YES

Problem:
 Ap(Ap(Ap(S(),x),y),z) -> Ap(Ap(x,z),Ap(y,z))
 Ap(Ap(K(),x),y) -> x
 Ap(I(),x) -> x
 Ap(Ap(Ap(B(),true()),x),y) -> x
 Ap(Ap(Ap(B(),false()),x),y) -> y
 Ap(Ap(Ap(B(),z),x),x) -> x

Proof:
 Church Rosser Transformation Processor (chew):
  The clusters for
   r1 = Ap(Ap(Ap(B(),true()),x),y) -> x
   r2 = Ap(Ap(Ap(B(),z),x),x) -> x
  have a trivial peak:
   x409 <- Ap(Ap(Ap(B(),true()),x409),x410) -> x409
  The clusters for
   r1 = Ap(Ap(Ap(B(),false()),x),y) -> y
   r2 = Ap(Ap(Ap(B(),z),x),x) -> x
  have a trivial peak:
   x410 <- Ap(Ap(Ap(B(),false()),x409),x410) -> x410
  UNC by Chew's theorem.
  Qed