MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { app(nil(), xs) -> nil() , app(cons(x, xs), ys) -> cons(x, app(xs, ys)) , rev(nil()) -> nil() , rev(cons(x, xs)) -> append(xs, rev(cons(x, nil()))) } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { app^#(nil(), xs) -> c_1() , app^#(cons(x, xs), ys) -> c_2(app^#(xs, ys)) , rev^#(nil()) -> c_3() , rev^#(cons(x, xs)) -> c_4(rev^#(cons(x, nil()))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { app^#(nil(), xs) -> c_1() , app^#(cons(x, xs), ys) -> c_2(app^#(xs, ys)) , rev^#(nil()) -> c_3() , rev^#(cons(x, xs)) -> c_4(rev^#(cons(x, nil()))) } Strict Trs: { app(nil(), xs) -> nil() , app(cons(x, xs), ys) -> cons(x, app(xs, ys)) , rev(nil()) -> nil() , rev(cons(x, xs)) -> append(xs, rev(cons(x, nil()))) } 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: { app^#(nil(), xs) -> c_1() , app^#(cons(x, xs), ys) -> c_2(app^#(xs, ys)) , rev^#(nil()) -> c_3() , rev^#(cons(x, xs)) -> c_4(rev^#(cons(x, nil()))) } 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_2) = {1}, Uargs(c_4) = {1} TcT has computed following constructor-restricted matrix interpretation. [nil] = [1] [cons](x1, x2) = [1] x1 + [0] [app^#](x1, x2) = [2] x2 + [1] [c_1] = [0] [c_2](x1) = [1] x1 + [1] [rev^#](x1) = [1] x1 + [0] [c_3] = [0] [c_4](x1) = [1] x1 + [1] 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: { app^#(cons(x, xs), ys) -> c_2(app^#(xs, ys)) , rev^#(cons(x, xs)) -> c_4(rev^#(cons(x, nil()))) } Weak DPs: { app^#(nil(), xs) -> c_1() , rev^#(nil()) -> c_3() } 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. { app^#(nil(), xs) -> c_1() , rev^#(nil()) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { app^#(cons(x, xs), ys) -> c_2(app^#(xs, ys)) , rev^#(cons(x, xs)) -> c_4(rev^#(cons(x, nil()))) } 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..