MAYBE 1044.03/297.02 MAYBE 1044.03/297.02 1044.03/297.02 We are left with following problem, upon which TcT provides the 1044.03/297.02 certificate MAYBE. 1044.03/297.02 1044.03/297.02 Strict Trs: 1044.03/297.02 { is_empty(nil()) -> true() 1044.03/297.02 , is_empty(cons(x, l)) -> false() 1044.03/297.02 , hd(cons(x, l)) -> x 1044.03/297.02 , tl(cons(x, l)) -> cons(x, l) 1044.03/297.02 , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 1044.03/297.02 , ifappend(l1, l2, true()) -> l2 1044.03/297.02 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } 1044.03/297.02 Obligation: 1044.03/297.02 runtime complexity 1044.03/297.02 Answer: 1044.03/297.02 MAYBE 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1044.03/297.02 following reason: 1044.03/297.02 1044.03/297.02 Computation stopped due to timeout after 297.0 seconds. 1044.03/297.02 1044.03/297.02 2) 'Best' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1044.03/297.02 seconds)' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'empty' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 2) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'empty' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 2) 'Fastest' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'empty' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 2) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'empty' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 2) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'empty' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 2) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 1044.03/297.02 1044.03/297.02 1044.03/297.02 2) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'empty' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 2) 'With Problem ...' failed due to the following reason: 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 1044.03/297.02 1044.03/297.02 1044.03/297.02 1044.03/297.02 2) 'Best' failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1044.03/297.02 to the following reason: 1044.03/297.02 1044.03/297.02 The processor is inapplicable, reason: 1044.03/297.02 Processor only applicable for innermost runtime complexity analysis 1044.03/297.02 1044.03/297.02 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1044.03/297.02 following reason: 1044.03/297.02 1044.03/297.02 The processor is inapplicable, reason: 1044.03/297.02 Processor only applicable for innermost runtime complexity analysis 1044.03/297.02 1044.03/297.02 1044.03/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1044.03/297.02 failed due to the following reason: 1044.03/297.02 1044.03/297.02 None of the processors succeeded. 1044.03/297.02 1044.03/297.02 Details of failed attempt(s): 1044.03/297.02 ----------------------------- 1044.03/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1044.03/297.02 failed due to the following reason: 1044.03/297.02 1044.03/297.02 match-boundness of the problem could not be verified. 1044.03/297.02 1044.03/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1044.03/297.02 failed due to the following reason: 1044.03/297.02 1044.03/297.02 match-boundness of the problem could not be verified. 1044.03/297.02 1044.03/297.02 1044.03/297.02 1044.03/297.02 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1044.03/297.02 the following reason: 1044.03/297.02 1044.03/297.02 We add the following weak dependency pairs: 1044.03/297.02 1044.03/297.02 Strict DPs: 1044.03/297.02 { is_empty^#(nil()) -> c_1() 1044.03/297.02 , is_empty^#(cons(x, l)) -> c_2() 1044.03/297.02 , hd^#(cons(x, l)) -> c_3(x) 1044.03/297.02 , tl^#(cons(x, l)) -> c_4(x, l) 1044.03/297.02 , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1044.03/297.02 , ifappend^#(l1, l2, true()) -> c_6(l2) 1044.03/297.02 , ifappend^#(l1, l2, false()) -> 1044.03/297.02 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1044.03/297.02 1044.03/297.02 and mark the set of starting terms. 1044.03/297.02 1044.03/297.02 We are left with following problem, upon which TcT provides the 1044.03/297.02 certificate MAYBE. 1044.03/297.02 1044.03/297.02 Strict DPs: 1044.03/297.02 { is_empty^#(nil()) -> c_1() 1044.03/297.02 , is_empty^#(cons(x, l)) -> c_2() 1044.03/297.02 , hd^#(cons(x, l)) -> c_3(x) 1044.03/297.02 , tl^#(cons(x, l)) -> c_4(x, l) 1044.03/297.02 , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1044.03/297.02 , ifappend^#(l1, l2, true()) -> c_6(l2) 1044.03/297.02 , ifappend^#(l1, l2, false()) -> 1044.03/297.02 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1044.03/297.02 Strict Trs: 1044.03/297.02 { is_empty(nil()) -> true() 1044.03/297.02 , is_empty(cons(x, l)) -> false() 1044.03/297.02 , hd(cons(x, l)) -> x 1044.03/297.02 , tl(cons(x, l)) -> cons(x, l) 1044.03/297.02 , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 1044.03/297.02 , ifappend(l1, l2, true()) -> l2 1044.03/297.02 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } 1044.03/297.02 Obligation: 1044.03/297.02 runtime complexity 1044.03/297.02 Answer: 1044.03/297.02 MAYBE 1044.03/297.02 1044.03/297.02 We estimate the number of application of {1,2} by applications of 1044.03/297.02 Pre({1,2}) = {3,4,6}. Here rules are labeled as follows: 1044.03/297.02 1044.03/297.02 DPs: 1044.03/297.02 { 1: is_empty^#(nil()) -> c_1() 1044.03/297.02 , 2: is_empty^#(cons(x, l)) -> c_2() 1044.03/297.02 , 3: hd^#(cons(x, l)) -> c_3(x) 1044.03/297.02 , 4: tl^#(cons(x, l)) -> c_4(x, l) 1044.03/297.02 , 5: append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1044.03/297.02 , 6: ifappend^#(l1, l2, true()) -> c_6(l2) 1044.03/297.02 , 7: ifappend^#(l1, l2, false()) -> 1044.03/297.02 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1044.03/297.02 1044.03/297.02 We are left with following problem, upon which TcT provides the 1044.03/297.02 certificate MAYBE. 1044.03/297.02 1044.03/297.02 Strict DPs: 1044.03/297.02 { hd^#(cons(x, l)) -> c_3(x) 1044.03/297.02 , tl^#(cons(x, l)) -> c_4(x, l) 1044.03/297.02 , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1044.03/297.02 , ifappend^#(l1, l2, true()) -> c_6(l2) 1044.03/297.02 , ifappend^#(l1, l2, false()) -> 1044.03/297.02 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1044.03/297.02 Strict Trs: 1044.03/297.02 { is_empty(nil()) -> true() 1044.03/297.02 , is_empty(cons(x, l)) -> false() 1044.03/297.02 , hd(cons(x, l)) -> x 1044.03/297.02 , tl(cons(x, l)) -> cons(x, l) 1044.03/297.02 , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 1044.03/297.02 , ifappend(l1, l2, true()) -> l2 1044.03/297.02 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } 1044.03/297.02 Weak DPs: 1044.03/297.02 { is_empty^#(nil()) -> c_1() 1044.03/297.02 , is_empty^#(cons(x, l)) -> c_2() } 1044.03/297.02 Obligation: 1044.03/297.02 runtime complexity 1044.03/297.02 Answer: 1044.03/297.02 MAYBE 1044.03/297.02 1044.03/297.02 Empty strict component of the problem is NOT empty. 1044.03/297.02 1044.03/297.02 1044.03/297.02 Arrrr.. 1044.77/297.78 EOF