let F = signature "0,1 : 0; + : AC; m : 2; i : 1;";
let X = variables "x, y, z";
let T = algebra F;

let p = precedence F " m > i > + > 1 = 0";

let s = status F " + : mul; 0,1 : mul; i,m : lrlex ";

let o = rpo T p s;

let R = trs T "
x + 0 -> x;
x + i (x) -> 0;
m(x, 1) -> x;
m(1, x) -> x;
m(m(x, y), z) -> m(x, m(y, z));
m(x + y, z) -> m(x, z) + m(y, z);
m(x, y + z) -> m(x, y) + m(x, z);
";

complete o R;

#quit;