def model1(inps, lims, logger=None):
    """
    x[i] = (a[i]/3-1)**i + c
    y[j] = a[j] - j
    """
    a_arr, c_ = inps
    ilim, jlim = lims

    i_bs = sympy.symbols('i_lb i_ub', integer=True)
    i = sympy.Idx('i', i_bs)

    j_bs = sympy.symbols('j_lb j_ub', integer=True)
    j = sympy.Idx('j', j_bs)

    a = sympy.IndexedBase('a')

    c = sympy.Symbol('c', real=True)

    x = sympy.IndexedBase('x')
    y = sympy.IndexedBase('y')

    eqs = [
        sympy.Eq(x[i], (a[i]/3-1)**i+c),
        sympy.Eq(y[j], a[j]-j),
    ]

    ex_code = ExampleCode(eqs, (a[i], c), (i, j),
                          logger=logger, save_temp=True)
    x_, y_ = ex_code(inps, bounds=(ilim, jlim))
    x_ref = (a_arr/3-1)**np.arange(ilim[0], ilim[1]) + c_
    y_ref = a_arr[jlim[0]:jlim[1]] - np.arange(jlim[0], jlim[1])
    assert np.allclose(x_, x_ref)
    assert np.allclose(y_, y_ref)
x[i] = (a[i]/3-1)**i + c
    y[j] = a[j] - j