A = {{X0, X1}, {X1, X2}},  b = X3[2]
    

Step 1: r = b - Ax
  r[0] = X3[0]

  r[1] = X3[1]

Step 2: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
  alpha = (X3[0]^2^+X3[1]^2^) / ((X3[1]^2^)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2^)*X0)

Step 3: r[i] = r - alpha * A[i][j] * p[j]
  r[0] = (-X3[1]*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)

  r[1] = (X3[0]*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^) 

Step 4: x[i] = x + alpha*p[i]
  x[0] = (X3[0]*(X3[0]^2^ + X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)

  x[1] = (X3[1]*(X3[0]^2^ + X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)

Step 5: beta = (rk[i]*rk[i]) / (r[i]*r[i])
  beta = (X1*X3[0]^2^ - X0*X3[0]*X3[1] + X2*X3[0]*X3[1] - X1*X3[1]^2^)^2^ / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)^2^

Step 6: p[i] = rk[i] +beta * p
  p[0] = (-1)*((X1*X3[0] + X2*X3[1])*(X3[0]^2^ + X3[1]^2^)*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)^2^

  p[1] = ((X0*X3[0] + X1*X3[1])*(X3[0]^2^ + X3[1]^2^)*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)^2^

Step 7: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
  alpha = (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^) / ((-X1^2^ + X0*X2) (X3[0]^2^ + X3[1]^2^))

Step 8: r[i] = r - alpha * A[i][j] * p[j]
  r[0] = 0

  r[1] = 0

Step 9: x[i] = x + alpha*p[i]
  x[0] = (X2*X3[0] - X1*X3[1]) / (X0*X2 - X1^2^)

  x[1] = (-X1*X3[0] + X0*X3[1]) / (X0*X2 - X1^2^)

END