MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(a(), X) -> f(X, X) , c() -> a() , c() -> b() } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { f^#(a(), X) -> c_1(f^#(X, X)) , c^#() -> c_2() , 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: { f^#(a(), X) -> c_1(f^#(X, X)) , c^#() -> c_2() , c^#() -> c_3() } Strict Trs: { f(a(), X) -> f(X, X) , c() -> a() , c() -> b() } 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: { f^#(a(), X) -> c_1(f^#(X, X)) , c^#() -> c_2() , c^#() -> c_3() } 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} TcT has computed following constructor-restricted matrix interpretation. [a] = [1] [f^#](x1, x2) = [1] x2 + [2] [c_1](x1) = [1] x1 + [1] [c^#] = [2] [c_2] = [1] [c_3] = [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: { f^#(a(), X) -> c_1(f^#(X, X)) } Weak DPs: { c^#() -> c_2() , c^#() -> 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. { c^#() -> c_2() , c^#() -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(a(), X) -> c_1(f^#(X, 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..