Here, first, is a derivation of B, C, and K from B' and CCCpCqprr:

 
 



 

          1. CCpqCCqrCpr                 [B']
          2. CCCpCqprr                      [2nd member of new two-base]
D1.1   =  3. CCCCpqCrqsCCrps
D2.1   =  4. CCCpqrCqr
D1.2   =  5. CCpqCCCrCsrpq
D3.1   =  6. CCpqCCCprsCCqrs
D3.3   =  7. CCpCqrCCsqCpCsr
D4.3   =  8. CpCCqrp
D4.4   =  9. CpCqp                                [K]
D4.6   = 10. CpCCCqrsCCprs
D7.5   = 11. CCpCCqCrqsCCstCpt
D8.2   = 12. CCpqCCCrCsrtt
D7.10  = 13. CCpCCqrsCtCpCCtrs
D13.12 = 14. CpCCqrCCpss
D11.14 = 15. CCCCpqqrCpr
D3.15  = 16. CCpCqrCqCpr              [C]
D16.1  = 17. CCpqCCrpCrq              [B]


And here, second, is a derivation of B' and CCCpCqprr from B, C, and K:

        1. CCpqCCrpCrq                         [B]
        2. CCpCqrCqCpr                         [C]
        3. CpCqp                                        [K]
D2.1 =  4. CCpqCCqrCpr                    [B']
D1.2 =  5. CCpCqCrsCpCrCqs
D2.2 =  6. CpCCqCprCqr
D5.2 =  7. CCpCqrCpCqr
D6.3 =  8. CCpCCqCrqsCps
D4.7 =  9. CCCpCqrsCCpCqrs
D8.9 = 10. CCCpCqprr                     [2nd member of new two-base]


I mention in passing that B cannot replace B' in the new two-base.  The matrix

                                                    E | 1 2 3 4 .
                                                  *1
 | 1 2 3 4
                                                  *2 | 1 1
 4 4
                                                    3 | 1 1  1  1
                                                    4 | 1 2  3 1

is a model of the corresponding two-base {B, CCCpCqprr} but rejects B'.

 
Dolph Ulrich, 2007