MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { 2nd(cons(X, cons(Y, Z))) -> Y , from(X) -> cons(X, from(s(X))) } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { 2nd^#(cons(X, cons(Y, Z))) -> c_1() , from^#(X) -> c_2(from^#(s(X))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { 2nd^#(cons(X, cons(Y, Z))) -> c_1() , from^#(X) -> c_2(from^#(s(X))) } Strict Trs: { 2nd(cons(X, cons(Y, Z))) -> Y , from(X) -> cons(X, from(s(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: { 2nd^#(cons(X, cons(Y, Z))) -> c_1() , from^#(X) -> c_2(from^#(s(X))) } 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} TcT has computed following constructor-restricted matrix interpretation. [cons](x1, x2) = [1] x2 + [1] [s](x1) = [1] x1 + [1] [2nd^#](x1) = [2] x1 + [2] [c_1] = [1] [from^#](x1) = [1] x1 + [2] [c_2](x1) = [1] x1 + [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_2(from^#(s(X))) } Weak DPs: { 2nd^#(cons(X, cons(Y, Z))) -> c_1() } 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. { 2nd^#(cons(X, cons(Y, Z))) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_2(from^#(s(X))) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..