computing conservation laws

Hello,

The following problem concerns the computation of all conservation laws
of the system

df(m,t)   = -df(m,x)*u-b*m*df(u,x)
df(u,x,2) = u-m

for the 2 functions m(x,t), u(x,t) with a second order characteristic
function, for any b, i.e. all such conservation laws for arbitrary b
but also for special b shall be found. This complicates the problem
as it becomes non-linear.
This boils down to an overdetermined system of 148 equations
for the 2 functions

q_1(u12, u11, m22, u2, u1, m2, u, m, x, t)
q_2(u12, u11, m22, u2, u1, m2, u, m, x, t)

of the 10 variables u12, u11, m22, u2, u1, m2, u, m, x, t

and the unknown constant b.

The program CRACK can solve many cases and find a number of solutions,
some for specific values of b (b=1, b=2, b=3,..) and also for general b
but was not able to automatically solve all cases.

The equations are  here .