	     MAYBE
504.53/166.26	   
504.53/166.26	   We estimate the number of application of {6,7,11} by applications
504.53/166.26	   of Pre({6,7,11}) = {8,9,12}. Here rules are labeled as follows:
504.53/166.26	   
504.53/166.26	     DPs:
504.53/166.26	       { 1: cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
504.53/166.26	       , 2: cond2^#(true(), x, y, z) ->
504.53/166.26	            c_2(cond1^#(gr(add(x, y), z), p(x), y, z))
504.53/166.26	       , 3: cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
504.53/166.26	       , 4: cond3^#(true(), x, y, z) ->
504.53/166.26	            c_11(cond1^#(gr(add(x, y), z), x, p(y), z))
504.53/166.26	       , 5: cond3^#(false(), x, y, z) ->
504.53/166.26	            c_12(cond1^#(gr(add(x, y), z), x, y, z))
504.53/166.26	       , 6: gr^#(0(), x) -> c_4()
504.53/166.26	       , 7: gr^#(s(x), 0()) -> c_5()
504.53/166.26	       , 8: gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
504.53/166.26	       , 9: add^#(0(), x) -> c_7(x)
504.53/166.26	       , 10: add^#(s(x), y) -> c_8(add^#(x, y))
504.53/166.26	       , 11: p^#(0()) -> c_9()
504.53/166.26	       , 12: p^#(s(x)) -> c_10(x) }
504.53/166.26	   
504.53/166.26	   We are left with following problem, upon which TcT provides the
504.53/166.26	   certificate MAYBE.
504.53/166.26	   
504.53/166.26	   Strict DPs:
504.53/166.26	     { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
504.53/166.26	     , cond2^#(true(), x, y, z) ->
504.53/166.26	       c_2(cond1^#(gr(add(x, y), z), p(x), y, z))
504.53/166.26	     , cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
504.53/166.26	     , cond3^#(true(), x, y, z) ->
504.53/166.26	       c_11(cond1^#(gr(add(x, y), z), x, p(y), z))
504.53/166.26	     , cond3^#(false(), x, y, z) ->
504.53/166.26	       c_12(cond1^#(gr(add(x, y), z), x, y, z))
504.53/166.26	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
504.53/166.26	     , add^#(0(), x) -> c_7(x)
504.53/166.26	     , add^#(s(x), y) -> c_8(add^#(x, y))
504.53/166.26	     , p^#(s(x)) -> c_10(x) }
504.53/166.26	   Strict Trs:
504.53/166.26	     { cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
504.53/166.26	     , cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p(x), y, z)
504.53/166.26	     , cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
504.53/166.26	     , gr(0(), x) -> false()
504.53/166.26	     , gr(s(x), 0()) -> true()
504.53/166.26	     , gr(s(x), s(y)) -> gr(x, y)
504.53/166.26	     , add(0(), x) -> x
504.53/166.26	     , add(s(x), y) -> s(add(x, y))
504.53/166.26	     , p(0()) -> 0()
504.53/166.26	     , p(s(x)) -> x
504.53/166.26	     , cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p(y), z)
504.53/166.26	     , cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z) }
504.53/166.26	   Weak DPs:
504.53/166.26	     { gr^#(0(), x) -> c_4()
504.53/166.26	     , gr^#(s(x), 0()) -> c_5()
504.53/166.26	     , p^#(0()) -> c_9() }
504.53/166.26	   Obligation:
504.53/166.26	     runtime complexity
504.53/166.26	   Answer:
504.53/166.26	     MAYBE
504.53/166.26	   
504.53/166.26	   Empty strict component of the problem is NOT empty.
504.53/166.26	
504.53/166.26	
504.53/166.26	Arrrr..
505.08/166.70	EOF