We are left with following problem, upon which TcT provides the certificate YES(O(1),O(n^1)). Strict Trs: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) } 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: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) } 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(+) = {1, 2} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [*](x1, x2) = [2] x2 + [0] [+](x1, x2) = [1] x1 + [1] x2 + [4] The order satisfies the following ordering constraints: [*(x, +(y, z))] = [2] y + [2] z + [8] > [2] y + [2] z + [4] = [+(*(x, y), *(x, z))] 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: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) } Obligation: runtime complexity Answer: YES(O(1),O(1)) Empty rules are trivially bounded Hurray, we answered YES(O(1),O(n^1))