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In this work, high order splitting methods of integration without negative steps are shown which can be used in irreversible problems, like reaction-diffusion or complex Ginzburg-Landau equations. The methods consist in a suitable affine combinations of Lie-Tortter schemes with different positive steps.The number of basic steps for these methods grows quadratically with the order, while for symplectic methods, the growth is exponential. Furthermore, the calculations can be performed in parallel, so thatthe computation time can be significantly reduced using multiple processors. Convergence results of these methods are proved for a large kind of semilinear problems, that includes reaction-diffusion systems anddissipative perturbation of Hamiltonian systems.