// 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;



// ------ DUP ------
dup(x1,x2)><Z => x1~Z, x2~Z;
dup(x1,x2)><S(x) => x1~S(w1), x2~S(w2), dup(w1,w2)~x;


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

//Add_Seq
//add(r,y)><Z => y~r;
//add(r,y)><S(x) => add(r, S(y))~x;


// Execution
// Fib 9
fib(r)~S(S(S(S(S(S(S(S(S(Z)))))))));
prnat r;
free r;