MAYBE 1041.81/297.03 MAYBE 1041.81/297.03 1041.81/297.03 We are left with following problem, upon which TcT provides the 1041.81/297.03 certificate MAYBE. 1041.81/297.03 1041.81/297.03 Strict Trs: 1041.81/297.03 { is_empty(nil()) -> true() 1041.81/297.03 , is_empty(cons(x, l)) -> false() 1041.81/297.03 , hd(cons(x, l)) -> x 1041.81/297.03 , tl(cons(x, l)) -> l 1041.81/297.03 , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 1041.81/297.03 , ifappend(l1, l2, true()) -> l2 1041.81/297.03 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } 1041.81/297.03 Obligation: 1041.81/297.03 runtime complexity 1041.81/297.03 Answer: 1041.81/297.03 MAYBE 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1041.81/297.03 following reason: 1041.81/297.03 1041.81/297.03 Computation stopped due to timeout after 297.0 seconds. 1041.81/297.03 1041.81/297.03 2) 'Best' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1041.81/297.03 seconds)' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'empty' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 2) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'empty' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 2) 'Fastest' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'empty' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 2) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'empty' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 2) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'empty' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 2) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 1041.81/297.03 1041.81/297.03 1041.81/297.03 2) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'empty' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 2) 'With Problem ...' failed due to the following reason: 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 1041.81/297.03 1041.81/297.03 1041.81/297.03 1041.81/297.03 2) 'Best' failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1041.81/297.03 following reason: 1041.81/297.03 1041.81/297.03 The processor is inapplicable, reason: 1041.81/297.03 Processor only applicable for innermost runtime complexity analysis 1041.81/297.03 1041.81/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1041.81/297.03 to the following reason: 1041.81/297.03 1041.81/297.03 The processor is inapplicable, reason: 1041.81/297.03 Processor only applicable for innermost runtime complexity analysis 1041.81/297.03 1041.81/297.03 1041.81/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1041.81/297.03 failed due to the following reason: 1041.81/297.03 1041.81/297.03 None of the processors succeeded. 1041.81/297.03 1041.81/297.03 Details of failed attempt(s): 1041.81/297.03 ----------------------------- 1041.81/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1041.81/297.03 failed due to the following reason: 1041.81/297.03 1041.81/297.03 match-boundness of the problem could not be verified. 1041.81/297.03 1041.81/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1041.81/297.03 failed due to the following reason: 1041.81/297.03 1041.81/297.03 match-boundness of the problem could not be verified. 1041.81/297.03 1041.81/297.03 1041.81/297.03 1041.81/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1041.81/297.03 the following reason: 1041.81/297.03 1041.81/297.03 We add the following weak dependency pairs: 1041.81/297.03 1041.81/297.03 Strict DPs: 1041.81/297.03 { is_empty^#(nil()) -> c_1() 1041.81/297.03 , is_empty^#(cons(x, l)) -> c_2() 1041.81/297.03 , hd^#(cons(x, l)) -> c_3(x) 1041.81/297.03 , tl^#(cons(x, l)) -> c_4(l) 1041.81/297.03 , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1041.81/297.03 , ifappend^#(l1, l2, true()) -> c_6(l2) 1041.81/297.03 , ifappend^#(l1, l2, false()) -> 1041.81/297.03 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1041.81/297.03 1041.81/297.03 and mark the set of starting terms. 1041.81/297.03 1041.81/297.03 We are left with following problem, upon which TcT provides the 1041.81/297.03 certificate MAYBE. 1041.81/297.03 1041.81/297.03 Strict DPs: 1041.81/297.03 { is_empty^#(nil()) -> c_1() 1041.81/297.03 , is_empty^#(cons(x, l)) -> c_2() 1041.81/297.03 , hd^#(cons(x, l)) -> c_3(x) 1041.81/297.03 , tl^#(cons(x, l)) -> c_4(l) 1041.81/297.03 , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1041.81/297.03 , ifappend^#(l1, l2, true()) -> c_6(l2) 1041.81/297.03 , ifappend^#(l1, l2, false()) -> 1041.81/297.03 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1041.81/297.03 Strict Trs: 1041.81/297.03 { is_empty(nil()) -> true() 1041.81/297.03 , is_empty(cons(x, l)) -> false() 1041.81/297.03 , hd(cons(x, l)) -> x 1041.81/297.03 , tl(cons(x, l)) -> l 1041.81/297.03 , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 1041.81/297.03 , ifappend(l1, l2, true()) -> l2 1041.81/297.03 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } 1041.81/297.03 Obligation: 1041.81/297.03 runtime complexity 1041.81/297.03 Answer: 1041.81/297.03 MAYBE 1041.81/297.03 1041.81/297.03 We estimate the number of application of {1,2} by applications of 1041.81/297.03 Pre({1,2}) = {3,4,6}. Here rules are labeled as follows: 1041.81/297.03 1041.81/297.03 DPs: 1041.81/297.03 { 1: is_empty^#(nil()) -> c_1() 1041.81/297.03 , 2: is_empty^#(cons(x, l)) -> c_2() 1041.81/297.03 , 3: hd^#(cons(x, l)) -> c_3(x) 1041.81/297.03 , 4: tl^#(cons(x, l)) -> c_4(l) 1041.81/297.03 , 5: append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1041.81/297.03 , 6: ifappend^#(l1, l2, true()) -> c_6(l2) 1041.81/297.03 , 7: ifappend^#(l1, l2, false()) -> 1041.81/297.03 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1041.81/297.03 1041.81/297.03 We are left with following problem, upon which TcT provides the 1041.81/297.03 certificate MAYBE. 1041.81/297.03 1041.81/297.03 Strict DPs: 1041.81/297.03 { hd^#(cons(x, l)) -> c_3(x) 1041.81/297.03 , tl^#(cons(x, l)) -> c_4(l) 1041.81/297.03 , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) 1041.81/297.03 , ifappend^#(l1, l2, true()) -> c_6(l2) 1041.81/297.03 , ifappend^#(l1, l2, false()) -> 1041.81/297.03 c_7(hd^#(l1), append^#(tl(l1), l2)) } 1041.81/297.03 Strict Trs: 1041.81/297.03 { is_empty(nil()) -> true() 1041.81/297.03 , is_empty(cons(x, l)) -> false() 1041.81/297.03 , hd(cons(x, l)) -> x 1041.81/297.03 , tl(cons(x, l)) -> l 1041.81/297.03 , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 1041.81/297.03 , ifappend(l1, l2, true()) -> l2 1041.81/297.03 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } 1041.81/297.03 Weak DPs: 1041.81/297.03 { is_empty^#(nil()) -> c_1() 1041.81/297.03 , is_empty^#(cons(x, l)) -> c_2() } 1041.81/297.03 Obligation: 1041.81/297.03 runtime complexity 1041.81/297.03 Answer: 1041.81/297.03 MAYBE 1041.81/297.03 1041.81/297.03 Empty strict component of the problem is NOT empty. 1041.81/297.03 1041.81/297.03 1041.81/297.03 Arrrr.. 1042.56/297.78 EOF