MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(x, s(y)) -> f(y, x) , f(s(x), y) -> f(x, s(x)) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(x, s(y)) -> c_1(f^#(y, x)) , f^#(s(x), y) -> c_2(f^#(x, s(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, s(y)) -> c_1(f^#(y, x)) , f^#(s(x), y) -> c_2(f^#(x, s(x))) } Weak Trs: { f(x, s(y)) -> f(y, x) , f(s(x), y) -> f(x, 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: { f^#(x, s(y)) -> c_1(f^#(y, x)) , f^#(s(x), y) -> c_2(f^#(x, s(x))) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..