MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(X) -> h(X) , h(d()) -> g(c()) , c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } Strict Trs: { g(X) -> h(X) , h(d()) -> g(c()) , c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Strict Usable Rules: { c() -> d() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } Strict Trs: { c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(g^#) = {1}, Uargs(c_1) = {1}, Uargs(c_2) = {1} TcT has computed following constructor-restricted matrix interpretation. [c] = [2] [d] = [1] [g^#](x1) = [1] x1 + [1] [c_1](x1) = [1] x1 + [2] [h^#](x1) = [1] x1 + [1] [c_2](x1) = [1] x1 + [1] [c^#] = [1] [c_3] = [1] This order satisfies following ordering constraints: [c()] = [2] > [1] = [d()] 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: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) , c^#() -> c_3() } Weak Trs: { c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {}. Here rules are labeled as follows: DPs: { 1: g^#(X) -> c_1(h^#(X)) , 2: h^#(d()) -> c_2(g^#(c())) , 3: c^#() -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) } Weak DPs: { c^#() -> c_3() } Weak Trs: { c() -> d() } 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. { c^#() -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(X) -> c_1(h^#(X)) , h^#(d()) -> c_2(g^#(c())) } Weak Trs: { c() -> d() } 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..