MAYBE
866.61/297.03	MAYBE
866.61/297.03	
866.61/297.03	We are left with following problem, upon which TcT provides the
866.61/297.03	certificate MAYBE.
866.61/297.03	
866.61/297.03	Strict Trs:
866.61/297.03	  { p(0()) -> 0()
866.61/297.03	  , p(s(x)) -> x
866.61/297.03	  , plus(x, 0()) -> x
866.61/297.03	  , plus(x, s(y)) -> s(plus(x, p(s(y))))
866.61/297.03	  , plus(0(), y) -> y
866.61/297.03	  , plus(s(x), y) -> s(plus(x, y))
866.61/297.03	  , plus(s(x), y) -> s(plus(p(s(x)), y))
866.61/297.03	  , times(0(), y) -> 0()
866.61/297.03	  , times(s(x), y) -> plus(y, times(x, y))
866.61/297.03	  , times(s(0()), y) -> y
866.61/297.03	  , div(x, y) -> quot(x, y, y)
866.61/297.03	  , div(0(), y) -> 0()
866.61/297.03	  , div(div(x, y), z) -> div(x, times(zero(y), z))
866.61/297.03	  , quot(x, 0(), s(z)) -> s(div(x, s(z)))
866.61/297.03	  , quot(s(x), s(y), z) -> quot(x, y, z)
866.61/297.03	  , quot(zero(y), s(y), z) -> 0()
866.61/297.03	  , zero(s(x)) ->
866.61/297.03	    if(eq(x, s(0())), plus(zero(0()), 0()), s(plus(0(), zero(0()))))
866.61/297.03	  , zero(times(x, x)) -> x
866.61/297.03	  , zero(div(x, x)) -> x
866.61/297.03	  , zero(quot(x, x, x)) -> x
866.61/297.03	  , zero(divides(x, x)) -> x
866.61/297.03	  , eq(0(), 0()) -> true()
866.61/297.03	  , eq(0(), s(y)) -> false()
866.61/297.03	  , eq(s(x), 0()) -> false()
866.61/297.03	  , eq(s(x), s(y)) -> eq(x, y)
866.61/297.03	  , divides(y, x) -> eq(x, times(div(x, y), y))
866.61/297.03	  , prime(s(s(x))) -> pr(s(s(x)), s(x))
866.61/297.03	  , pr(x, s(0())) -> true()
866.61/297.03	  , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
866.61/297.03	  , if(true(), x, y) -> false()
866.61/297.03	  , if(false(), x, y) -> pr(x, y) }
866.61/297.03	Obligation:
866.61/297.03	  runtime complexity
866.61/297.03	Answer:
866.61/297.03	  MAYBE
866.61/297.03	
866.61/297.03	None of the processors succeeded.
866.61/297.03	
866.61/297.03	Details of failed attempt(s):
866.61/297.03	-----------------------------
866.61/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
866.61/297.03	   following reason:
866.61/297.03	   
866.61/297.03	   Computation stopped due to timeout after 297.0 seconds.
866.61/297.03	
866.61/297.03	2) 'Best' failed due to the following reason:
866.61/297.03	   
866.61/297.03	   None of the processors succeeded.
866.61/297.03	   
866.61/297.03	   Details of failed attempt(s):
866.61/297.03	   -----------------------------
866.61/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
866.61/297.03	      seconds)' failed due to the following reason:
866.61/297.03	      
866.61/297.03	      Computation stopped due to timeout after 148.0 seconds.
866.61/297.03	   
866.61/297.03	   2) 'Best' failed due to the following reason:
866.61/297.03	      
866.61/297.03	      None of the processors succeeded.
866.61/297.03	      
866.61/297.03	      Details of failed attempt(s):
866.61/297.03	      -----------------------------
866.61/297.03	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
866.61/297.03	         following reason:
866.61/297.03	         
866.61/297.03	         The processor is inapplicable, reason:
866.61/297.03	           Processor only applicable for innermost runtime complexity analysis
866.61/297.03	      
866.61/297.03	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
866.61/297.03	         to the following reason:
866.61/297.03	         
866.61/297.03	         The processor is inapplicable, reason:
866.61/297.03	           Processor only applicable for innermost runtime complexity analysis
866.61/297.03	      
866.61/297.03	   
866.61/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
866.61/297.03	      failed due to the following reason:
866.61/297.03	      
866.61/297.03	      None of the processors succeeded.
866.61/297.03	      
866.61/297.03	      Details of failed attempt(s):
866.61/297.03	      -----------------------------
866.61/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
866.61/297.03	         failed due to the following reason:
866.61/297.03	         
866.61/297.03	         match-boundness of the problem could not be verified.
866.61/297.03	      
866.61/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
866.61/297.03	         failed due to the following reason:
866.61/297.03	         
866.61/297.03	         match-boundness of the problem could not be verified.
866.61/297.03	      
866.61/297.03	   
866.61/297.03	
866.61/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
866.61/297.03	   the following reason:
866.61/297.03	   
866.61/297.03	   We add the following weak dependency pairs:
866.61/297.03	   
866.61/297.03	   Strict DPs:
866.61/297.03	     { p^#(0()) -> c_1()
866.61/297.03	     , p^#(s(x)) -> c_2(x)
866.61/297.03	     , plus^#(x, 0()) -> c_3(x)
866.61/297.03	     , plus^#(x, s(y)) -> c_4(plus^#(x, p(s(y))))
866.61/297.03	     , plus^#(0(), y) -> c_5(y)
866.61/297.03	     , plus^#(s(x), y) -> c_6(plus^#(x, y))
866.61/297.03	     , plus^#(s(x), y) -> c_7(plus^#(p(s(x)), y))
866.61/297.03	     , times^#(0(), y) -> c_8()
866.61/297.03	     , times^#(s(x), y) -> c_9(plus^#(y, times(x, y)))
866.61/297.03	     , times^#(s(0()), y) -> c_10(y)
866.61/297.03	     , div^#(x, y) -> c_11(quot^#(x, y, y))
866.61/297.03	     , div^#(0(), y) -> c_12()
866.61/297.03	     , div^#(div(x, y), z) -> c_13(div^#(x, times(zero(y), z)))
866.61/297.03	     , quot^#(x, 0(), s(z)) -> c_14(div^#(x, s(z)))
866.61/297.03	     , quot^#(s(x), s(y), z) -> c_15(quot^#(x, y, z))
866.61/297.03	     , quot^#(zero(y), s(y), z) -> c_16()
866.61/297.03	     , zero^#(s(x)) ->
866.61/297.03	       c_17(if^#(eq(x, s(0())),
866.61/297.03	                 plus(zero(0()), 0()),
866.61/297.03	                 s(plus(0(), zero(0())))))
866.61/297.03	     , zero^#(times(x, x)) -> c_18(x)
866.61/297.03	     , zero^#(div(x, x)) -> c_19(x)
866.61/297.03	     , zero^#(quot(x, x, x)) -> c_20(x)
866.61/297.03	     , zero^#(divides(x, x)) -> c_21(x)
866.61/297.03	     , if^#(true(), x, y) -> c_30()
866.61/297.03	     , if^#(false(), x, y) -> c_31(pr^#(x, y))
866.61/297.03	     , eq^#(0(), 0()) -> c_22()
866.61/297.03	     , eq^#(0(), s(y)) -> c_23()
866.61/297.03	     , eq^#(s(x), 0()) -> c_24()
866.61/297.03	     , eq^#(s(x), s(y)) -> c_25(eq^#(x, y))
866.61/297.03	     , divides^#(y, x) -> c_26(eq^#(x, times(div(x, y), y)))
866.61/297.03	     , prime^#(s(s(x))) -> c_27(pr^#(s(s(x)), s(x)))
866.61/297.03	     , pr^#(x, s(0())) -> c_28()
866.61/297.03	     , pr^#(x, s(s(y))) -> c_29(if^#(divides(s(s(y)), x), x, s(y))) }
866.61/297.03	   
866.61/297.03	   and mark the set of starting terms.
866.61/297.03	   
866.61/297.03	   We are left with following problem, upon which TcT provides the
866.61/297.03	   certificate MAYBE.
866.61/297.03	   
866.61/297.03	   Strict DPs:
866.61/297.03	     { p^#(0()) -> c_1()
866.61/297.03	     , p^#(s(x)) -> c_2(x)
866.61/297.03	     , plus^#(x, 0()) -> c_3(x)
866.61/297.03	     , plus^#(x, s(y)) -> c_4(plus^#(x, p(s(y))))
866.61/297.03	     , plus^#(0(), y) -> c_5(y)
866.61/297.03	     , plus^#(s(x), y) -> c_6(plus^#(x, y))
866.61/297.03	     , plus^#(s(x), y) -> c_7(plus^#(p(s(x)), y))
866.61/297.03	     , times^#(0(), y) -> c_8()
866.61/297.03	     , times^#(s(x), y) -> c_9(plus^#(y, times(x, y)))
866.61/297.03	     , times^#(s(0()), y) -> c_10(y)
866.61/297.03	     , div^#(x, y) -> c_11(quot^#(x, y, y))
866.61/297.03	     , div^#(0(), y) -> c_12()
866.61/297.03	     , div^#(div(x, y), z) -> c_13(div^#(x, times(zero(y), z)))
866.61/297.03	     , quot^#(x, 0(), s(z)) -> c_14(div^#(x, s(z)))
866.61/297.03	     , quot^#(s(x), s(y), z) -> c_15(quot^#(x, y, z))
866.61/297.03	     , quot^#(zero(y), s(y), z) -> c_16()
866.61/297.03	     , zero^#(s(x)) ->
866.61/297.03	       c_17(if^#(eq(x, s(0())),
866.61/297.03	                 plus(zero(0()), 0()),
866.61/297.03	                 s(plus(0(), zero(0())))))
866.61/297.03	     , zero^#(times(x, x)) -> c_18(x)
866.61/297.03	     , zero^#(div(x, x)) -> c_19(x)
866.61/297.03	     , zero^#(quot(x, x, x)) -> c_20(x)
866.61/297.03	     , zero^#(divides(x, x)) -> c_21(x)
866.61/297.03	     , if^#(true(), x, y) -> c_30()
866.61/297.03	     , if^#(false(), x, y) -> c_31(pr^#(x, y))
866.61/297.03	     , eq^#(0(), 0()) -> c_22()
866.61/297.03	     , eq^#(0(), s(y)) -> c_23()
866.61/297.03	     , eq^#(s(x), 0()) -> c_24()
866.61/297.03	     , eq^#(s(x), s(y)) -> c_25(eq^#(x, y))
866.61/297.03	     , divides^#(y, x) -> c_26(eq^#(x, times(div(x, y), y)))
866.61/297.03	     , prime^#(s(s(x))) -> c_27(pr^#(s(s(x)), s(x)))
866.61/297.03	     , pr^#(x, s(0())) -> c_28()
866.61/297.03	     , pr^#(x, s(s(y))) -> c_29(if^#(divides(s(s(y)), x), x, s(y))) }
866.61/297.03	   Strict Trs:
866.61/297.03	     { p(0()) -> 0()
866.61/297.03	     , p(s(x)) -> x
866.61/297.03	     , plus(x, 0()) -> x
866.61/297.03	     , plus(x, s(y)) -> s(plus(x, p(s(y))))
866.61/297.03	     , plus(0(), y) -> y
866.61/297.03	     , plus(s(x), y) -> s(plus(x, y))
866.61/297.03	     , plus(s(x), y) -> s(plus(p(s(x)), y))
866.61/297.03	     , times(0(), y) -> 0()
866.61/297.03	     , times(s(x), y) -> plus(y, times(x, y))
866.61/297.03	     , times(s(0()), y) -> y
866.61/297.03	     , div(x, y) -> quot(x, y, y)
866.61/297.03	     , div(0(), y) -> 0()
866.61/297.03	     , div(div(x, y), z) -> div(x, times(zero(y), z))
866.61/297.03	     , quot(x, 0(), s(z)) -> s(div(x, s(z)))
866.61/297.03	     , quot(s(x), s(y), z) -> quot(x, y, z)
866.61/297.03	     , quot(zero(y), s(y), z) -> 0()
866.61/297.03	     , zero(s(x)) ->
866.61/297.03	       if(eq(x, s(0())), plus(zero(0()), 0()), s(plus(0(), zero(0()))))
866.61/297.03	     , zero(times(x, x)) -> x
866.61/297.03	     , zero(div(x, x)) -> x
866.61/297.03	     , zero(quot(x, x, x)) -> x
866.61/297.03	     , zero(divides(x, x)) -> x
866.61/297.03	     , eq(0(), 0()) -> true()
866.61/297.03	     , eq(0(), s(y)) -> false()
866.61/297.03	     , eq(s(x), 0()) -> false()
866.61/297.03	     , eq(s(x), s(y)) -> eq(x, y)
866.61/297.03	     , divides(y, x) -> eq(x, times(div(x, y), y))
866.61/297.03	     , prime(s(s(x))) -> pr(s(s(x)), s(x))
866.61/297.03	     , pr(x, s(0())) -> true()
866.61/297.03	     , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
866.61/297.03	     , if(true(), x, y) -> false()
866.61/297.03	     , if(false(), x, y) -> pr(x, y) }
866.61/297.03	   Obligation:
866.61/297.03	     runtime complexity
866.61/297.03	   Answer:
866.61/297.03	     MAYBE
866.61/297.03	   
866.61/297.03	   We estimate the number of application of {1,8,12,16,22,24,25,26,30}
866.61/297.03	   by applications of Pre({1,8,12,16,22,24,25,26,30}) =
866.61/297.03	   {2,3,5,10,11,13,14,15,17,18,19,20,21,23,27,28,29,31}. Here rules
866.61/297.03	   are labeled as follows:
866.61/297.03	   
866.61/297.03	     DPs:
866.61/297.03	       { 1: p^#(0()) -> c_1()
866.61/297.03	       , 2: p^#(s(x)) -> c_2(x)
866.61/297.03	       , 3: plus^#(x, 0()) -> c_3(x)
866.61/297.03	       , 4: plus^#(x, s(y)) -> c_4(plus^#(x, p(s(y))))
866.61/297.03	       , 5: plus^#(0(), y) -> c_5(y)
866.61/297.03	       , 6: plus^#(s(x), y) -> c_6(plus^#(x, y))
866.61/297.03	       , 7: plus^#(s(x), y) -> c_7(plus^#(p(s(x)), y))
866.61/297.03	       , 8: times^#(0(), y) -> c_8()
866.61/297.03	       , 9: times^#(s(x), y) -> c_9(plus^#(y, times(x, y)))
866.61/297.04	       , 10: times^#(s(0()), y) -> c_10(y)
866.61/297.04	       , 11: div^#(x, y) -> c_11(quot^#(x, y, y))
866.61/297.04	       , 12: div^#(0(), y) -> c_12()
866.61/297.04	       , 13: div^#(div(x, y), z) -> c_13(div^#(x, times(zero(y), z)))
866.61/297.04	       , 14: quot^#(x, 0(), s(z)) -> c_14(div^#(x, s(z)))
866.61/297.04	       , 15: quot^#(s(x), s(y), z) -> c_15(quot^#(x, y, z))
866.61/297.04	       , 16: quot^#(zero(y), s(y), z) -> c_16()
866.61/297.04	       , 17: zero^#(s(x)) ->
866.61/297.04	             c_17(if^#(eq(x, s(0())),
866.61/297.04	                       plus(zero(0()), 0()),
866.61/297.04	                       s(plus(0(), zero(0())))))
866.61/297.04	       , 18: zero^#(times(x, x)) -> c_18(x)
866.61/297.04	       , 19: zero^#(div(x, x)) -> c_19(x)
866.61/297.04	       , 20: zero^#(quot(x, x, x)) -> c_20(x)
866.61/297.04	       , 21: zero^#(divides(x, x)) -> c_21(x)
866.61/297.04	       , 22: if^#(true(), x, y) -> c_30()
866.61/297.04	       , 23: if^#(false(), x, y) -> c_31(pr^#(x, y))
866.61/297.04	       , 24: eq^#(0(), 0()) -> c_22()
866.61/297.04	       , 25: eq^#(0(), s(y)) -> c_23()
866.61/297.04	       , 26: eq^#(s(x), 0()) -> c_24()
866.61/297.04	       , 27: eq^#(s(x), s(y)) -> c_25(eq^#(x, y))
866.61/297.04	       , 28: divides^#(y, x) -> c_26(eq^#(x, times(div(x, y), y)))
866.61/297.04	       , 29: prime^#(s(s(x))) -> c_27(pr^#(s(s(x)), s(x)))
866.61/297.04	       , 30: pr^#(x, s(0())) -> c_28()
866.61/297.04	       , 31: pr^#(x, s(s(y))) ->
866.61/297.04	             c_29(if^#(divides(s(s(y)), x), x, s(y))) }
866.61/297.04	   
866.61/297.04	   We are left with following problem, upon which TcT provides the
866.61/297.04	   certificate MAYBE.
866.61/297.04	   
866.61/297.04	   Strict DPs:
866.61/297.04	     { p^#(s(x)) -> c_2(x)
866.61/297.04	     , plus^#(x, 0()) -> c_3(x)
866.61/297.04	     , plus^#(x, s(y)) -> c_4(plus^#(x, p(s(y))))
866.61/297.04	     , plus^#(0(), y) -> c_5(y)
866.61/297.04	     , plus^#(s(x), y) -> c_6(plus^#(x, y))
866.61/297.04	     , plus^#(s(x), y) -> c_7(plus^#(p(s(x)), y))
866.61/297.04	     , times^#(s(x), y) -> c_9(plus^#(y, times(x, y)))
866.61/297.04	     , times^#(s(0()), y) -> c_10(y)
866.61/297.04	     , div^#(x, y) -> c_11(quot^#(x, y, y))
866.61/297.04	     , div^#(div(x, y), z) -> c_13(div^#(x, times(zero(y), z)))
866.61/297.04	     , quot^#(x, 0(), s(z)) -> c_14(div^#(x, s(z)))
866.61/297.04	     , quot^#(s(x), s(y), z) -> c_15(quot^#(x, y, z))
866.61/297.04	     , zero^#(s(x)) ->
866.61/297.04	       c_17(if^#(eq(x, s(0())),
866.61/297.04	                 plus(zero(0()), 0()),
866.61/297.04	                 s(plus(0(), zero(0())))))
866.61/297.04	     , zero^#(times(x, x)) -> c_18(x)
866.61/297.04	     , zero^#(div(x, x)) -> c_19(x)
866.61/297.04	     , zero^#(quot(x, x, x)) -> c_20(x)
866.61/297.04	     , zero^#(divides(x, x)) -> c_21(x)
866.61/297.04	     , if^#(false(), x, y) -> c_31(pr^#(x, y))
866.61/297.04	     , eq^#(s(x), s(y)) -> c_25(eq^#(x, y))
866.61/297.04	     , divides^#(y, x) -> c_26(eq^#(x, times(div(x, y), y)))
866.61/297.04	     , prime^#(s(s(x))) -> c_27(pr^#(s(s(x)), s(x)))
866.61/297.04	     , pr^#(x, s(s(y))) -> c_29(if^#(divides(s(s(y)), x), x, s(y))) }
866.61/297.04	   Strict Trs:
866.61/297.04	     { p(0()) -> 0()
866.61/297.04	     , p(s(x)) -> x
866.61/297.04	     , plus(x, 0()) -> x
866.61/297.04	     , plus(x, s(y)) -> s(plus(x, p(s(y))))
866.61/297.04	     , plus(0(), y) -> y
866.61/297.04	     , plus(s(x), y) -> s(plus(x, y))
866.61/297.04	     , plus(s(x), y) -> s(plus(p(s(x)), y))
866.61/297.04	     , times(0(), y) -> 0()
866.61/297.04	     , times(s(x), y) -> plus(y, times(x, y))
866.61/297.04	     , times(s(0()), y) -> y
866.61/297.04	     , div(x, y) -> quot(x, y, y)
866.61/297.04	     , div(0(), y) -> 0()
866.61/297.04	     , div(div(x, y), z) -> div(x, times(zero(y), z))
866.61/297.04	     , quot(x, 0(), s(z)) -> s(div(x, s(z)))
866.61/297.04	     , quot(s(x), s(y), z) -> quot(x, y, z)
866.61/297.04	     , quot(zero(y), s(y), z) -> 0()
866.61/297.04	     , zero(s(x)) ->
866.61/297.04	       if(eq(x, s(0())), plus(zero(0()), 0()), s(plus(0(), zero(0()))))
866.61/297.04	     , zero(times(x, x)) -> x
866.61/297.04	     , zero(div(x, x)) -> x
866.61/297.04	     , zero(quot(x, x, x)) -> x
866.61/297.04	     , zero(divides(x, x)) -> x
866.61/297.04	     , eq(0(), 0()) -> true()
866.61/297.04	     , eq(0(), s(y)) -> false()
866.61/297.04	     , eq(s(x), 0()) -> false()
866.61/297.04	     , eq(s(x), s(y)) -> eq(x, y)
866.61/297.04	     , divides(y, x) -> eq(x, times(div(x, y), y))
866.61/297.04	     , prime(s(s(x))) -> pr(s(s(x)), s(x))
866.61/297.04	     , pr(x, s(0())) -> true()
866.61/297.04	     , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
866.61/297.04	     , if(true(), x, y) -> false()
866.61/297.04	     , if(false(), x, y) -> pr(x, y) }
866.61/297.04	   Weak DPs:
866.61/297.04	     { p^#(0()) -> c_1()
866.61/297.04	     , times^#(0(), y) -> c_8()
866.61/297.04	     , div^#(0(), y) -> c_12()
866.61/297.04	     , quot^#(zero(y), s(y), z) -> c_16()
866.61/297.04	     , if^#(true(), x, y) -> c_30()
866.61/297.04	     , eq^#(0(), 0()) -> c_22()
866.61/297.04	     , eq^#(0(), s(y)) -> c_23()
866.61/297.04	     , eq^#(s(x), 0()) -> c_24()
866.61/297.04	     , pr^#(x, s(0())) -> c_28() }
866.61/297.04	   Obligation:
866.61/297.04	     runtime complexity
866.61/297.04	   Answer:
866.61/297.04	     MAYBE
866.61/297.04	   
866.61/297.04	   Empty strict component of the problem is NOT empty.
866.61/297.04	
866.61/297.04	
866.61/297.04	Arrrr..
866.84/297.23	EOF