MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y , 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) , from(X) -> cons(X, from(s(X))) } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1() , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(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^#(cons1(X, cons(Y, Z))) -> c_1() , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(from^#(s(X))) } Strict Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y , 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) , 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^#(cons1(X, cons(Y, Z))) -> c_1() , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(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}, Uargs(c_3) = {1} TcT has computed following constructor-restricted matrix interpretation. [cons1](x1, x2) = [1] x1 + [2] [cons](x1, x2) = [1] x1 + [1] x2 + [0] [s](x1) = [1] x1 + [1] [2nd^#](x1) = [2] x1 + [0] [c_1] = [1] [c_2](x1) = [1] x1 + [1] [from^#](x1) = [1] x1 + [2] [c_3](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: { 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(from^#(s(X))) } Weak DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1} by applications of Pre({1}) = {}. Here rules are labeled as follows: DPs: { 1: 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , 2: from^#(X) -> c_3(from^#(s(X))) , 3: 2nd^#(cons1(X, cons(Y, Z))) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_3(from^#(s(X))) } Weak DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1() , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) } 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^#(cons1(X, cons(Y, Z))) -> c_1() , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_3(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..