YES
TRS:
 {u21(ackout(X), Y) -> u22(ackin(Y, X)),
  ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X)}
 DP:
  Strict:
   {u21#(ackout(X), Y) -> ackin#(Y, X),
    ackin#(s(X), s(Y)) -> u21#(ackin(s(X), Y), X),
    ackin#(s(X), s(Y)) -> ackin#(s(X), Y)}
  Weak:
  {u21(ackout(X), Y) -> u22(ackin(Y, X)),
   ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X)}
  EDG:
   {(u21#(ackout(X), Y) -> ackin#(Y, X), ackin#(s(X), s(Y)) -> u21#(ackin(s(X), Y), X))
    (u21#(ackout(X), Y) -> ackin#(Y, X), ackin#(s(X), s(Y)) -> ackin#(s(X), Y))
    (ackin#(s(X), s(Y)) -> ackin#(s(X), Y), ackin#(s(X), s(Y)) -> u21#(ackin(s(X), Y), X))
    (ackin#(s(X), s(Y)) -> ackin#(s(X), Y), ackin#(s(X), s(Y)) -> ackin#(s(X), Y))}
   SCCS:
    Scc:
     {ackin#(s(X), s(Y)) -> ackin#(s(X), Y)}
    SCC:
     Strict:
      {ackin#(s(X), s(Y)) -> ackin#(s(X), Y)}
     Weak:
     {u21(ackout(X), Y) -> u22(ackin(Y, X)),
      ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X)}
     SPSC:
      Simple Projection:
       pi(ackin#) = 1
      Strict:
       {}
      Qed