MAYBE 917.28/297.04 MAYBE 917.28/297.04 917.28/297.04 We are left with following problem, upon which TcT provides the 917.28/297.04 certificate MAYBE. 917.28/297.04 917.28/297.04 Strict Trs: 917.28/297.04 { average(x, y) -> if(ge(x, y), x, y) 917.28/297.04 , if(true(), x, y) -> averIter(y, x, y) 917.28/297.04 , if(false(), x, y) -> averIter(x, y, x) 917.28/297.04 , ge(x, 0()) -> true() 917.28/297.04 , ge(s(x), s(y)) -> ge(x, y) 917.28/297.04 , ge(0(), s(y)) -> false() 917.28/297.04 , averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 917.28/297.04 , ifIter(true(), x, y, z) -> z 917.28/297.04 , ifIter(false(), x, y, z) -> 917.28/297.04 averIter(plus(x, s(s(s(0())))), plus(y, s(0())), plus(z, s(0()))) 917.28/297.04 , plus(s(x), y) -> s(plus(x, y)) 917.28/297.04 , plus(0(), y) -> y 917.28/297.04 , append(nil(), y) -> y 917.28/297.04 , append(cons(n, x), y) -> cons(n, app(x, y)) 917.28/297.04 , low(n, nil()) -> nil() 917.28/297.04 , low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 917.28/297.04 , if_low(true(), n, cons(m, x)) -> low(n, x) 917.28/297.04 , if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)) 917.28/297.04 , high(n, nil()) -> nil() 917.28/297.04 , high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 917.28/297.04 , if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)) 917.28/297.04 , if_high(false(), n, cons(m, x)) -> high(n, x) 917.28/297.04 , quicksort(x) -> ifquick(isempty(x), x) 917.28/297.04 , ifquick(true(), x) -> nil() 917.28/297.04 , ifquick(false(), x) -> 917.28/297.04 append(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x))))) 917.28/297.04 , isempty(nil()) -> true() 917.28/297.04 , isempty(cons(n, x)) -> false() 917.28/297.04 , head(nil()) -> error() 917.28/297.04 , head(cons(n, x)) -> n 917.28/297.04 , tail(nil()) -> nil() 917.28/297.04 , tail(cons(n, x)) -> x 917.28/297.04 , a() -> b() 917.28/297.04 , a() -> c() } 917.28/297.04 Obligation: 917.28/297.04 runtime complexity 917.28/297.04 Answer: 917.28/297.04 MAYBE 917.28/297.04 917.28/297.04 None of the processors succeeded. 917.28/297.04 917.28/297.04 Details of failed attempt(s): 917.28/297.04 ----------------------------- 917.28/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 917.28/297.04 following reason: 917.28/297.04 917.28/297.04 Computation stopped due to timeout after 297.0 seconds. 917.28/297.04 917.28/297.04 2) 'Best' failed due to the following reason: 917.28/297.04 917.28/297.04 None of the processors succeeded. 917.28/297.04 917.28/297.04 Details of failed attempt(s): 917.28/297.04 ----------------------------- 917.28/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 917.28/297.04 seconds)' failed due to the following reason: 917.28/297.04 917.28/297.04 Computation stopped due to timeout after 148.0 seconds. 917.28/297.04 917.28/297.04 2) 'Best' failed due to the following reason: 917.28/297.04 917.28/297.04 None of the processors succeeded. 917.28/297.04 917.28/297.04 Details of failed attempt(s): 917.28/297.04 ----------------------------- 917.28/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 917.28/297.04 following reason: 917.28/297.04 917.28/297.04 The processor is inapplicable, reason: 917.28/297.04 Processor only applicable for innermost runtime complexity analysis 917.28/297.04 917.28/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 917.28/297.04 to the following reason: 917.28/297.04 917.28/297.04 The processor is inapplicable, reason: 917.28/297.04 Processor only applicable for innermost runtime complexity analysis 917.28/297.04 917.28/297.04 917.28/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 917.28/297.04 failed due to the following reason: 917.28/297.04 917.28/297.04 None of the processors succeeded. 917.28/297.04 917.28/297.04 Details of failed attempt(s): 917.28/297.04 ----------------------------- 917.28/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 917.28/297.04 failed due to the following reason: 917.28/297.04 917.28/297.04 match-boundness of the problem could not be verified. 917.28/297.04 917.28/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 917.28/297.04 failed due to the following reason: 917.28/297.04 917.28/297.04 match-boundness of the problem could not be verified. 917.28/297.04 917.28/297.04 917.28/297.04 917.28/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 917.28/297.04 the following reason: 917.28/297.04 917.28/297.04 We add the following weak dependency pairs: 917.28/297.04 917.28/297.04 Strict DPs: 917.28/297.04 { average^#(x, y) -> c_1(if^#(ge(x, y), x, y)) 917.28/297.04 , if^#(true(), x, y) -> c_2(averIter^#(y, x, y)) 917.28/297.04 , if^#(false(), x, y) -> c_3(averIter^#(x, y, x)) 917.28/297.04 , averIter^#(x, y, z) -> c_7(ifIter^#(ge(x, y), x, y, z)) 917.28/297.04 , ge^#(x, 0()) -> c_4() 917.28/297.04 , ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 917.28/297.04 , ge^#(0(), s(y)) -> c_6() 917.28/297.04 , ifIter^#(true(), x, y, z) -> c_8(z) 917.28/297.04 , ifIter^#(false(), x, y, z) -> 917.28/297.04 c_9(averIter^#(plus(x, s(s(s(0())))), 917.28/297.04 plus(y, s(0())), 917.28/297.04 plus(z, s(0())))) 917.28/297.04 , plus^#(s(x), y) -> c_10(plus^#(x, y)) 917.28/297.04 , plus^#(0(), y) -> c_11(y) 917.28/297.04 , append^#(nil(), y) -> c_12(y) 917.28/297.04 , append^#(cons(n, x), y) -> c_13(n, x, y) 917.28/297.04 , low^#(n, nil()) -> c_14() 917.28/297.04 , low^#(n, cons(m, x)) -> c_15(if_low^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , if_low^#(true(), n, cons(m, x)) -> c_16(low^#(n, x)) 917.28/297.04 , if_low^#(false(), n, cons(m, x)) -> c_17(m, low^#(n, x)) 917.28/297.04 , high^#(n, nil()) -> c_18() 917.28/297.04 , high^#(n, cons(m, x)) -> c_19(if_high^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , if_high^#(true(), n, cons(m, x)) -> 917.28/297.04 c_20(average^#(m, m), high^#(n, x)) 917.28/297.04 , if_high^#(false(), n, cons(m, x)) -> c_21(high^#(n, x)) 917.28/297.04 , quicksort^#(x) -> c_22(ifquick^#(isempty(x), x)) 917.28/297.04 , ifquick^#(true(), x) -> c_23() 917.28/297.04 , ifquick^#(false(), x) -> 917.28/297.04 c_24(append^#(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x)))))) 917.28/297.04 , isempty^#(nil()) -> c_25() 917.28/297.04 , isempty^#(cons(n, x)) -> c_26() 917.28/297.04 , head^#(nil()) -> c_27() 917.28/297.04 , head^#(cons(n, x)) -> c_28(n) 917.28/297.04 , tail^#(nil()) -> c_29() 917.28/297.04 , tail^#(cons(n, x)) -> c_30(x) 917.28/297.04 , a^#() -> c_31() 917.28/297.04 , a^#() -> c_32() } 917.28/297.04 917.28/297.04 and mark the set of starting terms. 917.28/297.04 917.28/297.04 We are left with following problem, upon which TcT provides the 917.28/297.04 certificate MAYBE. 917.28/297.04 917.28/297.04 Strict DPs: 917.28/297.04 { average^#(x, y) -> c_1(if^#(ge(x, y), x, y)) 917.28/297.04 , if^#(true(), x, y) -> c_2(averIter^#(y, x, y)) 917.28/297.04 , if^#(false(), x, y) -> c_3(averIter^#(x, y, x)) 917.28/297.04 , averIter^#(x, y, z) -> c_7(ifIter^#(ge(x, y), x, y, z)) 917.28/297.04 , ge^#(x, 0()) -> c_4() 917.28/297.04 , ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 917.28/297.04 , ge^#(0(), s(y)) -> c_6() 917.28/297.04 , ifIter^#(true(), x, y, z) -> c_8(z) 917.28/297.04 , ifIter^#(false(), x, y, z) -> 917.28/297.04 c_9(averIter^#(plus(x, s(s(s(0())))), 917.28/297.04 plus(y, s(0())), 917.28/297.04 plus(z, s(0())))) 917.28/297.04 , plus^#(s(x), y) -> c_10(plus^#(x, y)) 917.28/297.04 , plus^#(0(), y) -> c_11(y) 917.28/297.04 , append^#(nil(), y) -> c_12(y) 917.28/297.04 , append^#(cons(n, x), y) -> c_13(n, x, y) 917.28/297.04 , low^#(n, nil()) -> c_14() 917.28/297.04 , low^#(n, cons(m, x)) -> c_15(if_low^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , if_low^#(true(), n, cons(m, x)) -> c_16(low^#(n, x)) 917.28/297.04 , if_low^#(false(), n, cons(m, x)) -> c_17(m, low^#(n, x)) 917.28/297.04 , high^#(n, nil()) -> c_18() 917.28/297.04 , high^#(n, cons(m, x)) -> c_19(if_high^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , if_high^#(true(), n, cons(m, x)) -> 917.28/297.04 c_20(average^#(m, m), high^#(n, x)) 917.28/297.04 , if_high^#(false(), n, cons(m, x)) -> c_21(high^#(n, x)) 917.28/297.04 , quicksort^#(x) -> c_22(ifquick^#(isempty(x), x)) 917.28/297.04 , ifquick^#(true(), x) -> c_23() 917.28/297.04 , ifquick^#(false(), x) -> 917.28/297.04 c_24(append^#(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x)))))) 917.28/297.04 , isempty^#(nil()) -> c_25() 917.28/297.04 , isempty^#(cons(n, x)) -> c_26() 917.28/297.04 , head^#(nil()) -> c_27() 917.28/297.04 , head^#(cons(n, x)) -> c_28(n) 917.28/297.04 , tail^#(nil()) -> c_29() 917.28/297.04 , tail^#(cons(n, x)) -> c_30(x) 917.28/297.04 , a^#() -> c_31() 917.28/297.04 , a^#() -> c_32() } 917.28/297.04 Strict Trs: 917.28/297.04 { average(x, y) -> if(ge(x, y), x, y) 917.28/297.04 , if(true(), x, y) -> averIter(y, x, y) 917.28/297.04 , if(false(), x, y) -> averIter(x, y, x) 917.28/297.04 , ge(x, 0()) -> true() 917.28/297.04 , ge(s(x), s(y)) -> ge(x, y) 917.28/297.04 , ge(0(), s(y)) -> false() 917.28/297.04 , averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 917.28/297.04 , ifIter(true(), x, y, z) -> z 917.28/297.04 , ifIter(false(), x, y, z) -> 917.28/297.04 averIter(plus(x, s(s(s(0())))), plus(y, s(0())), plus(z, s(0()))) 917.28/297.04 , plus(s(x), y) -> s(plus(x, y)) 917.28/297.04 , plus(0(), y) -> y 917.28/297.04 , append(nil(), y) -> y 917.28/297.04 , append(cons(n, x), y) -> cons(n, app(x, y)) 917.28/297.04 , low(n, nil()) -> nil() 917.28/297.04 , low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 917.28/297.04 , if_low(true(), n, cons(m, x)) -> low(n, x) 917.28/297.04 , if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)) 917.28/297.04 , high(n, nil()) -> nil() 917.28/297.04 , high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 917.28/297.04 , if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)) 917.28/297.04 , if_high(false(), n, cons(m, x)) -> high(n, x) 917.28/297.04 , quicksort(x) -> ifquick(isempty(x), x) 917.28/297.04 , ifquick(true(), x) -> nil() 917.28/297.04 , ifquick(false(), x) -> 917.28/297.04 append(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x))))) 917.28/297.04 , isempty(nil()) -> true() 917.28/297.04 , isempty(cons(n, x)) -> false() 917.28/297.04 , head(nil()) -> error() 917.28/297.04 , head(cons(n, x)) -> n 917.28/297.04 , tail(nil()) -> nil() 917.28/297.04 , tail(cons(n, x)) -> x 917.28/297.04 , a() -> b() 917.28/297.04 , a() -> c() } 917.28/297.04 Obligation: 917.28/297.04 runtime complexity 917.28/297.04 Answer: 917.28/297.04 MAYBE 917.28/297.04 917.28/297.04 We estimate the number of application of 917.28/297.04 {5,7,14,18,23,25,26,27,29,31,32} by applications of 917.28/297.04 Pre({5,7,14,18,23,25,26,27,29,31,32}) = 917.28/297.04 {6,8,11,12,13,16,17,20,21,22,28,30}. Here rules are labeled as 917.28/297.04 follows: 917.28/297.04 917.28/297.04 DPs: 917.28/297.04 { 1: average^#(x, y) -> c_1(if^#(ge(x, y), x, y)) 917.28/297.04 , 2: if^#(true(), x, y) -> c_2(averIter^#(y, x, y)) 917.28/297.04 , 3: if^#(false(), x, y) -> c_3(averIter^#(x, y, x)) 917.28/297.04 , 4: averIter^#(x, y, z) -> c_7(ifIter^#(ge(x, y), x, y, z)) 917.28/297.04 , 5: ge^#(x, 0()) -> c_4() 917.28/297.04 , 6: ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 917.28/297.04 , 7: ge^#(0(), s(y)) -> c_6() 917.28/297.04 , 8: ifIter^#(true(), x, y, z) -> c_8(z) 917.28/297.04 , 9: ifIter^#(false(), x, y, z) -> 917.28/297.04 c_9(averIter^#(plus(x, s(s(s(0())))), 917.28/297.04 plus(y, s(0())), 917.28/297.04 plus(z, s(0())))) 917.28/297.04 , 10: plus^#(s(x), y) -> c_10(plus^#(x, y)) 917.28/297.04 , 11: plus^#(0(), y) -> c_11(y) 917.28/297.04 , 12: append^#(nil(), y) -> c_12(y) 917.28/297.04 , 13: append^#(cons(n, x), y) -> c_13(n, x, y) 917.28/297.04 , 14: low^#(n, nil()) -> c_14() 917.28/297.04 , 15: low^#(n, cons(m, x)) -> 917.28/297.04 c_15(if_low^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , 16: if_low^#(true(), n, cons(m, x)) -> c_16(low^#(n, x)) 917.28/297.04 , 17: if_low^#(false(), n, cons(m, x)) -> c_17(m, low^#(n, x)) 917.28/297.04 , 18: high^#(n, nil()) -> c_18() 917.28/297.04 , 19: high^#(n, cons(m, x)) -> 917.28/297.04 c_19(if_high^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , 20: if_high^#(true(), n, cons(m, x)) -> 917.28/297.04 c_20(average^#(m, m), high^#(n, x)) 917.28/297.04 , 21: if_high^#(false(), n, cons(m, x)) -> c_21(high^#(n, x)) 917.28/297.04 , 22: quicksort^#(x) -> c_22(ifquick^#(isempty(x), x)) 917.28/297.04 , 23: ifquick^#(true(), x) -> c_23() 917.28/297.04 , 24: ifquick^#(false(), x) -> 917.28/297.04 c_24(append^#(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x)))))) 917.28/297.04 , 25: isempty^#(nil()) -> c_25() 917.28/297.04 , 26: isempty^#(cons(n, x)) -> c_26() 917.28/297.04 , 27: head^#(nil()) -> c_27() 917.28/297.04 , 28: head^#(cons(n, x)) -> c_28(n) 917.28/297.04 , 29: tail^#(nil()) -> c_29() 917.28/297.04 , 30: tail^#(cons(n, x)) -> c_30(x) 917.28/297.04 , 31: a^#() -> c_31() 917.28/297.04 , 32: a^#() -> c_32() } 917.28/297.04 917.28/297.04 We are left with following problem, upon which TcT provides the 917.28/297.04 certificate MAYBE. 917.28/297.04 917.28/297.04 Strict DPs: 917.28/297.04 { average^#(x, y) -> c_1(if^#(ge(x, y), x, y)) 917.28/297.04 , if^#(true(), x, y) -> c_2(averIter^#(y, x, y)) 917.28/297.04 , if^#(false(), x, y) -> c_3(averIter^#(x, y, x)) 917.28/297.04 , averIter^#(x, y, z) -> c_7(ifIter^#(ge(x, y), x, y, z)) 917.28/297.04 , ge^#(s(x), s(y)) -> c_5(ge^#(x, y)) 917.28/297.04 , ifIter^#(true(), x, y, z) -> c_8(z) 917.28/297.04 , ifIter^#(false(), x, y, z) -> 917.28/297.04 c_9(averIter^#(plus(x, s(s(s(0())))), 917.28/297.04 plus(y, s(0())), 917.28/297.04 plus(z, s(0())))) 917.28/297.04 , plus^#(s(x), y) -> c_10(plus^#(x, y)) 917.28/297.04 , plus^#(0(), y) -> c_11(y) 917.28/297.04 , append^#(nil(), y) -> c_12(y) 917.28/297.04 , append^#(cons(n, x), y) -> c_13(n, x, y) 917.28/297.04 , low^#(n, cons(m, x)) -> c_15(if_low^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , if_low^#(true(), n, cons(m, x)) -> c_16(low^#(n, x)) 917.28/297.04 , if_low^#(false(), n, cons(m, x)) -> c_17(m, low^#(n, x)) 917.28/297.04 , high^#(n, cons(m, x)) -> c_19(if_high^#(ge(m, n), n, cons(m, x))) 917.28/297.04 , if_high^#(true(), n, cons(m, x)) -> 917.28/297.04 c_20(average^#(m, m), high^#(n, x)) 917.28/297.04 , if_high^#(false(), n, cons(m, x)) -> c_21(high^#(n, x)) 917.28/297.04 , quicksort^#(x) -> c_22(ifquick^#(isempty(x), x)) 917.28/297.04 , ifquick^#(false(), x) -> 917.28/297.04 c_24(append^#(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x)))))) 917.28/297.04 , head^#(cons(n, x)) -> c_28(n) 917.28/297.04 , tail^#(cons(n, x)) -> c_30(x) } 917.28/297.04 Strict Trs: 917.28/297.04 { average(x, y) -> if(ge(x, y), x, y) 917.28/297.04 , if(true(), x, y) -> averIter(y, x, y) 917.28/297.04 , if(false(), x, y) -> averIter(x, y, x) 917.28/297.04 , ge(x, 0()) -> true() 917.28/297.04 , ge(s(x), s(y)) -> ge(x, y) 917.28/297.04 , ge(0(), s(y)) -> false() 917.28/297.04 , averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 917.28/297.04 , ifIter(true(), x, y, z) -> z 917.28/297.04 , ifIter(false(), x, y, z) -> 917.28/297.04 averIter(plus(x, s(s(s(0())))), plus(y, s(0())), plus(z, s(0()))) 917.28/297.04 , plus(s(x), y) -> s(plus(x, y)) 917.28/297.04 , plus(0(), y) -> y 917.28/297.04 , append(nil(), y) -> y 917.28/297.04 , append(cons(n, x), y) -> cons(n, app(x, y)) 917.28/297.04 , low(n, nil()) -> nil() 917.28/297.04 , low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 917.28/297.04 , if_low(true(), n, cons(m, x)) -> low(n, x) 917.28/297.04 , if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)) 917.28/297.04 , high(n, nil()) -> nil() 917.28/297.04 , high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 917.28/297.04 , if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)) 917.28/297.04 , if_high(false(), n, cons(m, x)) -> high(n, x) 917.28/297.04 , quicksort(x) -> ifquick(isempty(x), x) 917.28/297.04 , ifquick(true(), x) -> nil() 917.28/297.04 , ifquick(false(), x) -> 917.28/297.04 append(quicksort(low(head(x), tail(x))), 917.28/297.04 cons(tail(x), quicksort(high(head(x), tail(x))))) 917.28/297.04 , isempty(nil()) -> true() 917.28/297.04 , isempty(cons(n, x)) -> false() 917.28/297.04 , head(nil()) -> error() 917.28/297.04 , head(cons(n, x)) -> n 917.28/297.04 , tail(nil()) -> nil() 917.28/297.04 , tail(cons(n, x)) -> x 917.28/297.04 , a() -> b() 917.28/297.04 , a() -> c() } 917.28/297.04 Weak DPs: 917.28/297.04 { ge^#(x, 0()) -> c_4() 917.28/297.04 , ge^#(0(), s(y)) -> c_6() 917.28/297.04 , low^#(n, nil()) -> c_14() 917.28/297.04 , high^#(n, nil()) -> c_18() 917.28/297.04 , ifquick^#(true(), x) -> c_23() 917.28/297.04 , isempty^#(nil()) -> c_25() 917.28/297.04 , isempty^#(cons(n, x)) -> c_26() 917.28/297.04 , head^#(nil()) -> c_27() 917.28/297.04 , tail^#(nil()) -> c_29() 917.28/297.04 , a^#() -> c_31() 917.28/297.04 , a^#() -> c_32() } 917.28/297.04 Obligation: 917.28/297.04 runtime complexity 917.28/297.04 Answer: 917.28/297.04 MAYBE 917.28/297.04 917.28/297.04 Empty strict component of the problem is NOT empty. 917.28/297.04 917.28/297.04 917.28/297.04 Arrrr.. 917.42/297.12 EOF