MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(x) -> s(x) , f(s(s(x))) -> s(f(f(x))) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(x) -> c_1() , f^#(s(s(x))) -> c_2(f^#(f(x)), f^#(x)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x) -> c_1() , f^#(s(s(x))) -> c_2(f^#(f(x)), f^#(x)) } Weak Trs: { f(x) -> s(x) , f(s(s(x))) -> s(f(f(x))) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1} by applications of Pre({1}) = {2}. Here rules are labeled as follows: DPs: { 1: f^#(x) -> c_1() , 2: f^#(s(s(x))) -> c_2(f^#(f(x)), f^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(s(x))) -> c_2(f^#(f(x)), f^#(x)) } Weak DPs: { f^#(x) -> c_1() } Weak Trs: { f(x) -> s(x) , f(s(s(x))) -> s(f(f(x))) } 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. { f^#(x) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(s(x))) -> c_2(f^#(f(x)), f^#(x)) } Weak Trs: { f(x) -> s(x) , f(s(s(x))) -> s(f(f(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..