MAYBE 772.92/297.04 MAYBE 772.92/297.04 772.92/297.04 We are left with following problem, upon which TcT provides the 772.92/297.04 certificate MAYBE. 772.92/297.04 772.92/297.04 Strict Trs: 772.92/297.04 { plus(x, 0()) -> x 772.92/297.04 , plus(0(), y) -> y 772.92/297.04 , plus(s(x), y) -> s(plus(x, y)) 772.92/297.04 , times(0(), y) -> 0() 772.92/297.04 , times(s(x), y) -> plus(y, times(x, y)) 772.92/297.04 , times(s(0()), y) -> y 772.92/297.04 , div(x, y) -> quot(x, y, y) 772.92/297.04 , div(0(), y) -> 0() 772.92/297.04 , div(div(x, y), z) -> div(x, times(y, z)) 772.92/297.04 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 772.92/297.04 , quot(0(), s(y), z) -> 0() 772.92/297.04 , quot(s(x), s(y), z) -> quot(x, y, z) 772.92/297.04 , eq(0(), 0()) -> true() 772.92/297.04 , eq(0(), s(y)) -> false() 772.92/297.04 , eq(s(x), 0()) -> false() 772.92/297.04 , eq(s(x), s(y)) -> eq(x, y) 772.92/297.04 , divides(y, x) -> eq(x, times(div(x, y), y)) 772.92/297.04 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 772.92/297.04 , pr(x, s(0())) -> true() 772.92/297.04 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 772.92/297.04 , if(true(), x, y) -> false() 772.92/297.04 , if(false(), x, y) -> pr(x, y) } 772.92/297.04 Obligation: 772.92/297.04 runtime complexity 772.92/297.04 Answer: 772.92/297.04 MAYBE 772.92/297.04 772.92/297.04 None of the processors succeeded. 772.92/297.04 772.92/297.04 Details of failed attempt(s): 772.92/297.04 ----------------------------- 772.92/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 772.92/297.04 following reason: 772.92/297.04 772.92/297.04 Computation stopped due to timeout after 297.0 seconds. 772.92/297.04 772.92/297.04 2) 'Best' failed due to the following reason: 772.92/297.04 772.92/297.04 None of the processors succeeded. 772.92/297.04 772.92/297.04 Details of failed attempt(s): 772.92/297.04 ----------------------------- 772.92/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 772.92/297.04 seconds)' failed due to the following reason: 772.92/297.04 772.92/297.04 Computation stopped due to timeout after 148.0 seconds. 772.92/297.04 772.92/297.04 2) 'Best' failed due to the following reason: 772.92/297.04 772.92/297.04 None of the processors succeeded. 772.92/297.04 772.92/297.04 Details of failed attempt(s): 772.92/297.04 ----------------------------- 772.92/297.04 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 772.92/297.04 to the following reason: 772.92/297.04 772.92/297.04 The processor is inapplicable, reason: 772.92/297.04 Processor only applicable for innermost runtime complexity analysis 772.92/297.04 772.92/297.04 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 772.92/297.04 following reason: 772.92/297.04 772.92/297.04 The processor is inapplicable, reason: 772.92/297.04 Processor only applicable for innermost runtime complexity analysis 772.92/297.04 772.92/297.04 772.92/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 772.92/297.04 failed due to the following reason: 772.92/297.04 772.92/297.04 None of the processors succeeded. 772.92/297.04 772.92/297.04 Details of failed attempt(s): 772.92/297.04 ----------------------------- 772.92/297.04 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 772.92/297.04 failed due to the following reason: 772.92/297.04 772.92/297.04 match-boundness of the problem could not be verified. 772.92/297.04 772.92/297.04 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 772.92/297.04 failed due to the following reason: 772.92/297.04 772.92/297.04 match-boundness of the problem could not be verified. 772.92/297.04 772.92/297.04 772.92/297.04 772.92/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 772.92/297.04 the following reason: 772.92/297.04 772.92/297.04 We add the following weak dependency pairs: 772.92/297.04 772.92/297.04 Strict DPs: 772.92/297.04 { plus^#(x, 0()) -> c_1(x) 772.92/297.04 , plus^#(0(), y) -> c_2(y) 772.92/297.04 , plus^#(s(x), y) -> c_3(plus^#(x, y)) 772.92/297.04 , times^#(0(), y) -> c_4() 772.92/297.04 , times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 772.92/297.04 , times^#(s(0()), y) -> c_6(y) 772.92/297.04 , div^#(x, y) -> c_7(quot^#(x, y, y)) 772.92/297.04 , div^#(0(), y) -> c_8() 772.92/297.04 , div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 772.92/297.04 , quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 772.92/297.04 , quot^#(0(), s(y), z) -> c_11() 772.92/297.04 , quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) 772.92/297.04 , eq^#(0(), 0()) -> c_13() 772.92/297.04 , eq^#(0(), s(y)) -> c_14() 772.92/297.04 , eq^#(s(x), 0()) -> c_15() 772.92/297.04 , eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 772.92/297.04 , divides^#(y, x) -> c_17(eq^#(x, times(div(x, y), y))) 772.92/297.04 , prime^#(s(s(x))) -> c_18(pr^#(s(s(x)), s(x))) 772.92/297.04 , pr^#(x, s(0())) -> c_19() 772.92/297.04 , pr^#(x, s(s(y))) -> c_20(if^#(divides(s(s(y)), x), x, s(y))) 772.92/297.04 , if^#(true(), x, y) -> c_21() 772.92/297.04 , if^#(false(), x, y) -> c_22(pr^#(x, y)) } 772.92/297.04 772.92/297.04 and mark the set of starting terms. 772.92/297.04 772.92/297.04 We are left with following problem, upon which TcT provides the 772.92/297.04 certificate MAYBE. 772.92/297.04 772.92/297.04 Strict DPs: 772.92/297.04 { plus^#(x, 0()) -> c_1(x) 772.92/297.04 , plus^#(0(), y) -> c_2(y) 772.92/297.04 , plus^#(s(x), y) -> c_3(plus^#(x, y)) 772.92/297.04 , times^#(0(), y) -> c_4() 772.92/297.04 , times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 772.92/297.04 , times^#(s(0()), y) -> c_6(y) 772.92/297.04 , div^#(x, y) -> c_7(quot^#(x, y, y)) 772.92/297.04 , div^#(0(), y) -> c_8() 772.92/297.04 , div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 772.92/297.04 , quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 772.92/297.04 , quot^#(0(), s(y), z) -> c_11() 772.92/297.04 , quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) 772.92/297.04 , eq^#(0(), 0()) -> c_13() 772.92/297.04 , eq^#(0(), s(y)) -> c_14() 772.92/297.04 , eq^#(s(x), 0()) -> c_15() 772.92/297.04 , eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 772.92/297.04 , divides^#(y, x) -> c_17(eq^#(x, times(div(x, y), y))) 772.92/297.04 , prime^#(s(s(x))) -> c_18(pr^#(s(s(x)), s(x))) 772.92/297.04 , pr^#(x, s(0())) -> c_19() 772.92/297.04 , pr^#(x, s(s(y))) -> c_20(if^#(divides(s(s(y)), x), x, s(y))) 772.92/297.04 , if^#(true(), x, y) -> c_21() 772.92/297.04 , if^#(false(), x, y) -> c_22(pr^#(x, y)) } 772.92/297.04 Strict Trs: 772.92/297.04 { plus(x, 0()) -> x 772.92/297.04 , plus(0(), y) -> y 772.92/297.04 , plus(s(x), y) -> s(plus(x, y)) 772.92/297.04 , times(0(), y) -> 0() 772.92/297.04 , times(s(x), y) -> plus(y, times(x, y)) 772.92/297.04 , times(s(0()), y) -> y 772.92/297.04 , div(x, y) -> quot(x, y, y) 772.92/297.04 , div(0(), y) -> 0() 772.92/297.04 , div(div(x, y), z) -> div(x, times(y, z)) 772.92/297.04 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 772.92/297.04 , quot(0(), s(y), z) -> 0() 772.92/297.04 , quot(s(x), s(y), z) -> quot(x, y, z) 772.92/297.04 , eq(0(), 0()) -> true() 772.92/297.04 , eq(0(), s(y)) -> false() 772.92/297.04 , eq(s(x), 0()) -> false() 772.92/297.04 , eq(s(x), s(y)) -> eq(x, y) 772.92/297.04 , divides(y, x) -> eq(x, times(div(x, y), y)) 772.92/297.04 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 772.92/297.04 , pr(x, s(0())) -> true() 772.92/297.04 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 772.92/297.04 , if(true(), x, y) -> false() 772.92/297.04 , if(false(), x, y) -> pr(x, y) } 772.92/297.04 Obligation: 772.92/297.04 runtime complexity 772.92/297.04 Answer: 772.92/297.04 MAYBE 772.92/297.04 772.92/297.04 We estimate the number of application of {4,8,11,13,14,15,19,21} by 772.92/297.04 applications of Pre({4,8,11,13,14,15,19,21}) = 772.92/297.04 {1,2,6,7,9,10,12,16,17,18,20,22}. Here rules are labeled as 772.92/297.04 follows: 772.92/297.04 772.92/297.04 DPs: 772.92/297.04 { 1: plus^#(x, 0()) -> c_1(x) 772.92/297.04 , 2: plus^#(0(), y) -> c_2(y) 772.92/297.04 , 3: plus^#(s(x), y) -> c_3(plus^#(x, y)) 772.92/297.04 , 4: times^#(0(), y) -> c_4() 772.92/297.04 , 5: times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 772.92/297.04 , 6: times^#(s(0()), y) -> c_6(y) 772.92/297.04 , 7: div^#(x, y) -> c_7(quot^#(x, y, y)) 772.92/297.04 , 8: div^#(0(), y) -> c_8() 772.92/297.04 , 9: div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 772.92/297.04 , 10: quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 772.92/297.04 , 11: quot^#(0(), s(y), z) -> c_11() 772.92/297.04 , 12: quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) 772.92/297.04 , 13: eq^#(0(), 0()) -> c_13() 772.92/297.04 , 14: eq^#(0(), s(y)) -> c_14() 772.92/297.04 , 15: eq^#(s(x), 0()) -> c_15() 772.92/297.04 , 16: eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 772.92/297.04 , 17: divides^#(y, x) -> c_17(eq^#(x, times(div(x, y), y))) 772.92/297.04 , 18: prime^#(s(s(x))) -> c_18(pr^#(s(s(x)), s(x))) 772.92/297.04 , 19: pr^#(x, s(0())) -> c_19() 772.92/297.04 , 20: pr^#(x, s(s(y))) -> c_20(if^#(divides(s(s(y)), x), x, s(y))) 772.92/297.04 , 21: if^#(true(), x, y) -> c_21() 772.92/297.04 , 22: if^#(false(), x, y) -> c_22(pr^#(x, y)) } 772.92/297.04 772.92/297.04 We are left with following problem, upon which TcT provides the 772.92/297.04 certificate MAYBE. 772.92/297.04 772.92/297.04 Strict DPs: 772.92/297.04 { plus^#(x, 0()) -> c_1(x) 772.92/297.04 , plus^#(0(), y) -> c_2(y) 772.92/297.04 , plus^#(s(x), y) -> c_3(plus^#(x, y)) 772.92/297.04 , times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 772.92/297.04 , times^#(s(0()), y) -> c_6(y) 772.92/297.04 , div^#(x, y) -> c_7(quot^#(x, y, y)) 772.92/297.04 , div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 772.92/297.04 , quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 772.92/297.04 , quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) 772.92/297.04 , eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 772.92/297.04 , divides^#(y, x) -> c_17(eq^#(x, times(div(x, y), y))) 772.92/297.04 , prime^#(s(s(x))) -> c_18(pr^#(s(s(x)), s(x))) 772.92/297.04 , pr^#(x, s(s(y))) -> c_20(if^#(divides(s(s(y)), x), x, s(y))) 772.92/297.04 , if^#(false(), x, y) -> c_22(pr^#(x, y)) } 772.92/297.04 Strict Trs: 772.92/297.04 { plus(x, 0()) -> x 772.92/297.04 , plus(0(), y) -> y 772.92/297.04 , plus(s(x), y) -> s(plus(x, y)) 772.92/297.04 , times(0(), y) -> 0() 772.92/297.04 , times(s(x), y) -> plus(y, times(x, y)) 772.92/297.04 , times(s(0()), y) -> y 772.92/297.04 , div(x, y) -> quot(x, y, y) 772.92/297.04 , div(0(), y) -> 0() 772.92/297.04 , div(div(x, y), z) -> div(x, times(y, z)) 772.92/297.04 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 772.92/297.04 , quot(0(), s(y), z) -> 0() 772.92/297.04 , quot(s(x), s(y), z) -> quot(x, y, z) 772.92/297.04 , eq(0(), 0()) -> true() 772.92/297.04 , eq(0(), s(y)) -> false() 772.92/297.04 , eq(s(x), 0()) -> false() 772.92/297.04 , eq(s(x), s(y)) -> eq(x, y) 772.92/297.04 , divides(y, x) -> eq(x, times(div(x, y), y)) 772.92/297.04 , prime(s(s(x))) -> pr(s(s(x)), s(x)) 772.92/297.04 , pr(x, s(0())) -> true() 772.92/297.04 , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 772.92/297.04 , if(true(), x, y) -> false() 772.92/297.04 , if(false(), x, y) -> pr(x, y) } 772.92/297.04 Weak DPs: 772.92/297.04 { times^#(0(), y) -> c_4() 772.92/297.04 , div^#(0(), y) -> c_8() 772.92/297.04 , quot^#(0(), s(y), z) -> c_11() 772.92/297.04 , eq^#(0(), 0()) -> c_13() 772.92/297.04 , eq^#(0(), s(y)) -> c_14() 772.92/297.04 , eq^#(s(x), 0()) -> c_15() 772.92/297.04 , pr^#(x, s(0())) -> c_19() 772.92/297.04 , if^#(true(), x, y) -> c_21() } 772.92/297.04 Obligation: 772.92/297.04 runtime complexity 772.92/297.04 Answer: 772.92/297.04 MAYBE 772.92/297.04 772.92/297.04 Empty strict component of the problem is NOT empty. 772.92/297.04 772.92/297.04 772.92/297.04 Arrrr.. 773.23/297.37 EOF