// Fibonacci number on unary natural numbers
fib(r)><Z => r~Z;
fib(r)><S(x) => fibS(r)~x;
fibS(r)><Z => r~S(Z);
fibS(r)><S(x) => Dup(x1,x2)~x, add(r,r2)~r1, fib(r2)~x2, fibS(r1)~x1;


//------ ADD ------
add(r,x)><Z => r~x;
add(r,x)><S(y) => r~S(w), add(w,x)~y;


// Execution
// Fib 31
//     1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
fib(r)~S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(Z)))))))))))))))))))))))))))))));
prnat r;
free r;