MAYBE
488.53/148.03	MAYBE
488.53/148.03	
488.53/148.03	We are left with following problem, upon which TcT provides the
488.53/148.03	certificate MAYBE.
488.53/148.03	
488.53/148.03	Strict Trs:
488.53/148.03	  { cond1(true(), x, y) -> cond2(gr(y, 0()), x, y)
488.53/148.03	  , cond2(true(), x, y) -> cond2(gr(y, 0()), p(x), p(y))
488.53/148.03	  , cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y)
488.53/148.03	  , gr(0(), x) -> false()
488.53/148.03	  , gr(s(x), 0()) -> true()
488.53/148.03	  , gr(s(x), s(y)) -> gr(x, y)
488.53/148.03	  , p(0()) -> 0()
488.53/148.03	  , p(s(x)) -> x
488.53/148.03	  , and(x, false()) -> false()
488.53/148.03	  , and(true(), true()) -> true()
488.53/148.03	  , and(false(), x) -> false()
488.53/148.03	  , eq(0(), 0()) -> true()
488.53/148.03	  , eq(0(), s(x)) -> false()
488.53/148.03	  , eq(s(x), 0()) -> false()
488.53/148.03	  , eq(s(x), s(y)) -> eq(x, y) }
488.53/148.03	Obligation:
488.53/148.03	  runtime complexity
488.53/148.03	Answer:
488.53/148.03	  MAYBE
488.53/148.03	
488.53/148.03	None of the processors succeeded.
488.53/148.03	
488.53/148.03	Details of failed attempt(s):
488.53/148.03	-----------------------------
488.53/148.03	1) 'Best' failed due to the following reason:
488.53/148.03	   
488.53/148.03	   None of the processors succeeded.
488.53/148.03	   
488.53/148.03	   Details of failed attempt(s):
488.53/148.03	   -----------------------------
488.53/148.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
488.53/148.03	      seconds)' failed due to the following reason:
488.53/148.03	      
488.53/148.03	      Computation stopped due to timeout after 148.0 seconds.
488.53/148.03	   
488.53/148.03	   2) 'Best' failed due to the following reason:
488.53/148.03	      
488.53/148.03	      None of the processors succeeded.
488.53/148.03	      
488.53/148.03	      Details of failed attempt(s):
488.53/148.03	      -----------------------------
488.53/148.03	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
488.53/148.03	         to the following reason:
488.53/148.03	         
488.53/148.03	         The processor is inapplicable, reason:
488.53/148.03	           Processor only applicable for innermost runtime complexity analysis
488.53/148.03	      
488.53/148.03	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
488.53/148.03	         following reason:
488.53/148.03	         
488.53/148.03	         The processor is inapplicable, reason:
488.53/148.03	           Processor only applicable for innermost runtime complexity analysis
488.53/148.03	      
488.53/148.03	   
488.53/148.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
488.53/148.03	      failed due to the following reason:
488.53/148.03	      
488.53/148.03	      None of the processors succeeded.
488.53/148.03	      
488.53/148.03	      Details of failed attempt(s):
488.53/148.03	      -----------------------------
488.53/148.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
488.53/148.03	         failed due to the following reason:
488.53/148.03	         
488.53/148.03	         match-boundness of the problem could not be verified.
488.53/148.03	      
488.53/148.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
488.53/148.03	         failed due to the following reason:
488.53/148.03	         
488.53/148.03	         match-boundness of the problem could not be verified.
488.53/148.03	      
488.53/148.03	   
488.53/148.03	
488.53/148.03	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
488.53/148.03	   the following reason:
488.53/148.03	   
488.53/148.03	   We add the following weak dependency pairs:
488.53/148.03	   
488.53/148.03	   Strict DPs:
488.53/148.03	     { cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y))
488.53/148.03	     , cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), p(x), p(y)))
488.53/148.03	     , cond2^#(false(), x, y) ->
488.53/148.03	       c_3(cond1^#(and(eq(x, y), gr(x, 0())), x, y))
488.53/148.03	     , gr^#(0(), x) -> c_4()
488.53/148.03	     , gr^#(s(x), 0()) -> c_5()
488.53/148.03	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
488.53/148.03	     , p^#(0()) -> c_7()
488.53/148.03	     , p^#(s(x)) -> c_8(x)
488.53/148.03	     , and^#(x, false()) -> c_9()
488.53/148.03	     , and^#(true(), true()) -> c_10()
488.53/148.03	     , and^#(false(), x) -> c_11()
488.53/148.03	     , eq^#(0(), 0()) -> c_12()
488.53/148.03	     , eq^#(0(), s(x)) -> c_13()
488.53/148.03	     , eq^#(s(x), 0()) -> c_14()
488.53/148.03	     , eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) }
488.53/148.03	   
488.53/148.03	   and mark the set of starting terms.
488.53/148.03	   
488.53/148.03	   We are left with following problem, upon which TcT provides the
488.53/148.03	   certificate MAYBE.
488.53/148.03	   
488.53/148.03	   Strict DPs:
488.53/148.03	     { cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y))
488.53/148.03	     , cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), p(x), p(y)))
488.53/148.03	     , cond2^#(false(), x, y) ->
488.53/148.03	       c_3(cond1^#(and(eq(x, y), gr(x, 0())), x, y))
488.53/148.03	     , gr^#(0(), x) -> c_4()
488.53/148.03	     , gr^#(s(x), 0()) -> c_5()
488.53/148.03	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
488.53/148.03	     , p^#(0()) -> c_7()
488.53/148.03	     , p^#(s(x)) -> c_8(x)
488.53/148.03	     , and^#(x, false()) -> c_9()
488.53/148.03	     , and^#(true(), true()) -> c_10()
488.53/148.03	     , and^#(false(), x) -> c_11()
488.53/148.03	     , eq^#(0(), 0()) -> c_12()
488.53/148.03	     , eq^#(0(), s(x)) -> c_13()
488.53/148.03	     , eq^#(s(x), 0()) -> c_14()
488.53/148.03	     , eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) }
488.53/148.03	   Strict Trs:
488.53/148.03	     { cond1(true(), x, y) -> cond2(gr(y, 0()), x, y)
488.53/148.03	     , cond2(true(), x, y) -> cond2(gr(y, 0()), p(x), p(y))
488.53/148.03	     , cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y)
488.53/148.03	     , gr(0(), x) -> false()
488.53/148.03	     , gr(s(x), 0()) -> true()
488.53/148.03	     , gr(s(x), s(y)) -> gr(x, y)
488.53/148.03	     , p(0()) -> 0()
488.53/148.03	     , p(s(x)) -> x
488.53/148.03	     , and(x, false()) -> false()
488.53/148.03	     , and(true(), true()) -> true()
488.53/148.03	     , and(false(), x) -> false()
488.53/148.03	     , eq(0(), 0()) -> true()
488.53/148.03	     , eq(0(), s(x)) -> false()
488.53/148.03	     , eq(s(x), 0()) -> false()
488.53/148.03	     , eq(s(x), s(y)) -> eq(x, y) }
488.53/148.03	   Obligation:
488.53/148.03	     runtime complexity
488.53/148.03	   Answer:
488.53/148.03	     MAYBE
488.53/148.03	   
488.53/148.03	   We estimate the number of application of {4,5,7,9,10,11,12,13,14}
488.53/148.03	   by applications of Pre({4,5,7,9,10,11,12,13,14}) = {6,8,15}. Here
488.53/148.03	   rules are labeled as follows:
488.53/148.03	   
488.53/148.03	     DPs:
488.53/148.03	       { 1: cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y))
488.53/148.03	       , 2: cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), p(x), p(y)))
488.53/148.03	       , 3: cond2^#(false(), x, y) ->
488.53/148.03	            c_3(cond1^#(and(eq(x, y), gr(x, 0())), x, y))
488.53/148.03	       , 4: gr^#(0(), x) -> c_4()
488.53/148.03	       , 5: gr^#(s(x), 0()) -> c_5()
488.53/148.03	       , 6: gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
488.53/148.03	       , 7: p^#(0()) -> c_7()
488.53/148.03	       , 8: p^#(s(x)) -> c_8(x)
488.53/148.03	       , 9: and^#(x, false()) -> c_9()
488.53/148.03	       , 10: and^#(true(), true()) -> c_10()
488.53/148.03	       , 11: and^#(false(), x) -> c_11()
488.53/148.03	       , 12: eq^#(0(), 0()) -> c_12()
488.53/148.03	       , 13: eq^#(0(), s(x)) -> c_13()
488.53/148.03	       , 14: eq^#(s(x), 0()) -> c_14()
488.53/148.03	       , 15: eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) }
488.53/148.03	   
488.53/148.03	   We are left with following problem, upon which TcT provides the
488.53/148.03	   certificate MAYBE.
488.53/148.03	   
488.53/148.03	   Strict DPs:
488.53/148.03	     { cond1^#(true(), x, y) -> c_1(cond2^#(gr(y, 0()), x, y))
488.53/148.03	     , cond2^#(true(), x, y) -> c_2(cond2^#(gr(y, 0()), p(x), p(y)))
488.53/148.03	     , cond2^#(false(), x, y) ->
488.53/148.03	       c_3(cond1^#(and(eq(x, y), gr(x, 0())), x, y))
488.53/148.03	     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
488.53/148.03	     , p^#(s(x)) -> c_8(x)
488.53/148.03	     , eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) }
488.53/148.03	   Strict Trs:
488.53/148.03	     { cond1(true(), x, y) -> cond2(gr(y, 0()), x, y)
488.53/148.03	     , cond2(true(), x, y) -> cond2(gr(y, 0()), p(x), p(y))
488.53/148.03	     , cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y)
488.53/148.03	     , gr(0(), x) -> false()
488.53/148.03	     , gr(s(x), 0()) -> true()
488.53/148.03	     , gr(s(x), s(y)) -> gr(x, y)
488.53/148.03	     , p(0()) -> 0()
488.53/148.03	     , p(s(x)) -> x
488.53/148.03	     , and(x, false()) -> false()
488.53/148.03	     , and(true(), true()) -> true()
488.53/148.03	     , and(false(), x) -> false()
488.53/148.03	     , eq(0(), 0()) -> true()
488.53/148.03	     , eq(0(), s(x)) -> false()
488.53/148.03	     , eq(s(x), 0()) -> false()
488.53/148.03	     , eq(s(x), s(y)) -> eq(x, y) }
488.53/148.03	   Weak DPs:
488.53/148.03	     { gr^#(0(), x) -> c_4()
488.53/148.03	     , gr^#(s(x), 0()) -> c_5()
488.53/148.03	     , p^#(0()) -> c_7()
488.53/148.03	     , and^#(x, false()) -> c_9()
488.53/148.03	     , and^#(true(), true()) -> c_10()
488.53/148.03	     , and^#(false(), x) -> c_11()
488.53/148.03	     , eq^#(0(), 0()) -> c_12()
488.53/148.03	     , eq^#(0(), s(x)) -> c_13()
488.53/148.03	     , eq^#(s(x), 0()) -> c_14() }
488.53/148.03	   Obligation:
488.53/148.03	     runtime complexity
488.53/148.03	   Answer:
488.53/148.03	     MAYBE
488.53/148.03	   
488.53/148.03	   Empty strict component of the problem is NOT empty.
488.53/148.03	
488.53/148.03	
488.53/148.03	Arrrr..
489.00/148.45	EOF