YES

Problem:
 b(a(b(b(x)))) -> b(b(b(a(b(x)))))
 b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))
 b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))

Proof:
 Church Rosser Transformation Processor (no redundant rules):
  strict:
   b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))
   b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))
   b(a(b(b(x)))) -> b(b(b(a(b(x)))))
  weak:
   
  critical peaks: 9
   b(a(a(a(b(b(a(a(b(b(a(a(a(b(x46)))))))))))))) <-0|0,0,0,0,0[]- b(a
                                                                    (
                                                                    a(a(b(b(a(a(a(b(b(x46))))))))))) -0|
                                                                  []-> 
                                                                  b(a
                                                                    (
                                                                    a
                                                                    (
                                                                    b
                                                                    (
                                                                    b
                                                                    (
                                                                    a(a(a(b(a(a(a(b(b(x46))))))))))))))
   b(a(a(b(b(a(a(b(b(a(a(a(b(x47))))))))))))) <-0|0,0,0,0[]- b(a(a(b(b(a(a(a(b(b(x47)))))))))) -1|
                                                             []-> b(a
                                                                    (
                                                                    b
                                                                    (
                                                                    b(a(a(b(a(a(a(b(b(x47))))))))))))
   b(a(b(b(a(a(b(b(a(a(a(b(x48)))))))))))) <-0|0,0,0[]- b(a(b(b(a(a(a(b(b(x48))))))))) -2|
                                                        []-> b(b(b(a(b(a(a(a(b(b(x48))))))))))
   b(a(a(a(b(b(a(b(b(a(a(b(x49)))))))))))) <-1|0,0,0,0,0[]- b(a(a(a(b(b(a(a(b(b(x49)))))))))) -0|
                                                            []-> b(a(
                                                                    a
                                                                    (
                                                                    b
                                                                    (
                                                                    b(a(a(a(b(a(a(b(b(x49)))))))))))))
   b(a(a(b(b(a(b(b(a(a(b(x50))))))))))) <-1|0,0,0,0[]- b(a(a(b(b(a(a(b(b(x50))))))))) -1|
                                                       []-> b(a(b(b(a(a(b(a(a(b(b(x50)))))))))))
   b(a(b(b(a(b(b(a(a(b(x51)))))))))) <-1|0,0,0[]- b(a(b(b(a(a(b(b(x51)))))))) -2|
                                                  []-> b(b(b(a(b(a(a(b(b(x51)))))))))
   b(a(a(a(b(b(b(b(a(b(x52)))))))))) <-2|0,0,0,0,0[]- b(a(a(a(b(b(a(b(b(x52))))))))) -0|
                                                      []-> b(a(a(b(b(a(a(a(b(a(b(b(x52))))))))))))
   b(a(a(b(b(b(b(a(b(x53))))))))) <-2|0,0,0,0[]- b(a(a(b(b(a(b(b(x53)))))))) -1|
                                                 []-> b(a(b(b(a(a(b(a(b(b(x53))))))))))
   b(a(b(b(b(b(a(b(x54)))))))) <-2|0,0,0[]- b(a(b(b(a(b(b(x54))))))) -2|
                                            []-> b(b(b(a(b(a(b(b(x54))))))))
  Closedness Processor (*strongly -- <=7 steps*):
   
   Qed