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 The input cannot be shown compatible Arrrr..