MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> f(X) , c() -> a() , c() -> b() } Obligation: innermost runtime complexity Answer: MAYBE We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. Trs: { c() -> a() , c() -> b() } 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). [f](x1) = [3] x1 + [3] [c] = [3] [a] = [1] [b] = [1] This order satisfies the following ordering constraints: [f(X)] = [3] X + [3] >= [3] X + [3] = [f(X)] [c()] = [3] > [1] = [a()] [c()] = [3] > [1] = [b()] We return to the main proof. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> f(X) } Weak Trs: { c() -> a() , c() -> b() } Obligation: innermost runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..