MAYBE 788.99/297.03 MAYBE 788.99/297.03 788.99/297.03 We are left with following problem, upon which TcT provides the 788.99/297.03 certificate MAYBE. 788.99/297.03 788.99/297.03 Strict Trs: 788.99/297.03 { le(s(x), s(y)) -> le(x, y) 788.99/297.03 , le(s(x), 0()) -> false() 788.99/297.03 , le(0(), y) -> true() 788.99/297.03 , double(s(x)) -> s(s(double(x))) 788.99/297.03 , double(0()) -> 0() 788.99/297.03 , log(s(x)) -> loop(s(x), s(0()), 0()) 788.99/297.03 , log(0()) -> logError() 788.99/297.03 , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) 788.99/297.03 , if(false(), x, y, z) -> loop(x, double(y), s(z)) 788.99/297.03 , if(true(), x, y, z) -> z 788.99/297.03 , maplog(xs) -> mapIter(xs, nil()) 788.99/297.03 , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys) 788.99/297.03 , ifmap(false(), xs, ys) -> 788.99/297.03 mapIter(droplast(xs), cons(log(last(xs)), ys)) 788.99/297.03 , ifmap(true(), xs, ys) -> ys 788.99/297.03 , isempty(nil()) -> true() 788.99/297.03 , isempty(cons(x, xs)) -> false() 788.99/297.03 , droplast(nil()) -> nil() 788.99/297.03 , droplast(cons(x, nil())) -> nil() 788.99/297.03 , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs))) 788.99/297.03 , last(nil()) -> error() 788.99/297.03 , last(cons(x, nil())) -> x 788.99/297.03 , last(cons(x, cons(y, xs))) -> last(cons(y, xs)) 788.99/297.03 , a() -> b() 788.99/297.03 , a() -> c() } 788.99/297.03 Obligation: 788.99/297.03 runtime complexity 788.99/297.03 Answer: 788.99/297.03 MAYBE 788.99/297.03 788.99/297.03 None of the processors succeeded. 788.99/297.03 788.99/297.03 Details of failed attempt(s): 788.99/297.03 ----------------------------- 788.99/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 788.99/297.03 following reason: 788.99/297.03 788.99/297.03 Computation stopped due to timeout after 297.0 seconds. 788.99/297.03 788.99/297.03 2) 'Best' failed due to the following reason: 788.99/297.03 788.99/297.03 None of the processors succeeded. 788.99/297.03 788.99/297.03 Details of failed attempt(s): 788.99/297.03 ----------------------------- 788.99/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 788.99/297.03 seconds)' failed due to the following reason: 788.99/297.03 788.99/297.03 Computation stopped due to timeout after 148.0 seconds. 788.99/297.03 788.99/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 788.99/297.03 failed due to the following reason: 788.99/297.03 788.99/297.03 None of the processors succeeded. 788.99/297.03 788.99/297.03 Details of failed attempt(s): 788.99/297.03 ----------------------------- 788.99/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 788.99/297.03 failed due to the following reason: 788.99/297.03 788.99/297.03 match-boundness of the problem could not be verified. 788.99/297.03 788.99/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 788.99/297.03 failed due to the following reason: 788.99/297.03 788.99/297.03 match-boundness of the problem could not be verified. 788.99/297.03 788.99/297.03 788.99/297.03 3) 'Best' failed due to the following reason: 788.99/297.03 788.99/297.03 None of the processors succeeded. 788.99/297.03 788.99/297.03 Details of failed attempt(s): 788.99/297.03 ----------------------------- 788.99/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 788.99/297.03 following reason: 788.99/297.03 788.99/297.03 The processor is inapplicable, reason: 788.99/297.03 Processor only applicable for innermost runtime complexity analysis 788.99/297.03 788.99/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 788.99/297.03 to the following reason: 788.99/297.03 788.99/297.03 The processor is inapplicable, reason: 788.99/297.03 Processor only applicable for innermost runtime complexity analysis 788.99/297.03 788.99/297.03 788.99/297.03 788.99/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 788.99/297.03 the following reason: 788.99/297.03 788.99/297.03 We add the following weak dependency pairs: 788.99/297.03 788.99/297.03 Strict DPs: 788.99/297.03 { le^#(s(x), s(y)) -> c_1(le^#(x, y)) 788.99/297.03 , le^#(s(x), 0()) -> c_2() 788.99/297.03 , le^#(0(), y) -> c_3() 788.99/297.03 , double^#(s(x)) -> c_4(double^#(x)) 788.99/297.03 , double^#(0()) -> c_5() 788.99/297.03 , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) 788.99/297.03 , log^#(0()) -> c_7() 788.99/297.03 , loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) 788.99/297.03 , if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) 788.99/297.03 , if^#(true(), x, y, z) -> c_10(z) 788.99/297.03 , maplog^#(xs) -> c_11(mapIter^#(xs, nil())) 788.99/297.03 , mapIter^#(xs, ys) -> c_12(ifmap^#(isempty(xs), xs, ys)) 788.99/297.03 , ifmap^#(false(), xs, ys) -> 788.99/297.03 c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys))) 788.99/297.03 , ifmap^#(true(), xs, ys) -> c_14(ys) 788.99/297.03 , isempty^#(nil()) -> c_15() 788.99/297.03 , isempty^#(cons(x, xs)) -> c_16() 788.99/297.03 , droplast^#(nil()) -> c_17() 788.99/297.03 , droplast^#(cons(x, nil())) -> c_18() 788.99/297.03 , droplast^#(cons(x, cons(y, xs))) -> 788.99/297.03 c_19(x, droplast^#(cons(y, xs))) 788.99/297.03 , last^#(nil()) -> c_20() 788.99/297.03 , last^#(cons(x, nil())) -> c_21(x) 788.99/297.03 , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs))) 788.99/297.03 , a^#() -> c_23() 788.99/297.03 , a^#() -> c_24() } 788.99/297.03 788.99/297.03 and mark the set of starting terms. 788.99/297.03 788.99/297.03 We are left with following problem, upon which TcT provides the 788.99/297.03 certificate MAYBE. 788.99/297.03 788.99/297.03 Strict DPs: 788.99/297.03 { le^#(s(x), s(y)) -> c_1(le^#(x, y)) 788.99/297.03 , le^#(s(x), 0()) -> c_2() 788.99/297.03 , le^#(0(), y) -> c_3() 788.99/297.03 , double^#(s(x)) -> c_4(double^#(x)) 788.99/297.03 , double^#(0()) -> c_5() 788.99/297.03 , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) 788.99/297.03 , log^#(0()) -> c_7() 788.99/297.03 , loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) 788.99/297.03 , if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) 788.99/297.03 , if^#(true(), x, y, z) -> c_10(z) 788.99/297.03 , maplog^#(xs) -> c_11(mapIter^#(xs, nil())) 788.99/297.03 , mapIter^#(xs, ys) -> c_12(ifmap^#(isempty(xs), xs, ys)) 788.99/297.03 , ifmap^#(false(), xs, ys) -> 788.99/297.03 c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys))) 788.99/297.03 , ifmap^#(true(), xs, ys) -> c_14(ys) 788.99/297.03 , isempty^#(nil()) -> c_15() 788.99/297.03 , isempty^#(cons(x, xs)) -> c_16() 788.99/297.03 , droplast^#(nil()) -> c_17() 788.99/297.03 , droplast^#(cons(x, nil())) -> c_18() 788.99/297.03 , droplast^#(cons(x, cons(y, xs))) -> 788.99/297.03 c_19(x, droplast^#(cons(y, xs))) 788.99/297.03 , last^#(nil()) -> c_20() 788.99/297.03 , last^#(cons(x, nil())) -> c_21(x) 788.99/297.03 , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs))) 788.99/297.03 , a^#() -> c_23() 788.99/297.03 , a^#() -> c_24() } 788.99/297.03 Strict Trs: 788.99/297.03 { le(s(x), s(y)) -> le(x, y) 788.99/297.03 , le(s(x), 0()) -> false() 788.99/297.03 , le(0(), y) -> true() 788.99/297.03 , double(s(x)) -> s(s(double(x))) 788.99/297.03 , double(0()) -> 0() 788.99/297.03 , log(s(x)) -> loop(s(x), s(0()), 0()) 788.99/297.03 , log(0()) -> logError() 788.99/297.03 , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) 788.99/297.03 , if(false(), x, y, z) -> loop(x, double(y), s(z)) 788.99/297.03 , if(true(), x, y, z) -> z 788.99/297.03 , maplog(xs) -> mapIter(xs, nil()) 788.99/297.03 , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys) 788.99/297.03 , ifmap(false(), xs, ys) -> 788.99/297.03 mapIter(droplast(xs), cons(log(last(xs)), ys)) 788.99/297.03 , ifmap(true(), xs, ys) -> ys 788.99/297.03 , isempty(nil()) -> true() 788.99/297.03 , isempty(cons(x, xs)) -> false() 788.99/297.03 , droplast(nil()) -> nil() 788.99/297.03 , droplast(cons(x, nil())) -> nil() 788.99/297.03 , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs))) 788.99/297.03 , last(nil()) -> error() 788.99/297.03 , last(cons(x, nil())) -> x 788.99/297.03 , last(cons(x, cons(y, xs))) -> last(cons(y, xs)) 788.99/297.03 , a() -> b() 788.99/297.03 , a() -> c() } 788.99/297.03 Obligation: 788.99/297.03 runtime complexity 788.99/297.03 Answer: 788.99/297.03 MAYBE 788.99/297.03 788.99/297.03 We estimate the number of application of 788.99/297.03 {2,3,5,7,15,16,17,18,20,23,24} by applications of 788.99/297.03 Pre({2,3,5,7,15,16,17,18,20,23,24}) = {1,4,10,14,19,21}. Here rules 788.99/297.03 are labeled as follows: 788.99/297.03 788.99/297.03 DPs: 788.99/297.03 { 1: le^#(s(x), s(y)) -> c_1(le^#(x, y)) 788.99/297.03 , 2: le^#(s(x), 0()) -> c_2() 788.99/297.03 , 3: le^#(0(), y) -> c_3() 788.99/297.03 , 4: double^#(s(x)) -> c_4(double^#(x)) 788.99/297.03 , 5: double^#(0()) -> c_5() 788.99/297.03 , 6: log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) 788.99/297.03 , 7: log^#(0()) -> c_7() 788.99/297.03 , 8: loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) 788.99/297.03 , 9: if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) 788.99/297.03 , 10: if^#(true(), x, y, z) -> c_10(z) 788.99/297.03 , 11: maplog^#(xs) -> c_11(mapIter^#(xs, nil())) 788.99/297.03 , 12: mapIter^#(xs, ys) -> c_12(ifmap^#(isempty(xs), xs, ys)) 788.99/297.03 , 13: ifmap^#(false(), xs, ys) -> 788.99/297.03 c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys))) 788.99/297.03 , 14: ifmap^#(true(), xs, ys) -> c_14(ys) 788.99/297.03 , 15: isempty^#(nil()) -> c_15() 788.99/297.03 , 16: isempty^#(cons(x, xs)) -> c_16() 788.99/297.03 , 17: droplast^#(nil()) -> c_17() 788.99/297.03 , 18: droplast^#(cons(x, nil())) -> c_18() 788.99/297.03 , 19: droplast^#(cons(x, cons(y, xs))) -> 788.99/297.03 c_19(x, droplast^#(cons(y, xs))) 788.99/297.03 , 20: last^#(nil()) -> c_20() 788.99/297.03 , 21: last^#(cons(x, nil())) -> c_21(x) 788.99/297.03 , 22: last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs))) 788.99/297.03 , 23: a^#() -> c_23() 788.99/297.03 , 24: a^#() -> c_24() } 788.99/297.03 788.99/297.03 We are left with following problem, upon which TcT provides the 788.99/297.03 certificate MAYBE. 788.99/297.03 788.99/297.03 Strict DPs: 788.99/297.03 { le^#(s(x), s(y)) -> c_1(le^#(x, y)) 788.99/297.03 , double^#(s(x)) -> c_4(double^#(x)) 788.99/297.03 , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) 788.99/297.03 , loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) 788.99/297.03 , if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) 788.99/297.03 , if^#(true(), x, y, z) -> c_10(z) 788.99/297.03 , maplog^#(xs) -> c_11(mapIter^#(xs, nil())) 788.99/297.03 , mapIter^#(xs, ys) -> c_12(ifmap^#(isempty(xs), xs, ys)) 788.99/297.03 , ifmap^#(false(), xs, ys) -> 788.99/297.03 c_13(mapIter^#(droplast(xs), cons(log(last(xs)), ys))) 788.99/297.03 , ifmap^#(true(), xs, ys) -> c_14(ys) 788.99/297.03 , droplast^#(cons(x, cons(y, xs))) -> 788.99/297.03 c_19(x, droplast^#(cons(y, xs))) 788.99/297.03 , last^#(cons(x, nil())) -> c_21(x) 788.99/297.03 , last^#(cons(x, cons(y, xs))) -> c_22(last^#(cons(y, xs))) } 788.99/297.03 Strict Trs: 788.99/297.03 { le(s(x), s(y)) -> le(x, y) 788.99/297.03 , le(s(x), 0()) -> false() 788.99/297.03 , le(0(), y) -> true() 788.99/297.03 , double(s(x)) -> s(s(double(x))) 788.99/297.03 , double(0()) -> 0() 788.99/297.03 , log(s(x)) -> loop(s(x), s(0()), 0()) 788.99/297.03 , log(0()) -> logError() 788.99/297.03 , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) 788.99/297.03 , if(false(), x, y, z) -> loop(x, double(y), s(z)) 788.99/297.03 , if(true(), x, y, z) -> z 788.99/297.03 , maplog(xs) -> mapIter(xs, nil()) 788.99/297.03 , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys) 788.99/297.03 , ifmap(false(), xs, ys) -> 788.99/297.03 mapIter(droplast(xs), cons(log(last(xs)), ys)) 788.99/297.03 , ifmap(true(), xs, ys) -> ys 788.99/297.03 , isempty(nil()) -> true() 788.99/297.03 , isempty(cons(x, xs)) -> false() 788.99/297.03 , droplast(nil()) -> nil() 788.99/297.03 , droplast(cons(x, nil())) -> nil() 788.99/297.03 , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs))) 788.99/297.03 , last(nil()) -> error() 788.99/297.03 , last(cons(x, nil())) -> x 788.99/297.03 , last(cons(x, cons(y, xs))) -> last(cons(y, xs)) 788.99/297.03 , a() -> b() 788.99/297.03 , a() -> c() } 788.99/297.03 Weak DPs: 788.99/297.03 { le^#(s(x), 0()) -> c_2() 788.99/297.03 , le^#(0(), y) -> c_3() 788.99/297.03 , double^#(0()) -> c_5() 788.99/297.03 , log^#(0()) -> c_7() 788.99/297.03 , isempty^#(nil()) -> c_15() 788.99/297.03 , isempty^#(cons(x, xs)) -> c_16() 788.99/297.03 , droplast^#(nil()) -> c_17() 788.99/297.03 , droplast^#(cons(x, nil())) -> c_18() 788.99/297.03 , last^#(nil()) -> c_20() 788.99/297.03 , a^#() -> c_23() 788.99/297.03 , a^#() -> c_24() } 788.99/297.03 Obligation: 788.99/297.03 runtime complexity 788.99/297.03 Answer: 788.99/297.03 MAYBE 788.99/297.03 788.99/297.03 Empty strict component of the problem is NOT empty. 788.99/297.03 788.99/297.03 788.99/297.03 Arrrr.. 789.20/297.24 EOF