(VAR DDX DX DY X Y )
(RULES 
        din(der(plus(X, Y))) -> u21(din(der(X)), X, Y)
        u21(dout(DX), X, Y) -> u22(din(der(Y)), X, Y, DX)
        u22(dout(DY), X, Y, DX) -> dout(plus(DX, DY))
        din(der(times(X, Y))) -> u31(din(der(X)), X, Y)
        u31(dout(DX), X, Y) -> u32(din(der(Y)), X, Y, DX)
        u32(dout(DY), X, Y, DX) -> dout(plus(times(X, DY), times(Y, DX)))
        din(der(der(X))) -> u41(din(der(X)), X)
        u41(dout(DX), X) -> u42(din(der(DX)), X, DX)
        u42(dout(DDX), X, DX) -> dout(DDX)
        
)