We are left with following problem, upon which TcT provides the certificate YES(O(1),O(n^1)). Strict Trs: { f(g(x), y, y) -> g(f(x, x, y)) } Obligation: runtime complexity Answer: YES(O(1),O(n^1)) We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. Trs: { f(g(x), y, y) -> g(f(x, x, y)) } 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: ---------- The following argument positions are usable: Uargs(g) = {1} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [f](x1, x2, x3) = [2] x1 + [0] [g](x1) = [1] x1 + [4] The order satisfies the following ordering constraints: [f(g(x), y, y)] = [2] x + [8] > [2] x + [4] = [g(f(x, x, y))] We return to the main proof. We are left with following problem, upon which TcT provides the certificate YES(O(1),O(1)). Weak Trs: { f(g(x), y, y) -> g(f(x, x, y)) } Obligation: runtime complexity Answer: YES(O(1),O(1)) Empty rules are trivially bounded Hurray, we answered YES(O(1),O(n^1))