x(n):=sum(x[i],i,1,n)$

x[x(1)]^x(1)+1;

x[x(1)]^x(10)+1;

x[x(10)]^x(1)+1;

x[x(100)]^x(100)+1;

x[x[x[x[1]]]]^y^z^a^b;

a^b^c^d;