TRS: { D(t()) -> 1(), D(constant()) -> 0(), D(+(x, y)) -> +(D(x), D(y)), D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))), D(-(x, y)) -> -(D(x), D(y)), D(minus(x)) -> minus(D(x)), D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2()))), D(ln(x)) -> div(D(x), x), D(pow(x, y)) -> +(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))} Cdiprover: Interpretation class: pizerosimplemixed Complexity bound: POLYTIME COMPUTABLE ln(X12) = + 1*X12 + 1 2 = + 1 pow(X11, X10) = + 1*X10 + 1*X11 + 2 div(X9, X8) = + 1*X8 + 1*X9 + 3 minus(X7) = + 1*X7 + 1 -(X6, X5) = + 1*X5 + 1*X6 + 1 *(X4, X3) = + 1*X3 + 1*X4 + 1 +(X2, X1) = + 1*X1 + 1*X2 + 1 constant = + 1 0 = + 3 t = + 1 D(X0) = + 3*X0^2 + 2 + 3*X0 1 = + 1 Qed