Funtion or something that finds the smaller integer

Try something like this:

process(clkwork,reset)
  begin
--first pipeline stage
  if(reset = '1') then
    pipeline1_0_result <= "0000";
  elsif (rising_edge(clkwork)) then
    if (TaoA< TaoB) then
      pipeline0_0_result <= decodedBitA;
      pipeline0_0_int <= TaoA;
    else
      pipeline0_0_result <= decodedBitB;
      pipeline0_0_int <= TaoB;
    end if;
    if (TaoC < TaoD) then
      pipeline0_1_result <= decodedBitC;
      pipeline0_1_int <= TaoC;
    else
      pipeline0_1_result <= decodedBitD;
      pipeline0_1_int <= TaoD;
    end if;
  --second pipeline stage
    if (pipeline0_0_result < pipeline0_1_result ) then
      pipeline1_0_result <= pipeline0_0_result ;
      pipeline1_0_int <= pipeline0_0_int ;
    else
      pipeline1_0_result <= pipeline0_1_result ;
      pipeline1_0_int <= pipeline0_1_int;
    end if;
  end if;
end process;

The result is updated in pipeline1_0_result every clock with a delay.

This is a 2 pipeline stage example using 4 inputs. I have written this long-hand to make it readable. It may be a good idea to wrap this into a for loop for ease of coding.