MAYBE 745.08/297.06 MAYBE 745.08/297.06 745.08/297.06 We are left with following problem, upon which TcT provides the 745.08/297.06 certificate MAYBE. 745.08/297.06 745.08/297.06 Strict Trs: 745.08/297.06 { plus(x, y) -> plusIter(x, y, 0()) 745.08/297.06 , plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) 745.08/297.06 , ifPlus(true(), x, y, z) -> y 745.08/297.06 , ifPlus(false(), x, y, z) -> plusIter(x, s(y), s(z)) 745.08/297.06 , le(0(), y) -> true() 745.08/297.06 , le(s(x), 0()) -> false() 745.08/297.06 , le(s(x), s(y)) -> le(x, y) 745.08/297.06 , sum(xs) -> sumIter(xs, 0()) 745.08/297.06 , sumIter(xs, x) -> ifSum(isempty(xs), xs, x, plus(x, head(xs))) 745.08/297.06 , ifSum(true(), xs, x, y) -> x 745.08/297.06 , ifSum(false(), xs, x, y) -> sumIter(tail(xs), y) 745.08/297.06 , isempty(nil()) -> true() 745.08/297.06 , isempty(cons(x, xs)) -> false() 745.08/297.06 , head(nil()) -> error() 745.08/297.06 , head(cons(x, xs)) -> x 745.08/297.06 , tail(nil()) -> nil() 745.08/297.06 , tail(cons(x, xs)) -> xs 745.08/297.06 , a() -> b() 745.08/297.06 , a() -> c() } 745.08/297.06 Obligation: 745.08/297.06 runtime complexity 745.08/297.06 Answer: 745.08/297.06 MAYBE 745.08/297.06 745.08/297.06 None of the processors succeeded. 745.08/297.06 745.08/297.06 Details of failed attempt(s): 745.08/297.06 ----------------------------- 745.08/297.06 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 745.08/297.06 following reason: 745.08/297.06 745.08/297.06 Computation stopped due to timeout after 297.0 seconds. 745.08/297.06 745.08/297.06 2) 'Best' failed due to the following reason: 745.08/297.06 745.08/297.06 None of the processors succeeded. 745.08/297.06 745.08/297.06 Details of failed attempt(s): 745.08/297.06 ----------------------------- 745.08/297.06 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 745.08/297.06 seconds)' failed due to the following reason: 745.08/297.06 745.08/297.06 Computation stopped due to timeout after 148.0 seconds. 745.08/297.06 745.08/297.06 2) 'Best' failed due to the following reason: 745.08/297.06 745.08/297.06 None of the processors succeeded. 745.08/297.06 745.08/297.06 Details of failed attempt(s): 745.08/297.06 ----------------------------- 745.08/297.06 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 745.08/297.06 to the following reason: 745.08/297.06 745.08/297.06 The processor is inapplicable, reason: 745.08/297.06 Processor only applicable for innermost runtime complexity analysis 745.08/297.06 745.08/297.06 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 745.08/297.06 following reason: 745.08/297.06 745.08/297.06 The processor is inapplicable, reason: 745.08/297.06 Processor only applicable for innermost runtime complexity analysis 745.08/297.06 745.08/297.06 745.08/297.06 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 745.08/297.06 failed due to the following reason: 745.08/297.06 745.08/297.06 None of the processors succeeded. 745.08/297.06 745.08/297.06 Details of failed attempt(s): 745.08/297.06 ----------------------------- 745.08/297.06 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 745.08/297.06 failed due to the following reason: 745.08/297.06 745.08/297.06 match-boundness of the problem could not be verified. 745.08/297.06 745.08/297.06 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 745.08/297.06 failed due to the following reason: 745.08/297.06 745.08/297.06 match-boundness of the problem could not be verified. 745.08/297.06 745.08/297.06 745.08/297.06 745.08/297.06 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 745.08/297.06 the following reason: 745.08/297.06 745.08/297.06 We add the following weak dependency pairs: 745.08/297.06 745.08/297.06 Strict DPs: 745.08/297.06 { plus^#(x, y) -> c_1(plusIter^#(x, y, 0())) 745.08/297.06 , plusIter^#(x, y, z) -> c_2(ifPlus^#(le(x, z), x, y, z)) 745.08/297.06 , ifPlus^#(true(), x, y, z) -> c_3(y) 745.08/297.06 , ifPlus^#(false(), x, y, z) -> c_4(plusIter^#(x, s(y), s(z))) 745.08/297.06 , le^#(0(), y) -> c_5() 745.08/297.06 , le^#(s(x), 0()) -> c_6() 745.08/297.06 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 745.08/297.06 , sum^#(xs) -> c_8(sumIter^#(xs, 0())) 745.08/297.06 , sumIter^#(xs, x) -> 745.08/297.06 c_9(ifSum^#(isempty(xs), xs, x, plus(x, head(xs)))) 745.08/297.06 , ifSum^#(true(), xs, x, y) -> c_10(x) 745.08/297.06 , ifSum^#(false(), xs, x, y) -> c_11(sumIter^#(tail(xs), y)) 745.08/297.06 , isempty^#(nil()) -> c_12() 745.08/297.06 , isempty^#(cons(x, xs)) -> c_13() 745.08/297.06 , head^#(nil()) -> c_14() 745.08/297.06 , head^#(cons(x, xs)) -> c_15(x) 745.08/297.06 , tail^#(nil()) -> c_16() 745.08/297.06 , tail^#(cons(x, xs)) -> c_17(xs) 745.08/297.06 , a^#() -> c_18() 745.08/297.06 , a^#() -> c_19() } 745.08/297.06 745.08/297.06 and mark the set of starting terms. 745.08/297.06 745.08/297.06 We are left with following problem, upon which TcT provides the 745.08/297.06 certificate MAYBE. 745.08/297.06 745.08/297.06 Strict DPs: 745.08/297.06 { plus^#(x, y) -> c_1(plusIter^#(x, y, 0())) 745.08/297.06 , plusIter^#(x, y, z) -> c_2(ifPlus^#(le(x, z), x, y, z)) 745.08/297.06 , ifPlus^#(true(), x, y, z) -> c_3(y) 745.08/297.06 , ifPlus^#(false(), x, y, z) -> c_4(plusIter^#(x, s(y), s(z))) 745.08/297.06 , le^#(0(), y) -> c_5() 745.08/297.06 , le^#(s(x), 0()) -> c_6() 745.08/297.06 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 745.08/297.06 , sum^#(xs) -> c_8(sumIter^#(xs, 0())) 745.08/297.06 , sumIter^#(xs, x) -> 745.08/297.06 c_9(ifSum^#(isempty(xs), xs, x, plus(x, head(xs)))) 745.08/297.06 , ifSum^#(true(), xs, x, y) -> c_10(x) 745.08/297.06 , ifSum^#(false(), xs, x, y) -> c_11(sumIter^#(tail(xs), y)) 745.08/297.06 , isempty^#(nil()) -> c_12() 745.08/297.06 , isempty^#(cons(x, xs)) -> c_13() 745.08/297.06 , head^#(nil()) -> c_14() 745.08/297.06 , head^#(cons(x, xs)) -> c_15(x) 745.08/297.06 , tail^#(nil()) -> c_16() 745.08/297.06 , tail^#(cons(x, xs)) -> c_17(xs) 745.08/297.06 , a^#() -> c_18() 745.08/297.06 , a^#() -> c_19() } 745.08/297.06 Strict Trs: 745.08/297.06 { plus(x, y) -> plusIter(x, y, 0()) 745.08/297.06 , plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) 745.08/297.06 , ifPlus(true(), x, y, z) -> y 745.08/297.06 , ifPlus(false(), x, y, z) -> plusIter(x, s(y), s(z)) 745.08/297.06 , le(0(), y) -> true() 745.08/297.06 , le(s(x), 0()) -> false() 745.08/297.06 , le(s(x), s(y)) -> le(x, y) 745.08/297.06 , sum(xs) -> sumIter(xs, 0()) 745.08/297.06 , sumIter(xs, x) -> ifSum(isempty(xs), xs, x, plus(x, head(xs))) 745.08/297.06 , ifSum(true(), xs, x, y) -> x 745.08/297.06 , ifSum(false(), xs, x, y) -> sumIter(tail(xs), y) 745.08/297.06 , isempty(nil()) -> true() 745.08/297.06 , isempty(cons(x, xs)) -> false() 745.08/297.06 , head(nil()) -> error() 745.08/297.06 , head(cons(x, xs)) -> x 745.08/297.06 , tail(nil()) -> nil() 745.08/297.06 , tail(cons(x, xs)) -> xs 745.08/297.06 , a() -> b() 745.08/297.06 , a() -> c() } 745.08/297.06 Obligation: 745.08/297.06 runtime complexity 745.08/297.06 Answer: 745.08/297.06 MAYBE 745.08/297.06 745.08/297.06 We estimate the number of application of {5,6,12,13,14,16,18,19} by 745.08/297.06 applications of Pre({5,6,12,13,14,16,18,19}) = {3,7,10,15,17}. Here 745.08/297.06 rules are labeled as follows: 745.08/297.06 745.08/297.06 DPs: 745.08/297.06 { 1: plus^#(x, y) -> c_1(plusIter^#(x, y, 0())) 745.08/297.06 , 2: plusIter^#(x, y, z) -> c_2(ifPlus^#(le(x, z), x, y, z)) 745.08/297.06 , 3: ifPlus^#(true(), x, y, z) -> c_3(y) 745.08/297.06 , 4: ifPlus^#(false(), x, y, z) -> c_4(plusIter^#(x, s(y), s(z))) 745.08/297.06 , 5: le^#(0(), y) -> c_5() 745.08/297.06 , 6: le^#(s(x), 0()) -> c_6() 745.08/297.06 , 7: le^#(s(x), s(y)) -> c_7(le^#(x, y)) 745.08/297.06 , 8: sum^#(xs) -> c_8(sumIter^#(xs, 0())) 745.08/297.06 , 9: sumIter^#(xs, x) -> 745.08/297.06 c_9(ifSum^#(isempty(xs), xs, x, plus(x, head(xs)))) 745.08/297.06 , 10: ifSum^#(true(), xs, x, y) -> c_10(x) 745.08/297.06 , 11: ifSum^#(false(), xs, x, y) -> c_11(sumIter^#(tail(xs), y)) 745.08/297.06 , 12: isempty^#(nil()) -> c_12() 745.08/297.06 , 13: isempty^#(cons(x, xs)) -> c_13() 745.08/297.06 , 14: head^#(nil()) -> c_14() 745.08/297.06 , 15: head^#(cons(x, xs)) -> c_15(x) 745.08/297.06 , 16: tail^#(nil()) -> c_16() 745.08/297.06 , 17: tail^#(cons(x, xs)) -> c_17(xs) 745.08/297.06 , 18: a^#() -> c_18() 745.08/297.06 , 19: a^#() -> c_19() } 745.08/297.06 745.08/297.06 We are left with following problem, upon which TcT provides the 745.08/297.06 certificate MAYBE. 745.08/297.06 745.08/297.06 Strict DPs: 745.08/297.06 { plus^#(x, y) -> c_1(plusIter^#(x, y, 0())) 745.08/297.06 , plusIter^#(x, y, z) -> c_2(ifPlus^#(le(x, z), x, y, z)) 745.08/297.06 , ifPlus^#(true(), x, y, z) -> c_3(y) 745.08/297.06 , ifPlus^#(false(), x, y, z) -> c_4(plusIter^#(x, s(y), s(z))) 745.08/297.06 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 745.08/297.06 , sum^#(xs) -> c_8(sumIter^#(xs, 0())) 745.08/297.06 , sumIter^#(xs, x) -> 745.08/297.06 c_9(ifSum^#(isempty(xs), xs, x, plus(x, head(xs)))) 745.08/297.06 , ifSum^#(true(), xs, x, y) -> c_10(x) 745.08/297.06 , ifSum^#(false(), xs, x, y) -> c_11(sumIter^#(tail(xs), y)) 745.08/297.06 , head^#(cons(x, xs)) -> c_15(x) 745.08/297.06 , tail^#(cons(x, xs)) -> c_17(xs) } 745.08/297.06 Strict Trs: 745.08/297.06 { plus(x, y) -> plusIter(x, y, 0()) 745.08/297.06 , plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) 745.08/297.06 , ifPlus(true(), x, y, z) -> y 745.08/297.06 , ifPlus(false(), x, y, z) -> plusIter(x, s(y), s(z)) 745.08/297.06 , le(0(), y) -> true() 745.08/297.06 , le(s(x), 0()) -> false() 745.08/297.06 , le(s(x), s(y)) -> le(x, y) 745.08/297.06 , sum(xs) -> sumIter(xs, 0()) 745.08/297.06 , sumIter(xs, x) -> ifSum(isempty(xs), xs, x, plus(x, head(xs))) 745.08/297.06 , ifSum(true(), xs, x, y) -> x 745.08/297.06 , ifSum(false(), xs, x, y) -> sumIter(tail(xs), y) 745.08/297.06 , isempty(nil()) -> true() 745.08/297.06 , isempty(cons(x, xs)) -> false() 745.08/297.06 , head(nil()) -> error() 745.08/297.06 , head(cons(x, xs)) -> x 745.08/297.06 , tail(nil()) -> nil() 745.08/297.06 , tail(cons(x, xs)) -> xs 745.08/297.06 , a() -> b() 745.08/297.06 , a() -> c() } 745.08/297.06 Weak DPs: 745.08/297.06 { le^#(0(), y) -> c_5() 745.08/297.06 , le^#(s(x), 0()) -> c_6() 745.08/297.06 , isempty^#(nil()) -> c_12() 745.08/297.06 , isempty^#(cons(x, xs)) -> c_13() 745.08/297.06 , head^#(nil()) -> c_14() 745.08/297.06 , tail^#(nil()) -> c_16() 745.08/297.06 , a^#() -> c_18() 745.08/297.06 , a^#() -> c_19() } 745.08/297.06 Obligation: 745.08/297.06 runtime complexity 745.08/297.06 Answer: 745.08/297.06 MAYBE 745.08/297.06 745.08/297.06 Empty strict component of the problem is NOT empty. 745.08/297.06 745.08/297.06 745.08/297.06 Arrrr.. 745.31/297.29 EOF