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