This is a dynamic programming algorithm known as *Simple Tree Matching*:

```
int simple_tree_match(a,b){

    if (a != b) return 0

    m = the number of first-level sub-trees of a
    n = the number of first-level sub-trees of b
    M[i,0] := 0 for i = 0,...,m
    M[0,j] := 0 for j = 0,...,n
    for(i := 1 to m){
        for(i := 1 to n){
            x := M[i,j-1]
            y := M[i-1,j]
            z := M[i-1,j-1]+ simple_tree_match(a_i,b_j)
            M[i,j] = max(x,y,z)
        }
    }
}
return M[m,n] + 1
}
```

int simple_tree_match(a,b){

    if (a != b) return 0

    m = the number of first-level sub-trees of a
    n = the number of first-level sub-trees of b
    M[i,0] := 0 for i = 0,...,m
    M[0,j] := 0 for j = 0,...,n
    for(i := 1 to m){
        for(i := 1 to n){
            x := M[i,j-1]
            y := M[i-1,j]
            z := M[i-1,j-1]+ simple_tree_match(a_i,b_j)
            M[i,j] = max(x,y,z)
        }
    }
}
return M[m,n] + 1
}