MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g() -> h() , h() -> g() , c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. Trs: { c() -> d() } The induced complexity on above rules (modulo remaining rules) is YES(?,O(n^1)) . These rules are moved into the corresponding weak component(s). Sub-proof: ---------- TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [g] = [3] [h] = [3] [c] = [3] [d] = [1] This order satisfies the following ordering constraints: [g()] = [3] >= [3] = [h()] [h()] = [3] >= [3] = [g()] [c()] = [3] > [1] = [d()] We return to the main proof. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g() -> h() , h() -> g() } Weak Trs: { c() -> d() } Obligation: innermost runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..