Verifikation reaktiver Systeme - Universität Kaiserslautern

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function Presburger N Presburger Z (φ)
case φ of
ADD N (x, y, z): return ADD Z (x, y, z);
x 1
. = x2 : return x 1
. = x2;
¬ϕ : return ¬ϕ;
ϕ ∧ ψ : return ϕ ∧ ψ;
∃x.ϕ : return ∃x. ≥ 0(x) ∧ ϕ;
end
end
function Presburger Z Presburger N (φ)
case φ of
≥ 0(x) : return ∃y.ADD N (y, y,x);
ADD Z (x, y, z) :
ϕ(x) := Presburger Z Presburger N (≥ 0(x));
ψ ≥≥ (x, y, z) := x + N y = . z;
ψ