MAYBE
802.08/297.04	MAYBE
802.08/297.04	
802.08/297.04	We are left with following problem, upon which TcT provides the
802.08/297.04	certificate MAYBE.
802.08/297.04	
802.08/297.04	Strict Trs:
802.08/297.04	  { p(s(x)) -> x
802.08/297.04	  , plus(x, s(y)) -> s(plus(x, p(s(y))))
802.08/297.04	  , plus(x, 0()) -> x
802.08/297.04	  , plus(s(x), y) -> s(plus(x, y))
802.08/297.04	  , plus(s(x), y) -> s(plus(p(s(x)), y))
802.08/297.04	  , plus(0(), y) -> y
802.08/297.04	  , times(s(x), y) -> plus(y, times(x, y))
802.08/297.04	  , times(s(0()), y) -> y
802.08/297.04	  , times(0(), y) -> 0()
802.08/297.04	  , div(x, y) -> quot(x, y, y)
802.08/297.04	  , div(0(), y) -> 0()
802.08/297.04	  , div(div(x, y), z) -> div(x, times(y, z))
802.08/297.04	  , quot(x, 0(), s(z)) -> s(div(x, s(z)))
802.08/297.04	  , quot(s(x), s(y), z) -> quot(x, y, z)
802.08/297.04	  , quot(0(), s(y), z) -> 0()
802.08/297.04	  , eq(s(x), s(y)) -> eq(x, y)
802.08/297.04	  , eq(s(x), 0()) -> false()
802.08/297.04	  , eq(0(), s(y)) -> false()
802.08/297.04	  , eq(0(), 0()) -> true()
802.08/297.04	  , divides(y, x) -> eq(x, times(div(x, y), y))
802.08/297.04	  , prime(s(s(x))) -> pr(s(s(x)), s(x))
802.08/297.04	  , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
802.08/297.04	  , pr(x, s(0())) -> true()
802.08/297.04	  , if(true(), x, y) -> false()
802.08/297.04	  , if(false(), x, y) -> pr(x, y) }
802.08/297.04	Obligation:
802.08/297.04	  runtime complexity
802.08/297.04	Answer:
802.08/297.04	  MAYBE
802.08/297.04	
802.08/297.04	None of the processors succeeded.
802.08/297.04	
802.08/297.04	Details of failed attempt(s):
802.08/297.04	-----------------------------
802.08/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
802.08/297.04	   following reason:
802.08/297.04	   
802.08/297.04	   Computation stopped due to timeout after 297.0 seconds.
802.08/297.04	
802.08/297.04	2) 'Best' failed due to the following reason:
802.08/297.04	   
802.08/297.04	   None of the processors succeeded.
802.08/297.04	   
802.08/297.04	   Details of failed attempt(s):
802.08/297.04	   -----------------------------
802.08/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
802.08/297.04	      seconds)' failed due to the following reason:
802.08/297.04	      
802.08/297.04	      Computation stopped due to timeout after 148.0 seconds.
802.08/297.04	   
802.08/297.04	   2) 'Best' failed due to the following reason:
802.08/297.04	      
802.08/297.04	      None of the processors succeeded.
802.08/297.04	      
802.08/297.04	      Details of failed attempt(s):
802.08/297.04	      -----------------------------
802.08/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
802.08/297.04	         following reason:
802.08/297.04	         
802.08/297.04	         The processor is inapplicable, reason:
802.08/297.04	           Processor only applicable for innermost runtime complexity analysis
802.08/297.04	      
802.08/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
802.08/297.04	         to the following reason:
802.08/297.04	         
802.08/297.04	         The processor is inapplicable, reason:
802.08/297.04	           Processor only applicable for innermost runtime complexity analysis
802.08/297.04	      
802.08/297.04	   
802.08/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
802.08/297.04	      failed due to the following reason:
802.08/297.04	      
802.08/297.04	      None of the processors succeeded.
802.08/297.04	      
802.08/297.04	      Details of failed attempt(s):
802.08/297.04	      -----------------------------
802.08/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
802.08/297.04	         failed due to the following reason:
802.08/297.04	         
802.08/297.04	         match-boundness of the problem could not be verified.
802.08/297.04	      
802.08/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
802.08/297.04	         failed due to the following reason:
802.08/297.04	         
802.08/297.04	         match-boundness of the problem could not be verified.
802.08/297.04	      
802.08/297.04	   
802.08/297.04	
802.08/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
802.08/297.04	   the following reason:
802.08/297.04	   
802.08/297.04	   We add the following weak dependency pairs:
802.08/297.04	   
802.08/297.04	   Strict DPs:
802.08/297.04	     { p^#(s(x)) -> c_1(x)
802.08/297.04	     , plus^#(x, s(y)) -> c_2(plus^#(x, p(s(y))))
802.08/297.04	     , plus^#(x, 0()) -> c_3(x)
802.08/297.04	     , plus^#(s(x), y) -> c_4(plus^#(x, y))
802.08/297.04	     , plus^#(s(x), y) -> c_5(plus^#(p(s(x)), y))
802.08/297.04	     , plus^#(0(), y) -> c_6(y)
802.08/297.04	     , times^#(s(x), y) -> c_7(plus^#(y, times(x, y)))
802.08/297.04	     , times^#(s(0()), y) -> c_8(y)
802.08/297.04	     , times^#(0(), y) -> c_9()
802.08/297.04	     , div^#(x, y) -> c_10(quot^#(x, y, y))
802.08/297.04	     , div^#(0(), y) -> c_11()
802.08/297.04	     , div^#(div(x, y), z) -> c_12(div^#(x, times(y, z)))
802.08/297.04	     , quot^#(x, 0(), s(z)) -> c_13(div^#(x, s(z)))
802.08/297.04	     , quot^#(s(x), s(y), z) -> c_14(quot^#(x, y, z))
802.08/297.04	     , quot^#(0(), s(y), z) -> c_15()
802.08/297.04	     , eq^#(s(x), s(y)) -> c_16(eq^#(x, y))
802.08/297.04	     , eq^#(s(x), 0()) -> c_17()
802.08/297.04	     , eq^#(0(), s(y)) -> c_18()
802.08/297.04	     , eq^#(0(), 0()) -> c_19()
802.08/297.04	     , divides^#(y, x) -> c_20(eq^#(x, times(div(x, y), y)))
802.08/297.04	     , prime^#(s(s(x))) -> c_21(pr^#(s(s(x)), s(x)))
802.08/297.04	     , pr^#(x, s(s(y))) -> c_22(if^#(divides(s(s(y)), x), x, s(y)))
802.08/297.04	     , pr^#(x, s(0())) -> c_23()
802.08/297.04	     , if^#(true(), x, y) -> c_24()
802.08/297.04	     , if^#(false(), x, y) -> c_25(pr^#(x, y)) }
802.08/297.04	   
802.08/297.04	   and mark the set of starting terms.
802.08/297.04	   
802.08/297.04	   We are left with following problem, upon which TcT provides the
802.08/297.04	   certificate MAYBE.
802.08/297.04	   
802.08/297.04	   Strict DPs:
802.08/297.04	     { p^#(s(x)) -> c_1(x)
802.08/297.04	     , plus^#(x, s(y)) -> c_2(plus^#(x, p(s(y))))
802.08/297.04	     , plus^#(x, 0()) -> c_3(x)
802.08/297.04	     , plus^#(s(x), y) -> c_4(plus^#(x, y))
802.08/297.04	     , plus^#(s(x), y) -> c_5(plus^#(p(s(x)), y))
802.08/297.04	     , plus^#(0(), y) -> c_6(y)
802.08/297.04	     , times^#(s(x), y) -> c_7(plus^#(y, times(x, y)))
802.08/297.04	     , times^#(s(0()), y) -> c_8(y)
802.08/297.04	     , times^#(0(), y) -> c_9()
802.08/297.04	     , div^#(x, y) -> c_10(quot^#(x, y, y))
802.08/297.04	     , div^#(0(), y) -> c_11()
802.08/297.04	     , div^#(div(x, y), z) -> c_12(div^#(x, times(y, z)))
802.08/297.04	     , quot^#(x, 0(), s(z)) -> c_13(div^#(x, s(z)))
802.08/297.04	     , quot^#(s(x), s(y), z) -> c_14(quot^#(x, y, z))
802.08/297.04	     , quot^#(0(), s(y), z) -> c_15()
802.08/297.04	     , eq^#(s(x), s(y)) -> c_16(eq^#(x, y))
802.08/297.04	     , eq^#(s(x), 0()) -> c_17()
802.08/297.04	     , eq^#(0(), s(y)) -> c_18()
802.08/297.04	     , eq^#(0(), 0()) -> c_19()
802.08/297.04	     , divides^#(y, x) -> c_20(eq^#(x, times(div(x, y), y)))
802.08/297.04	     , prime^#(s(s(x))) -> c_21(pr^#(s(s(x)), s(x)))
802.08/297.04	     , pr^#(x, s(s(y))) -> c_22(if^#(divides(s(s(y)), x), x, s(y)))
802.08/297.04	     , pr^#(x, s(0())) -> c_23()
802.08/297.04	     , if^#(true(), x, y) -> c_24()
802.08/297.04	     , if^#(false(), x, y) -> c_25(pr^#(x, y)) }
802.08/297.04	   Strict Trs:
802.08/297.04	     { p(s(x)) -> x
802.08/297.04	     , plus(x, s(y)) -> s(plus(x, p(s(y))))
802.08/297.04	     , plus(x, 0()) -> x
802.08/297.04	     , plus(s(x), y) -> s(plus(x, y))
802.08/297.04	     , plus(s(x), y) -> s(plus(p(s(x)), y))
802.08/297.04	     , plus(0(), y) -> y
802.08/297.04	     , times(s(x), y) -> plus(y, times(x, y))
802.08/297.04	     , times(s(0()), y) -> y
802.08/297.04	     , times(0(), y) -> 0()
802.08/297.04	     , div(x, y) -> quot(x, y, y)
802.08/297.04	     , div(0(), y) -> 0()
802.08/297.04	     , div(div(x, y), z) -> div(x, times(y, z))
802.08/297.04	     , quot(x, 0(), s(z)) -> s(div(x, s(z)))
802.08/297.04	     , quot(s(x), s(y), z) -> quot(x, y, z)
802.08/297.04	     , quot(0(), s(y), z) -> 0()
802.08/297.04	     , eq(s(x), s(y)) -> eq(x, y)
802.08/297.04	     , eq(s(x), 0()) -> false()
802.08/297.04	     , eq(0(), s(y)) -> false()
802.08/297.04	     , eq(0(), 0()) -> true()
802.08/297.04	     , divides(y, x) -> eq(x, times(div(x, y), y))
802.08/297.04	     , prime(s(s(x))) -> pr(s(s(x)), s(x))
802.08/297.04	     , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
802.08/297.04	     , pr(x, s(0())) -> true()
802.08/297.04	     , if(true(), x, y) -> false()
802.08/297.04	     , if(false(), x, y) -> pr(x, y) }
802.08/297.04	   Obligation:
802.08/297.04	     runtime complexity
802.08/297.04	   Answer:
802.08/297.04	     MAYBE
802.08/297.04	   
802.08/297.04	   We estimate the number of application of {9,11,15,17,18,19,23,24}
802.08/297.04	   by applications of Pre({9,11,15,17,18,19,23,24}) =
802.08/297.04	   {1,3,6,8,10,12,13,14,16,20,21,22,25}. Here rules are labeled as
802.08/297.04	   follows:
802.08/297.04	   
802.08/297.04	     DPs:
802.08/297.04	       { 1: p^#(s(x)) -> c_1(x)
802.08/297.04	       , 2: plus^#(x, s(y)) -> c_2(plus^#(x, p(s(y))))
802.08/297.04	       , 3: plus^#(x, 0()) -> c_3(x)
802.08/297.04	       , 4: plus^#(s(x), y) -> c_4(plus^#(x, y))
802.08/297.04	       , 5: plus^#(s(x), y) -> c_5(plus^#(p(s(x)), y))
802.08/297.04	       , 6: plus^#(0(), y) -> c_6(y)
802.08/297.04	       , 7: times^#(s(x), y) -> c_7(plus^#(y, times(x, y)))
802.08/297.04	       , 8: times^#(s(0()), y) -> c_8(y)
802.08/297.04	       , 9: times^#(0(), y) -> c_9()
802.08/297.04	       , 10: div^#(x, y) -> c_10(quot^#(x, y, y))
802.08/297.04	       , 11: div^#(0(), y) -> c_11()
802.08/297.04	       , 12: div^#(div(x, y), z) -> c_12(div^#(x, times(y, z)))
802.08/297.04	       , 13: quot^#(x, 0(), s(z)) -> c_13(div^#(x, s(z)))
802.08/297.04	       , 14: quot^#(s(x), s(y), z) -> c_14(quot^#(x, y, z))
802.08/297.04	       , 15: quot^#(0(), s(y), z) -> c_15()
802.08/297.04	       , 16: eq^#(s(x), s(y)) -> c_16(eq^#(x, y))
802.08/297.04	       , 17: eq^#(s(x), 0()) -> c_17()
802.08/297.04	       , 18: eq^#(0(), s(y)) -> c_18()
802.08/297.04	       , 19: eq^#(0(), 0()) -> c_19()
802.08/297.04	       , 20: divides^#(y, x) -> c_20(eq^#(x, times(div(x, y), y)))
802.08/297.04	       , 21: prime^#(s(s(x))) -> c_21(pr^#(s(s(x)), s(x)))
802.08/297.04	       , 22: pr^#(x, s(s(y))) -> c_22(if^#(divides(s(s(y)), x), x, s(y)))
802.08/297.04	       , 23: pr^#(x, s(0())) -> c_23()
802.08/297.04	       , 24: if^#(true(), x, y) -> c_24()
802.08/297.04	       , 25: if^#(false(), x, y) -> c_25(pr^#(x, y)) }
802.08/297.04	   
802.08/297.04	   We are left with following problem, upon which TcT provides the
802.08/297.04	   certificate MAYBE.
802.08/297.04	   
802.08/297.04	   Strict DPs:
802.08/297.04	     { p^#(s(x)) -> c_1(x)
802.08/297.04	     , plus^#(x, s(y)) -> c_2(plus^#(x, p(s(y))))
802.08/297.04	     , plus^#(x, 0()) -> c_3(x)
802.08/297.04	     , plus^#(s(x), y) -> c_4(plus^#(x, y))
802.08/297.04	     , plus^#(s(x), y) -> c_5(plus^#(p(s(x)), y))
802.08/297.04	     , plus^#(0(), y) -> c_6(y)
802.08/297.04	     , times^#(s(x), y) -> c_7(plus^#(y, times(x, y)))
802.08/297.04	     , times^#(s(0()), y) -> c_8(y)
802.08/297.04	     , div^#(x, y) -> c_10(quot^#(x, y, y))
802.08/297.04	     , div^#(div(x, y), z) -> c_12(div^#(x, times(y, z)))
802.08/297.04	     , quot^#(x, 0(), s(z)) -> c_13(div^#(x, s(z)))
802.08/297.04	     , quot^#(s(x), s(y), z) -> c_14(quot^#(x, y, z))
802.08/297.04	     , eq^#(s(x), s(y)) -> c_16(eq^#(x, y))
802.08/297.04	     , divides^#(y, x) -> c_20(eq^#(x, times(div(x, y), y)))
802.08/297.04	     , prime^#(s(s(x))) -> c_21(pr^#(s(s(x)), s(x)))
802.08/297.04	     , pr^#(x, s(s(y))) -> c_22(if^#(divides(s(s(y)), x), x, s(y)))
802.08/297.04	     , if^#(false(), x, y) -> c_25(pr^#(x, y)) }
802.08/297.04	   Strict Trs:
802.08/297.04	     { p(s(x)) -> x
802.08/297.04	     , plus(x, s(y)) -> s(plus(x, p(s(y))))
802.08/297.04	     , plus(x, 0()) -> x
802.08/297.04	     , plus(s(x), y) -> s(plus(x, y))
802.08/297.04	     , plus(s(x), y) -> s(plus(p(s(x)), y))
802.08/297.04	     , plus(0(), y) -> y
802.08/297.04	     , times(s(x), y) -> plus(y, times(x, y))
802.08/297.04	     , times(s(0()), y) -> y
802.08/297.04	     , times(0(), y) -> 0()
802.08/297.04	     , div(x, y) -> quot(x, y, y)
802.08/297.04	     , div(0(), y) -> 0()
802.08/297.04	     , div(div(x, y), z) -> div(x, times(y, z))
802.08/297.04	     , quot(x, 0(), s(z)) -> s(div(x, s(z)))
802.08/297.04	     , quot(s(x), s(y), z) -> quot(x, y, z)
802.08/297.04	     , quot(0(), s(y), z) -> 0()
802.08/297.04	     , eq(s(x), s(y)) -> eq(x, y)
802.08/297.04	     , eq(s(x), 0()) -> false()
802.08/297.04	     , eq(0(), s(y)) -> false()
802.08/297.04	     , eq(0(), 0()) -> true()
802.08/297.04	     , divides(y, x) -> eq(x, times(div(x, y), y))
802.08/297.04	     , prime(s(s(x))) -> pr(s(s(x)), s(x))
802.08/297.04	     , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
802.08/297.04	     , pr(x, s(0())) -> true()
802.08/297.04	     , if(true(), x, y) -> false()
802.08/297.04	     , if(false(), x, y) -> pr(x, y) }
802.08/297.04	   Weak DPs:
802.08/297.04	     { times^#(0(), y) -> c_9()
802.08/297.04	     , div^#(0(), y) -> c_11()
802.08/297.04	     , quot^#(0(), s(y), z) -> c_15()
802.08/297.04	     , eq^#(s(x), 0()) -> c_17()
802.08/297.04	     , eq^#(0(), s(y)) -> c_18()
802.08/297.04	     , eq^#(0(), 0()) -> c_19()
802.08/297.04	     , pr^#(x, s(0())) -> c_23()
802.08/297.04	     , if^#(true(), x, y) -> c_24() }
802.08/297.04	   Obligation:
802.08/297.04	     runtime complexity
802.08/297.04	   Answer:
802.08/297.04	     MAYBE
802.08/297.04	   
802.08/297.04	   Empty strict component of the problem is NOT empty.
802.08/297.04	
802.08/297.04	
802.08/297.04	Arrrr..
802.30/297.29	EOF