MAYBE
424.15/148.02	MAYBE
424.15/148.02	
424.15/148.02	We are left with following problem, upon which TcT provides the
424.15/148.02	certificate MAYBE.
424.15/148.02	
424.15/148.02	Strict Trs:
424.15/148.02	  { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
424.15/148.02	  , and(x, false()) -> false()
424.15/148.02	  , and(true(), true()) -> true()
424.15/148.02	  , and(false(), x) -> false()
424.15/148.02	  , even(0()) -> true()
424.15/148.02	  , even(s(0())) -> false()
424.15/148.02	  , even(s(s(x))) -> even(x)
424.15/148.02	  , gr(0(), x) -> false()
424.15/148.02	  , gr(s(x), 0()) -> true()
424.15/148.02	  , gr(s(x), s(y())) -> gr(x, y())
424.15/148.02	  , p(0()) -> 0()
424.15/148.02	  , p(s(x)) -> x }
424.15/148.02	Obligation:
424.15/148.02	  runtime complexity
424.15/148.02	Answer:
424.15/148.02	  MAYBE
424.15/148.02	
424.15/148.02	None of the processors succeeded.
424.15/148.02	
424.15/148.02	Details of failed attempt(s):
424.15/148.02	-----------------------------
424.15/148.02	1) 'Best' failed due to the following reason:
424.15/148.02	   
424.15/148.02	   None of the processors succeeded.
424.15/148.02	   
424.15/148.02	   Details of failed attempt(s):
424.15/148.02	   -----------------------------
424.15/148.02	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
424.15/148.02	      seconds)' failed due to the following reason:
424.15/148.02	      
424.15/148.02	      Computation stopped due to timeout after 148.0 seconds.
424.15/148.02	   
424.15/148.02	   2) 'Best' failed due to the following reason:
424.15/148.02	      
424.15/148.02	      None of the processors succeeded.
424.15/148.02	      
424.15/148.02	      Details of failed attempt(s):
424.15/148.02	      -----------------------------
424.15/148.02	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
424.15/148.02	         following reason:
424.15/148.02	         
424.15/148.02	         The processor is inapplicable, reason:
424.15/148.02	           Processor only applicable for innermost runtime complexity analysis
424.15/148.02	      
424.15/148.02	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
424.15/148.02	         to the following reason:
424.15/148.02	         
424.15/148.02	         The processor is inapplicable, reason:
424.15/148.02	           Processor only applicable for innermost runtime complexity analysis
424.15/148.02	      
424.15/148.02	   
424.15/148.02	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
424.15/148.02	      failed due to the following reason:
424.15/148.02	      
424.15/148.02	      None of the processors succeeded.
424.15/148.02	      
424.15/148.02	      Details of failed attempt(s):
424.15/148.02	      -----------------------------
424.15/148.02	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
424.15/148.02	         failed due to the following reason:
424.15/148.02	         
424.15/148.02	         match-boundness of the problem could not be verified.
424.15/148.02	      
424.15/148.02	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
424.15/148.02	         failed due to the following reason:
424.15/148.02	         
424.15/148.02	         match-boundness of the problem could not be verified.
424.15/148.02	      
424.15/148.02	   
424.15/148.02	
424.15/148.02	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
424.15/148.02	   the following reason:
424.15/148.02	   
424.15/148.02	   We add the following weak dependency pairs:
424.15/148.02	   
424.15/148.02	   Strict DPs:
424.15/148.02	     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
424.15/148.02	     , and^#(x, false()) -> c_2()
424.15/148.02	     , and^#(true(), true()) -> c_3()
424.15/148.02	     , and^#(false(), x) -> c_4()
424.15/148.02	     , even^#(0()) -> c_5()
424.15/148.02	     , even^#(s(0())) -> c_6()
424.15/148.02	     , even^#(s(s(x))) -> c_7(even^#(x))
424.15/148.02	     , gr^#(0(), x) -> c_8()
424.15/148.02	     , gr^#(s(x), 0()) -> c_9()
424.15/148.02	     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
424.15/148.02	     , p^#(0()) -> c_11()
424.15/148.02	     , p^#(s(x)) -> c_12(x) }
424.15/148.02	   
424.15/148.02	   and mark the set of starting terms.
424.15/148.02	   
424.15/148.02	   We are left with following problem, upon which TcT provides the
424.15/148.02	   certificate MAYBE.
424.15/148.02	   
424.15/148.02	   Strict DPs:
424.15/148.02	     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
424.15/148.02	     , and^#(x, false()) -> c_2()
424.15/148.02	     , and^#(true(), true()) -> c_3()
424.15/148.02	     , and^#(false(), x) -> c_4()
424.15/148.02	     , even^#(0()) -> c_5()
424.15/148.02	     , even^#(s(0())) -> c_6()
424.15/148.02	     , even^#(s(s(x))) -> c_7(even^#(x))
424.15/148.02	     , gr^#(0(), x) -> c_8()
424.15/148.02	     , gr^#(s(x), 0()) -> c_9()
424.15/148.02	     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
424.15/148.02	     , p^#(0()) -> c_11()
424.15/148.02	     , p^#(s(x)) -> c_12(x) }
424.15/148.02	   Strict Trs:
424.15/148.02	     { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
424.15/148.02	     , and(x, false()) -> false()
424.15/148.02	     , and(true(), true()) -> true()
424.15/148.02	     , and(false(), x) -> false()
424.15/148.02	     , even(0()) -> true()
424.15/148.02	     , even(s(0())) -> false()
424.15/148.02	     , even(s(s(x))) -> even(x)
424.15/148.02	     , gr(0(), x) -> false()
424.15/148.02	     , gr(s(x), 0()) -> true()
424.15/148.02	     , gr(s(x), s(y())) -> gr(x, y())
424.15/148.02	     , p(0()) -> 0()
424.15/148.02	     , p(s(x)) -> x }
424.15/148.02	   Obligation:
424.15/148.02	     runtime complexity
424.15/148.02	   Answer:
424.15/148.02	     MAYBE
424.15/148.02	   
424.15/148.02	   We estimate the number of application of {2,3,4,5,6,8,9,11} by
424.15/148.02	   applications of Pre({2,3,4,5,6,8,9,11}) = {7,10,12}. Here rules are
424.15/148.02	   labeled as follows:
424.15/148.02	   
424.15/148.02	     DPs:
424.15/148.02	       { 1: cond^#(true(), x) ->
424.15/148.02	            c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
424.15/148.02	       , 2: and^#(x, false()) -> c_2()
424.15/148.02	       , 3: and^#(true(), true()) -> c_3()
424.15/148.02	       , 4: and^#(false(), x) -> c_4()
424.15/148.02	       , 5: even^#(0()) -> c_5()
424.15/148.02	       , 6: even^#(s(0())) -> c_6()
424.15/148.02	       , 7: even^#(s(s(x))) -> c_7(even^#(x))
424.15/148.02	       , 8: gr^#(0(), x) -> c_8()
424.15/148.02	       , 9: gr^#(s(x), 0()) -> c_9()
424.15/148.02	       , 10: gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
424.15/148.02	       , 11: p^#(0()) -> c_11()
424.15/148.02	       , 12: p^#(s(x)) -> c_12(x) }
424.15/148.02	   
424.15/148.02	   We are left with following problem, upon which TcT provides the
424.15/148.02	   certificate MAYBE.
424.15/148.02	   
424.15/148.02	   Strict DPs:
424.15/148.02	     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
424.15/148.02	     , even^#(s(s(x))) -> c_7(even^#(x))
424.15/148.02	     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
424.15/148.02	     , p^#(s(x)) -> c_12(x) }
424.15/148.02	   Strict Trs:
424.15/148.02	     { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
424.15/148.02	     , and(x, false()) -> false()
424.15/148.02	     , and(true(), true()) -> true()
424.15/148.02	     , and(false(), x) -> false()
424.15/148.02	     , even(0()) -> true()
424.15/148.02	     , even(s(0())) -> false()
424.15/148.02	     , even(s(s(x))) -> even(x)
424.15/148.02	     , gr(0(), x) -> false()
424.15/148.02	     , gr(s(x), 0()) -> true()
424.15/148.02	     , gr(s(x), s(y())) -> gr(x, y())
424.15/148.02	     , p(0()) -> 0()
424.15/148.02	     , p(s(x)) -> x }
424.15/148.02	   Weak DPs:
424.15/148.02	     { and^#(x, false()) -> c_2()
424.15/148.02	     , and^#(true(), true()) -> c_3()
424.15/148.02	     , and^#(false(), x) -> c_4()
424.15/148.02	     , even^#(0()) -> c_5()
424.15/148.02	     , even^#(s(0())) -> c_6()
424.15/148.02	     , gr^#(0(), x) -> c_8()
424.15/148.02	     , gr^#(s(x), 0()) -> c_9()
424.15/148.02	     , p^#(0()) -> c_11() }
424.15/148.02	   Obligation:
424.15/148.02	     runtime complexity
424.15/148.02	   Answer:
424.15/148.02	     MAYBE
424.15/148.02	   
424.15/148.02	   We estimate the number of application of {3} by applications of
424.15/148.02	   Pre({3}) = {4}. Here rules are labeled as follows:
424.15/148.02	   
424.15/148.02	     DPs:
424.15/148.02	       { 1: cond^#(true(), x) ->
424.15/148.02	            c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
424.15/148.02	       , 2: even^#(s(s(x))) -> c_7(even^#(x))
424.15/148.02	       , 3: gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
424.15/148.02	       , 4: p^#(s(x)) -> c_12(x)
424.15/148.02	       , 5: and^#(x, false()) -> c_2()
424.15/148.02	       , 6: and^#(true(), true()) -> c_3()
424.15/148.02	       , 7: and^#(false(), x) -> c_4()
424.15/148.02	       , 8: even^#(0()) -> c_5()
424.15/148.02	       , 9: even^#(s(0())) -> c_6()
424.15/148.02	       , 10: gr^#(0(), x) -> c_8()
424.15/148.02	       , 11: gr^#(s(x), 0()) -> c_9()
424.15/148.02	       , 12: p^#(0()) -> c_11() }
424.15/148.02	   
424.15/148.02	   We are left with following problem, upon which TcT provides the
424.15/148.02	   certificate MAYBE.
424.15/148.02	   
424.15/148.02	   Strict DPs:
424.15/148.02	     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
424.15/148.02	     , even^#(s(s(x))) -> c_7(even^#(x))
424.15/148.02	     , p^#(s(x)) -> c_12(x) }
424.15/148.02	   Strict Trs:
424.15/148.02	     { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
424.15/148.02	     , and(x, false()) -> false()
424.15/148.02	     , and(true(), true()) -> true()
424.15/148.02	     , and(false(), x) -> false()
424.15/148.02	     , even(0()) -> true()
424.15/148.02	     , even(s(0())) -> false()
424.15/148.02	     , even(s(s(x))) -> even(x)
424.15/148.02	     , gr(0(), x) -> false()
424.15/148.02	     , gr(s(x), 0()) -> true()
424.15/148.02	     , gr(s(x), s(y())) -> gr(x, y())
424.15/148.02	     , p(0()) -> 0()
424.15/148.02	     , p(s(x)) -> x }
424.15/148.02	   Weak DPs:
424.15/148.02	     { and^#(x, false()) -> c_2()
424.15/148.02	     , and^#(true(), true()) -> c_3()
424.15/148.02	     , and^#(false(), x) -> c_4()
424.15/148.02	     , even^#(0()) -> c_5()
424.15/148.02	     , even^#(s(0())) -> c_6()
424.15/148.02	     , gr^#(0(), x) -> c_8()
424.15/148.02	     , gr^#(s(x), 0()) -> c_9()
424.15/148.02	     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
424.15/148.02	     , p^#(0()) -> c_11() }
424.15/148.02	   Obligation:
424.15/148.02	     runtime complexity
424.15/148.02	   Answer:
424.15/148.02	     MAYBE
424.15/148.02	   
424.15/148.02	   Empty strict component of the problem is NOT empty.
424.15/148.02	
424.15/148.02	
424.15/148.02	Arrrr..
424.38/148.21	EOF