MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { from(X) -> cons(X, from(s(X))) , head(cons(X, XS)) -> X , 2nd(cons(X, XS)) -> head(XS) , take(s(N), cons(X, XS)) -> cons(X, take(N, XS)) , take(0(), XS) -> nil() , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , head^#(cons(X, XS)) -> c_2() , 2nd^#(cons(X, XS)) -> c_3(head^#(XS)) , take^#(s(N), cons(X, XS)) -> c_4(take^#(N, XS)) , take^#(0(), XS) -> c_5() , sel^#(s(N), cons(X, XS)) -> c_6(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_7() } 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(from^#(s(X))) , head^#(cons(X, XS)) -> c_2() , 2nd^#(cons(X, XS)) -> c_3(head^#(XS)) , take^#(s(N), cons(X, XS)) -> c_4(take^#(N, XS)) , take^#(0(), XS) -> c_5() , sel^#(s(N), cons(X, XS)) -> c_6(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_7() } Strict Trs: { from(X) -> cons(X, from(s(X))) , head(cons(X, XS)) -> X , 2nd(cons(X, XS)) -> head(XS) , take(s(N), cons(X, XS)) -> cons(X, take(N, XS)) , take(0(), XS) -> nil() , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X } Obligation: innermost runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , head^#(cons(X, XS)) -> c_2() , 2nd^#(cons(X, XS)) -> c_3(head^#(XS)) , take^#(s(N), cons(X, XS)) -> c_4(take^#(N, XS)) , take^#(0(), XS) -> c_5() , sel^#(s(N), cons(X, XS)) -> c_6(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_7() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_3) = {1}, Uargs(c_4) = {1}, Uargs(c_6) = {1} TcT has computed following constructor-restricted matrix interpretation. [cons](x1, x2) = [1] x2 + [1] [s](x1) = [1] x1 + [2] [0] = [2] [from^#](x1) = [1] x1 + [1] [c_1](x1) = [1] x1 + [0] [head^#](x1) = [2] x1 + [2] [c_2] = [1] [2nd^#](x1) = [2] x1 + [2] [c_3](x1) = [1] x1 + [1] [take^#](x1, x2) = [1] x1 + [1] x2 + [1] [c_4](x1) = [1] x1 + [1] [c_5] = [2] [sel^#](x1, x2) = [2] x1 + [2] x2 + [1] [c_6](x1) = [1] x1 + [1] [c_7] = [2] This order satisfies following ordering constraints: Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) } Weak DPs: { head^#(cons(X, XS)) -> c_2() , 2nd^#(cons(X, XS)) -> c_3(head^#(XS)) , take^#(s(N), cons(X, XS)) -> c_4(take^#(N, XS)) , take^#(0(), XS) -> c_5() , sel^#(s(N), cons(X, XS)) -> c_6(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_7() } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { head^#(cons(X, XS)) -> c_2() , 2nd^#(cons(X, XS)) -> c_3(head^#(XS)) , take^#(s(N), cons(X, XS)) -> c_4(take^#(N, XS)) , take^#(0(), XS) -> c_5() , sel^#(s(N), cons(X, XS)) -> c_6(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_7() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrices' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrix interpretation of dimension 4' failed due to the following reason: The input cannot be shown compatible 2) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 3) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 4) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 5) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 6) 'matrix interpretation of dimension 1' failed due to the following reason: The input cannot be shown compatible 2) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. Arrrr..