========================================================
The given Problem was:
0 0 0 0 -> 0 1 1 1 
1 1 0 1 -> 0 1 1 0 
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A self-embedding rewrite structure for the given SRS is:
   0 0 0 0 1 0 1 0 0 1 1 0 0 --(20)-> 0 0 0 0 1 0 1 0 0 1 1 0 0 (#292488)
   OC+OC at 8
      OC: 0 0 0 0 1 0 1 0 0 1 1 0 0 --(19)-> 0 0 0 0 1 0 1 0 1 1 0 1 0 (#226694)
          OC+OC at 7
             OC: 0 0 0 0 1 0 1 0 0 1 1 0 0 --(18)-> 0 0 0 0 1 0 1 1 1 0 1 1 0 (#158781)
                 OC+OC at 5
                    OC: 0 0 0 0 1 0 1 0 0 1 1 0 0 --(17)-> 0 0 0 0 1 0 0 0 0 0 1 1 0 (#120752)
                        OC+OC at 9
                           OC: 0 0 0 0 1 0 1 0 0 1 1 0 0 --(16)-> 0 0 0 0 1 0 0 0 0 1 1 0 1 (#87764)
                               OC+OC at 8
                                  OC: 0 0 0 0 1 0 1 0 0 1 1 0 0 --(15)-> 0 0 0 0 1 0 0 0 1 1 0 1 1 (#61478)
                                      OC+OC at 7
                                         OC: 0 0 0 0 1 0 1 0 0 1 1 0 0 --(14)-> 0 0 0 0 1 0 0 1 1 0 1 1 1 (#12487)
                                             OC+OC at 9
                                                OC: 0 0 0 0 1 0 1 0 0 1 1 --(13)-> 0 0 0 0 1 0 0 1 1 0 0 (#9232)
                                                    OC+OC at 6
                                                       OC: 0 0 0 0 1 0 1 0 0 1 1 --(12)-> 0 0 0 0 1 0 1 1 0 1 0 (#6691)
                                                           OC+OC at 5
                                                              OC: 0 0 0 0 1 0 1 0 0 1 1 --(11)-> 0 0 0 0 1 1 1 0 1 1 0 (#2715)
                                                                  OC+OC at 7
                                                                     OC: 0 0 0 0 1 0 1 0 0 1 --(10)-> 0 0 0 0 1 1 1 1 1 0 (#2002)
                                                                         OC+OC at 3
                                                                            OC: 0 0 0 0 1 0 1 0 0 1 --(9)-> 0 0 0 0 0 0 0 1 1 0 (#776)
                                                                                OC+OC at 6
                                                                                   OC: 0 0 0 0 1 0 1 0 0 --(8)-> 0 0 0 0 0 0 1 1 0 (#577)
                                                                                       OC+OC at 5
                                                                                          OC: 0 0 0 0 1 0 1 0 0 --(7)-> 0 0 0 0 0 1 1 0 1 (#401)
                                                                                              OC+OC at 4
                                                                                                 OC: 0 0 0 0 1 0 1 0 0 --(6)-> 0 0 0 0 1 1 0 1 1 (#275)
                                                                                                     OC+OC at 3
                                                                                                        OC: 0 0 0 0 1 0 1 0 0 --(5)-> 0 0 0 1 1 0 1 1 1 (#54)
                                                                                                            OC+OC at 5
                                                                                                               OC: 0 0 0 0 1 0 1 --(4)-> 0 0 0 1 1 0 0 (#40)
                                                                                                                   OC+OC at 2
                                                                                                                      OC: 0 0 0 0 1 0 1 --(3)-> 0 0 1 1 0 1 0 (#28)
                                                                                                                          OC+OC at 1
                                                                                                                             OC: 0 0 0 0 1 0 1 --(2)-> 0 1 1 0 1 1 0 (#6)
                                                                                                                                 OC+OC at 3
                                                                                                                                    OC: 0 0 0 0 --(1)-> 0 1 1 1 (#1)
                                                                                                                                        Rule
                                                                                                                                    OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                                                                        Rule
                                                                                                                             OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                                                                 Rule
                                                                                                                      OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                                                          Rule
                                                                                                               OC: 0 0 0 0 --(1)-> 0 1 1 1 (#1)
                                                                                                                   Rule
                                                                                                        OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                                            Rule
                                                                                                 OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                                     Rule
                                                                                          OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                              Rule
                                                                                   OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                                       Rule
                                                                            OC: 0 0 0 0 --(1)-> 0 1 1 1 (#1)
                                                                                Rule
                                                                     OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                         Rule
                                                              OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                                  Rule
                                                       OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                                           Rule
                                                OC: 0 0 0 0 --(1)-> 0 1 1 1 (#1)
                                                    Rule
                                         OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                             Rule
                                  OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                                      Rule
                           OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                               Rule
                    OC: 0 0 0 0 --(1)-> 0 1 1 1 (#1)
                        Rule
             OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
                 Rule
      OC: 1 1 0 1 --(1)-> 0 1 1 0 (#2)
          Rule
Hence, the SRS is non-terminating.