MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { is_empty(nil()) -> true() , is_empty(cons(x, l)) -> false() , hd(cons(x, l)) -> x , tl(cons(x, l)) -> l , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) , ifappend(l1, l2, true()) -> l2 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { is_empty^#(nil()) -> c_1() , is_empty^#(cons(x, l)) -> c_2() , hd^#(cons(x, l)) -> c_3(x) , tl^#(cons(x, l)) -> c_4(l) , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) , ifappend^#(l1, l2, true()) -> c_6(l2) , ifappend^#(l1, l2, false()) -> c_7(hd^#(l1), append^#(tl(l1), l2)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { is_empty^#(nil()) -> c_1() , is_empty^#(cons(x, l)) -> c_2() , hd^#(cons(x, l)) -> c_3(x) , tl^#(cons(x, l)) -> c_4(l) , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) , ifappend^#(l1, l2, true()) -> c_6(l2) , ifappend^#(l1, l2, false()) -> c_7(hd^#(l1), append^#(tl(l1), l2)) } Strict Trs: { is_empty(nil()) -> true() , is_empty(cons(x, l)) -> false() , hd(cons(x, l)) -> x , tl(cons(x, l)) -> l , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) , ifappend(l1, l2, true()) -> l2 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2} by applications of Pre({1,2}) = {3,4,6}. Here rules are labeled as follows: DPs: { 1: is_empty^#(nil()) -> c_1() , 2: is_empty^#(cons(x, l)) -> c_2() , 3: hd^#(cons(x, l)) -> c_3(x) , 4: tl^#(cons(x, l)) -> c_4(l) , 5: append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) , 6: ifappend^#(l1, l2, true()) -> c_6(l2) , 7: ifappend^#(l1, l2, false()) -> c_7(hd^#(l1), append^#(tl(l1), l2)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { hd^#(cons(x, l)) -> c_3(x) , tl^#(cons(x, l)) -> c_4(l) , append^#(l1, l2) -> c_5(ifappend^#(l1, l2, is_empty(l1))) , ifappend^#(l1, l2, true()) -> c_6(l2) , ifappend^#(l1, l2, false()) -> c_7(hd^#(l1), append^#(tl(l1), l2)) } Strict Trs: { is_empty(nil()) -> true() , is_empty(cons(x, l)) -> false() , hd(cons(x, l)) -> x , tl(cons(x, l)) -> l , append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) , ifappend(l1, l2, true()) -> l2 , ifappend(l1, l2, false()) -> cons(hd(l1), append(tl(l1), l2)) } Weak DPs: { is_empty^#(nil()) -> c_1() , is_empty^#(cons(x, l)) -> c_2() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..