MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) , head(cons(X, XS)) -> X , 2nd(cons(X, XS)) -> head(activate(XS)) , activate(X) -> X , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(activate(X)) , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) , take(X1, X2) -> n__take(X1, X2) , take(0(), XS) -> nil() , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) , s(X) -> n__s(X) , sel(0(), cons(X, XS)) -> X , sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) } 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: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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 2) '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 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: { from^#(X) -> c_1(X, X) , from^#(X) -> c_2(X) , head^#(cons(X, XS)) -> c_3(X) , 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS))) , activate^#(X) -> c_5(X) , activate^#(n__from(X)) -> c_6(from^#(activate(X))) , activate^#(n__s(X)) -> c_7(s^#(activate(X))) , activate^#(n__take(X1, X2)) -> c_8(take^#(activate(X1), activate(X2))) , s^#(X) -> c_12(X) , take^#(X1, X2) -> c_9(X1, X2) , take^#(0(), XS) -> c_10() , take^#(s(N), cons(X, XS)) -> c_11(X, N, activate^#(XS)) , sel^#(0(), cons(X, XS)) -> c_13(X) , sel^#(s(N), cons(X, XS)) -> c_14(sel^#(N, activate(XS))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(X, X) , from^#(X) -> c_2(X) , head^#(cons(X, XS)) -> c_3(X) , 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS))) , activate^#(X) -> c_5(X) , activate^#(n__from(X)) -> c_6(from^#(activate(X))) , activate^#(n__s(X)) -> c_7(s^#(activate(X))) , activate^#(n__take(X1, X2)) -> c_8(take^#(activate(X1), activate(X2))) , s^#(X) -> c_12(X) , take^#(X1, X2) -> c_9(X1, X2) , take^#(0(), XS) -> c_10() , take^#(s(N), cons(X, XS)) -> c_11(X, N, activate^#(XS)) , sel^#(0(), cons(X, XS)) -> c_13(X) , sel^#(s(N), cons(X, XS)) -> c_14(sel^#(N, activate(XS))) } Strict Trs: { from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) , head(cons(X, XS)) -> X , 2nd(cons(X, XS)) -> head(activate(XS)) , activate(X) -> X , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(activate(X)) , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) , take(X1, X2) -> n__take(X1, X2) , take(0(), XS) -> nil() , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) , s(X) -> n__s(X) , sel(0(), cons(X, XS)) -> X , sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {11} by applications of Pre({11}) = {1,2,3,5,8,9,10,12,13}. Here rules are labeled as follows: DPs: { 1: from^#(X) -> c_1(X, X) , 2: from^#(X) -> c_2(X) , 3: head^#(cons(X, XS)) -> c_3(X) , 4: 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS))) , 5: activate^#(X) -> c_5(X) , 6: activate^#(n__from(X)) -> c_6(from^#(activate(X))) , 7: activate^#(n__s(X)) -> c_7(s^#(activate(X))) , 8: activate^#(n__take(X1, X2)) -> c_8(take^#(activate(X1), activate(X2))) , 9: s^#(X) -> c_12(X) , 10: take^#(X1, X2) -> c_9(X1, X2) , 11: take^#(0(), XS) -> c_10() , 12: take^#(s(N), cons(X, XS)) -> c_11(X, N, activate^#(XS)) , 13: sel^#(0(), cons(X, XS)) -> c_13(X) , 14: sel^#(s(N), cons(X, XS)) -> c_14(sel^#(N, activate(XS))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(X, X) , from^#(X) -> c_2(X) , head^#(cons(X, XS)) -> c_3(X) , 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS))) , activate^#(X) -> c_5(X) , activate^#(n__from(X)) -> c_6(from^#(activate(X))) , activate^#(n__s(X)) -> c_7(s^#(activate(X))) , activate^#(n__take(X1, X2)) -> c_8(take^#(activate(X1), activate(X2))) , s^#(X) -> c_12(X) , take^#(X1, X2) -> c_9(X1, X2) , take^#(s(N), cons(X, XS)) -> c_11(X, N, activate^#(XS)) , sel^#(0(), cons(X, XS)) -> c_13(X) , sel^#(s(N), cons(X, XS)) -> c_14(sel^#(N, activate(XS))) } Strict Trs: { from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) , head(cons(X, XS)) -> X , 2nd(cons(X, XS)) -> head(activate(XS)) , activate(X) -> X , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(activate(X)) , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) , take(X1, X2) -> n__take(X1, X2) , take(0(), XS) -> nil() , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) , s(X) -> n__s(X) , sel(0(), cons(X, XS)) -> X , sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) } Weak DPs: { take^#(0(), XS) -> c_10() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..