MAYBE 1184.21/297.09 MAYBE 1184.21/297.09 1184.21/297.09 We are left with following problem, upon which TcT provides the 1184.21/297.09 certificate MAYBE. 1184.21/297.09 1184.21/297.09 Strict Trs: 1184.21/297.09 { isEmpty(nil()) -> true() 1184.21/297.09 , isEmpty(cons(x, xs)) -> false() 1184.21/297.09 , last(cons(x, nil())) -> x 1184.21/297.09 , last(cons(x, cons(y, ys))) -> last(cons(y, ys)) 1184.21/297.09 , dropLast(nil()) -> nil() 1184.21/297.09 , dropLast(cons(x, nil())) -> nil() 1184.21/297.09 , dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys))) 1184.21/297.09 , append(nil(), ys) -> ys 1184.21/297.09 , append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 1184.21/297.09 , reverse(xs) -> rev(xs, nil()) 1184.21/297.09 , rev(xs, ys) -> 1184.21/297.09 if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys) 1184.21/297.09 , if(true(), xs, ys, zs) -> zs 1184.21/297.09 , if(false(), xs, ys, zs) -> rev(xs, ys) } 1184.21/297.09 Obligation: 1184.21/297.09 runtime complexity 1184.21/297.09 Answer: 1184.21/297.09 MAYBE 1184.21/297.09 1184.21/297.09 None of the processors succeeded. 1184.21/297.09 1184.21/297.09 Details of failed attempt(s): 1184.21/297.09 ----------------------------- 1184.21/297.09 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.21/297.09 following reason: 1184.21/297.09 1184.21/297.09 Computation stopped due to timeout after 297.0 seconds. 1184.21/297.09 1184.21/297.09 2) 'Best' failed due to the following reason: 1184.21/297.09 1184.21/297.09 None of the processors succeeded. 1184.21/297.09 1184.21/297.09 Details of failed attempt(s): 1184.21/297.09 ----------------------------- 1184.21/297.09 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.21/297.09 seconds)' failed due to the following reason: 1184.21/297.09 1184.21/297.09 Computation stopped due to timeout after 148.0 seconds. 1184.21/297.09 1184.21/297.09 2) 'Best' failed due to the following reason: 1184.21/297.09 1184.21/297.09 None of the processors succeeded. 1184.21/297.09 1184.21/297.09 Details of failed attempt(s): 1184.21/297.09 ----------------------------- 1184.21/297.09 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.21/297.09 following reason: 1184.21/297.09 1184.21/297.09 The processor is inapplicable, reason: 1184.21/297.09 Processor only applicable for innermost runtime complexity analysis 1184.21/297.09 1184.21/297.09 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.21/297.09 to the following reason: 1184.21/297.09 1184.21/297.09 The processor is inapplicable, reason: 1184.21/297.09 Processor only applicable for innermost runtime complexity analysis 1184.21/297.09 1184.21/297.09 1184.21/297.09 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.21/297.09 failed due to the following reason: 1184.21/297.09 1184.21/297.09 None of the processors succeeded. 1184.21/297.09 1184.21/297.09 Details of failed attempt(s): 1184.21/297.09 ----------------------------- 1184.21/297.09 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.21/297.09 failed due to the following reason: 1184.21/297.09 1184.21/297.09 match-boundness of the problem could not be verified. 1184.21/297.09 1184.21/297.09 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.21/297.09 failed due to the following reason: 1184.21/297.09 1184.21/297.09 match-boundness of the problem could not be verified. 1184.21/297.09 1184.21/297.09 1184.21/297.09 1184.21/297.09 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.21/297.09 the following reason: 1184.21/297.09 1184.21/297.09 We add the following weak dependency pairs: 1184.21/297.09 1184.21/297.09 Strict DPs: 1184.21/297.09 { isEmpty^#(nil()) -> c_1() 1184.21/297.09 , isEmpty^#(cons(x, xs)) -> c_2() 1184.21/297.09 , last^#(cons(x, nil())) -> c_3(x) 1184.21/297.09 , last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys))) 1184.21/297.09 , dropLast^#(nil()) -> c_5() 1184.21/297.09 , dropLast^#(cons(x, nil())) -> c_6() 1184.21/297.09 , dropLast^#(cons(x, cons(y, ys))) -> 1184.21/297.09 c_7(x, dropLast^#(cons(y, ys))) 1184.21/297.09 , append^#(nil(), ys) -> c_8(ys) 1184.21/297.09 , append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys)) 1184.21/297.09 , reverse^#(xs) -> c_10(rev^#(xs, nil())) 1184.21/297.09 , rev^#(xs, ys) -> 1184.21/297.09 c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)) 1184.21/297.09 , if^#(true(), xs, ys, zs) -> c_12(zs) 1184.21/297.09 , if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) } 1184.21/297.09 1184.21/297.09 and mark the set of starting terms. 1184.21/297.09 1184.21/297.09 We are left with following problem, upon which TcT provides the 1184.21/297.09 certificate MAYBE. 1184.21/297.09 1184.21/297.09 Strict DPs: 1184.21/297.09 { isEmpty^#(nil()) -> c_1() 1184.21/297.09 , isEmpty^#(cons(x, xs)) -> c_2() 1184.21/297.09 , last^#(cons(x, nil())) -> c_3(x) 1184.21/297.09 , last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys))) 1184.21/297.09 , dropLast^#(nil()) -> c_5() 1184.21/297.09 , dropLast^#(cons(x, nil())) -> c_6() 1184.21/297.09 , dropLast^#(cons(x, cons(y, ys))) -> 1184.21/297.09 c_7(x, dropLast^#(cons(y, ys))) 1184.21/297.09 , append^#(nil(), ys) -> c_8(ys) 1184.21/297.09 , append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys)) 1184.21/297.09 , reverse^#(xs) -> c_10(rev^#(xs, nil())) 1184.21/297.09 , rev^#(xs, ys) -> 1184.21/297.09 c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)) 1184.21/297.09 , if^#(true(), xs, ys, zs) -> c_12(zs) 1184.21/297.09 , if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) } 1184.21/297.09 Strict Trs: 1184.21/297.09 { isEmpty(nil()) -> true() 1184.21/297.09 , isEmpty(cons(x, xs)) -> false() 1184.21/297.09 , last(cons(x, nil())) -> x 1184.21/297.09 , last(cons(x, cons(y, ys))) -> last(cons(y, ys)) 1184.21/297.09 , dropLast(nil()) -> nil() 1184.21/297.09 , dropLast(cons(x, nil())) -> nil() 1184.21/297.09 , dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys))) 1184.21/297.09 , append(nil(), ys) -> ys 1184.21/297.09 , append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 1184.21/297.09 , reverse(xs) -> rev(xs, nil()) 1184.21/297.09 , rev(xs, ys) -> 1184.21/297.09 if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys) 1184.21/297.09 , if(true(), xs, ys, zs) -> zs 1184.21/297.09 , if(false(), xs, ys, zs) -> rev(xs, ys) } 1184.21/297.09 Obligation: 1184.21/297.09 runtime complexity 1184.21/297.09 Answer: 1184.21/297.09 MAYBE 1184.21/297.09 1184.21/297.09 We estimate the number of application of {1,2,5,6} by applications 1184.21/297.09 of Pre({1,2,5,6}) = {3,7,8,9,12}. Here rules are labeled as 1184.21/297.09 follows: 1184.21/297.09 1184.21/297.09 DPs: 1184.21/297.09 { 1: isEmpty^#(nil()) -> c_1() 1184.21/297.09 , 2: isEmpty^#(cons(x, xs)) -> c_2() 1184.21/297.09 , 3: last^#(cons(x, nil())) -> c_3(x) 1184.21/297.09 , 4: last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys))) 1184.21/297.09 , 5: dropLast^#(nil()) -> c_5() 1184.21/297.09 , 6: dropLast^#(cons(x, nil())) -> c_6() 1184.21/297.09 , 7: dropLast^#(cons(x, cons(y, ys))) -> 1184.21/297.09 c_7(x, dropLast^#(cons(y, ys))) 1184.21/297.09 , 8: append^#(nil(), ys) -> c_8(ys) 1184.21/297.09 , 9: append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys)) 1184.21/297.09 , 10: reverse^#(xs) -> c_10(rev^#(xs, nil())) 1184.21/297.09 , 11: rev^#(xs, ys) -> 1184.21/297.09 c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)) 1184.21/297.09 , 12: if^#(true(), xs, ys, zs) -> c_12(zs) 1184.21/297.09 , 13: if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) } 1184.21/297.09 1184.21/297.09 We are left with following problem, upon which TcT provides the 1184.21/297.09 certificate MAYBE. 1184.21/297.09 1184.21/297.09 Strict DPs: 1184.21/297.09 { last^#(cons(x, nil())) -> c_3(x) 1184.21/297.09 , last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys))) 1184.21/297.09 , dropLast^#(cons(x, cons(y, ys))) -> 1184.21/297.09 c_7(x, dropLast^#(cons(y, ys))) 1184.21/297.09 , append^#(nil(), ys) -> c_8(ys) 1184.21/297.09 , append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys)) 1184.21/297.09 , reverse^#(xs) -> c_10(rev^#(xs, nil())) 1184.21/297.09 , rev^#(xs, ys) -> 1184.21/297.09 c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)) 1184.21/297.09 , if^#(true(), xs, ys, zs) -> c_12(zs) 1184.21/297.09 , if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) } 1184.21/297.09 Strict Trs: 1184.21/297.09 { isEmpty(nil()) -> true() 1184.21/297.09 , isEmpty(cons(x, xs)) -> false() 1184.21/297.09 , last(cons(x, nil())) -> x 1184.21/297.09 , last(cons(x, cons(y, ys))) -> last(cons(y, ys)) 1184.21/297.09 , dropLast(nil()) -> nil() 1184.21/297.09 , dropLast(cons(x, nil())) -> nil() 1184.21/297.09 , dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys))) 1184.21/297.09 , append(nil(), ys) -> ys 1184.21/297.09 , append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 1184.21/297.09 , reverse(xs) -> rev(xs, nil()) 1184.21/297.09 , rev(xs, ys) -> 1184.21/297.09 if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys) 1184.21/297.09 , if(true(), xs, ys, zs) -> zs 1184.21/297.09 , if(false(), xs, ys, zs) -> rev(xs, ys) } 1184.21/297.09 Weak DPs: 1184.21/297.09 { isEmpty^#(nil()) -> c_1() 1184.21/297.09 , isEmpty^#(cons(x, xs)) -> c_2() 1184.21/297.09 , dropLast^#(nil()) -> c_5() 1184.21/297.09 , dropLast^#(cons(x, nil())) -> c_6() } 1184.21/297.09 Obligation: 1184.21/297.09 runtime complexity 1184.21/297.09 Answer: 1184.21/297.09 MAYBE 1184.21/297.09 1184.21/297.09 Empty strict component of the problem is NOT empty. 1184.21/297.09 1184.21/297.09 1184.21/297.09 Arrrr.. 1185.17/297.78 EOF