Define x<n>y recursively as follows (this is a right associative version):
x<0>y = x+1;
x<1>0 = x;
x<2>0 = 0;
x<n>y = ( x<n>(y-1) ) <n-1> x for n>0 and y>0.
We have:
x<1>y = (...((x<0>y)<0>y)...y)(y nested parenthesis) = x+y;
x<2>y = (...((x<1>y)<1>y)...y)(y nested parenthesis) = x*y;
x<3>y = (...((x<2>y)<2>y)...y)(y nested parenthesis) = x^y;
x<4>y = (...((x<3>y)<3>y)...y)(y nested parenthesis) = (...((x^x)^x)...^x) (a height-y bottom-up tower power, NOT tetration) = x^x^(y-1).
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